Estimation of Radiated Sound Power: A Case Study on Common Approximation Methods

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Estimation of Radiated Sound Power: A Case Study on Common Approximation Methods"

Transcription

1 ACTA ACUSTICA UNITED WITH ACUSTICA DOI /AAA Estimation of Radiated Sound Power: A Case Study on Common Approximation Methods DennyFritze, Steffen Marburg, Hans-Jürgen Hardtke Technische Universität Dresden, Institut für Festkörpermechanik, Dresden, Germany Summary The radiated sound power value is often used to evaluate the sound radiation of a machine or a product. Since its estimation requires the sound pressure on a surrounding surface of the radiating object, the sound power value is mostly computed under high numerical costs due to the acoustic field that has to be modeled. Therefore, approximations of the sound pressure are widely popular. In this article three common methods namely the equivalent radiated power, the lumped parameter model and an approximation based on the volume velocity are investigated. It is the goal of this paper to test these methods on realistic examples. The radiated sound power functions of the floor panel of acar and the radiation of adiesel engine under realistic load cases are estimated. PACS no Rj 1. Introduction The radiated sound power is often used to express the general radiation behavior of a component or a machine [1]. It represents the integral of sound intensity over aclosed surface surrounding the radiating object. This surface can also be the surface of the radiator. Thus, the product of sound pressure and particle velocity must be integrated overthe surface. In the case of aradiator with hard reflecting surface, the particle velocity is identical to the structural normal velocity. However, evaluation of the sound power requires an estimation of the sound pressure on the structure s surface. This means that a global quantity, i.e. sound pressure on the surface of the underlying structure, is computed. For alarge-scale surface mesh and alarge frequency range, this computation becomes very expensive especially if the structure is analyzed repeatedly as in structural acoustic optimization problems [2]. Usually,the radiated sound power is computed for exterior problems only.when considering interior problems, a local quantity such as the sound pressure at a single point or several internal points is used to estimate the acoustic properties. For the computation, we can use the adjoint operator approach which has different names in the literature [3, 4, 5], see also [2] and references therein. In [1], global quantities such as potential and kinetic energies are proposed to estimate the acoustic behavior. Cunefare and Engelstad et al. [6, 7, 8] use the sound pressure at many internal points. There are only afew academic cases for which the radiated sound power can be calculated exactly. Therefore, numerical approximations are very popular [9]. The Received 15January 2009, accepted 2April physics behind the sound radiation requires the modeling of the fluid structure interaction. Forheavy structures and light fluids, an unidirectional coupling approach is preferred. This still means that the structural dynamics and the acoustic field must be solved. The vibration of the structure is often numerical computed via the finite element method. The solution of the structural problem, i.e. the structural particle velocity accounts for the boundary condition of the acoustic field problem. The solution of the acoustic boundary value problem can be very complicated for radiation problems. The boundary element method appears as very popular approach [9, 10, 11, 12, 13] but becomes computationally expensive for large-scale problems, cf. [14, 15]. For large-scale problems, fast methods of the BEM are used instead, e.g. fast multipole techniques [16, 17, 18, 19, 20, 21, 22, 23, 24]). If the structure is modified during an optimization process or if alarge frequency range is investigated these methods remain problematic. Thus, simplified estimations are introduced. They are usually aimed to circumvent the solution of the full acoustic boundary value problem. In this paper,three different approximation methods are compared. Firstly, weconsider an approach which is called the equivalent radiated power (ERP). It is similar to the squared particle velocity and very popular for industrial problems due to its simplicity. It will mostly overestimate the sound power since it does not contain compensation effects by acoustical short circuits. Further, the radiated sound power can be approximated by the volume velocity. This includes compensation effects in a primitive way. The third method is referred to in the literature as the lumped parameter model (LPM), cf. [1, 25, 26], and as the Direct FEM [27, 28, 29]. It was shown in [30] that both approaches lead to the same result. The lumped parameter model uses the Rayleigh integral to evaluate the sound S.Hirzel Verlag EAA 833

2 ACTA ACUSTICA UNITED WITH ACUSTICA power. Inthe papers of Herrin et al. [31, 32], the authors showed that the Rayleigh integral approximation might be very reliable for estimation of radiated sound power even for real applications such as radiation from an engine. In this article, we start with introducing these methods briefly.afterwards the methods are applied to realistic examples and, for better understanding, to some academic test cases. The first example is afloor panel of asedan s bodywork vibrating at low frequencies for arealistic load case. A higher frequency problem is investigated at a six cylinder diesel engine. There, we take into account a realistic load case and finally artificial boundary conditions including rigid body motion and pulsating behavior, both to satisfy academic interests rather than being relevant for practical applications. To appreciate the efficiency and the accuracy of these approximative methods we carry out a Multilevel Fast Multipole Analysis (MLFMA) for each example, cf. [16]. We use this result as our reference solution since there is no better estimation available for realistic examples. In practical applications efficient methods for the sound power computation are highly recommended, but there is alack of experience especially for complicated structures, i.e. very detailed surface meshes. The goal of this paper is to exercise a comparative study on such approximations. The results of the methods are often theoretically comprehensible butare consolidated by practical examples in this paper. Throughout this paper, aharmonic time dependence of e iωt is used. Furthermore, the term of coupling between structural and acoustic vibration is used in a one way sense, i.e. structural vibrations affect the acoustic radiation, but the sound field does not affect the structural vibrations. 2. Sound power evaluation and estimates The radiated sound power is often used to estimate the sound radiation of avibrating obstacle into the exterior. It is well known that the radiated sound power P is evaluated as the integral of sound intensity I in normal direction n over acircumscribing surface Γ. The intensity is calculated based on the sound pressure p and the particle velocity v.the circumscribing surface can be any surface including the surface of the radiating obstacle. The sound power is given by P = I n d Γ, where I = 1 2 pv (1) leads to P = 1 2 p(x)vn (x)dγ(x). (2) The asterisk denotes the conjugate complexvalue and {} is the real part of acomplex value. In what follows, we substitute the particle velocity v n = v n for v. Since v can be easily imported from structural dynamic analysis, the major focus for the efficient evaluation of the radiated sound power is situated in the estimation of the sound pressure. The formal way leads through the acoustic field analysis via numerical methods. (Herein, we concentrate on BEM) Evaluation based on BEM In numerical solutions, e.g. boundary element method and finite element method, the sound pressure and the particle velocity on the surface are usually interpolated by aset of basis functions assembled in an interpolation matrix Φ f as p(x) = Φ f (x)p and v(x) = Φ f (x)v. (3) Then, the sound power P can be formulated by the vector of sound pressure p and the particle velocity vector v as with P = 1 2 p T C ff v (4) C ff = Φ T f (x)φ f(x)dγ(x). In general, the matrix C ff is known as the boundary mass matrix; for the special case of constant elements, it is a diagonal matrix containing the element areas S µ as C ff = diag(s µ ) with S µ = dγ µ (x). (5) Consequently, the sound power can be computed by summing up over all N e elements as P = 1 2 N e µ=1 S µ p µ v µ, (6) wherein p µ and v µ represent the constant sound pressure and particle velocity values of the element µ.this summation approach can be used to estimate panel contribution on the overall radiating surface. Piecewise constant elements show excellent performance for BEM [11, 33, 34] and multilevel fast multipole analysis as discussed in the papers [16, 17, 18]. It is well known that simple boundary element solutions in the external domain suffer from the so called non uniqueness problem, also known as the problem of irregular or fictitious frequencies. There are many ways of solving this problem. Herein, we use the method of Burton and Miller [35] which is investigated in detail including investigation of the performance of constant elements in [36]. In general, the acoustic field solution provides an equation for the sound pressure. In the case of the boundary element method, the sound pressure vector p of the boundary of the acoustic domain can be formulated as p = Zv. (7) The matrix Z denotes the impedance condition of the boundary. It represents a complex non-symmetric matrix. 834

3 ACTA ACUSTICA UNITED WITH ACUSTICA If (7) is applied into (4), itisworth to mention that the radiated sound power P = 1 2 v T R ZT R C ffv R + v T I ZT R C ffv I (8) requires the real part of the impedance Z R only. The subscripts () R and () I denote the real and imaginary part, respectively Equivalent radiated power (ERP) A very common approach for the sound pressure can be found in the local relation p f c f v, (9) where f and c f represent the fluid smass density and the speed of sound, respectively. The relation between sound pressure and particle velocity is reduced to the fluid s characteristic impedance Z 0 = f c f.this is atypical approximation for high frequencies and for the far field. The acoustic field evaluation is avoided, so that the sound power is finally approximated by P ERP = 1 2 fc f v T C ff v. (10) This is completely equivalent to the squared velocity value integrated overthe radiating surface P ERP = 1 2 fc f v(x) 2 dγ(x). (11) If the surface is discretized by piecewise constant elements, we gain P ERP = 1 2 N e fc f S µ v µ vµ. (12) µ=1 The ERP does not contain any local acoustic effect since all sources (herein: all elements) have the same radiation efficiency of σ=1. Thus, the ERP will usually overestimate the radiation, but will give a qualitatively good approximation for structure induced acoustical fields especially as an upper bound. However: Note that the radiation efficiency can exceed the value of one. It should be mentioned that the sound power estimation by ERP is very similar to the high frequency solution for scattering, i.e. the Plane Wave Approximation [37]. Both approaches assume the radiation efficiencytobeσ=1and perform best for convex rigid bodies and high frequencies Lumped parameter model (LPM) The lumped parameter model presented by Fahnline and Koopmann [1, 25, 26] is based on an approximation of the Rayleigh integral with p(x) = ik f c f G(x, y)v(y)dγ(y) (13) G(x, y) = 1 2π x y e ik x y. The Green s function G(x, y) represents the fundamental solution of the Helmholtz equation for the three dimensional half space. The wavenumber k is the quotient of the circular frequencyand the speed of sound k = ω/c. The Rayleigh integral is gained as asimplification of the sound pressure representation formula known from integral methods. It is exact for plain radiating surfaces which are embedded in arigid baffle. The idea behind the lumped parameter model is to develop the Green s function as ataylor series for the source at x µ and the receiveraty ν G(x, y) = G(x µ,y ν )+(x x µ ) G(x, y ν) x x=xµ + (y y ν ) G(x µ,y) +... (14) y y=yν This can be understood as a multipole expansion. If we use piecewise constant interpolation again and include only the monopole (the first)term of equation (14) as G(x, y) G(x µ,y ν ) = G µν,wecan formulate the impedance matrix as Z = (z µν ) with z µν = ik f c f G µν S ν. (15) Finally,the sound power approximation via the lumped parameter model yields P LP M = 1 2 k N e N e fc f S µ S ν G µν vµ vν with µ=1 ν=1 (16) sin(k x y ) G µν =. (17) 2π x y Herein, the interaction of the radiating sources is weighted with the imaginary part of the Green s function. Note that the imaginary part of G µν remains finite (and negative) for x y 0 rather than the Green s function itself. Further, it can be seen that the interaction of two sources has no effect on the sound power if their distance is amultiple of half an acoustical wavelength. The double summation turns out to be computationally much more expensive than the single sum for the equivalent radiated power but much more efficient than the BEM solution of the full boundary value problem even when using the MLFMA. The accuracy of this approach significantly depends on the compliance with the Rayleigh integral assumptions and on the mesh refinement. 835

4 ACTA ACUSTICA UNITED WITH ACUSTICA Figure 2. Floor panel: sound power in terms of frequency. 3. Radiating floor panel Figure 1. Floor panel: original finite element model (upper) and boundary element half space model (lower) Volume velocity The volume velocity u is defined as the integral of the particle velocity over the radiating surface [1] N e u = v dγ = v µ S µ. (18) µ=1 Avolume velocity based radiated sound power P VV is formulated as P VV = k2 f c f 4π uu. (19) The authors are not aware of areference about sound power estimation based on volume velocity. However, since uu can be rewritten as N e N e uu = v µ vν Sµ S ν, (20) µ=1ν=1 this sound power estimate can be understood as areduction of P LP M,cf. Equation (16) with the weighting by the Green s function G µν and afactor of k/2π. Note that this factor is equal 1for µ = ν,i.e. x y,cf. [1]. The sound power estimation based on volume velocity contains local acoustic effects based on antiphase vibration of the sources (dipole effects) but requires the evaluation of a single sum only, ifequation (19) is solved on the basis of (18). The floor panel of asedan s bodywork accounts for the first example. The original FE model of this structural component is shown in the upper part of Figure 1. In order to compute a coupled FE BE solution, we need to enhance this model. The MLFMA realization of the boundary element solution requires a closed fluid surface, so that we introduce auxiliary elements creating aclosed obstacle with the half space plane, i.e. the half space plane is used as a symmetry plane. The structure consisting of multi layered sheets of steel is reduced to its outer surface. The final fluid surface model can be found in the lower part of Figure 1. The radiating elements of the FE structural model match with the elements of the fluid model so that acoupling is easily generated. The auxiliary elements are assumed to have zero particle velocity. The FE structural model s surface consists of nodes with adof of 6each and linear continuous shell elements. In the simulation the entire structural model is solved but only the elements on its surface are taken into account for the subsequent coupled acoustical simulation. The fluid boundary element model contains elements and nodes. Since constant elements are preferred for the BE solution, we end up with unknowns for the half space solution. The vibration of the model is excited by two single harmonic point forces at the rear part of the floor panel. The sound power solutions which are gained by the previously explained methods are computed over a frequency range of 10 to 200 Hz. They are shown in Figure 2. As expected, the ERP overestimates the actual radiated sound power. Moreover, it contains more peaks than the other curves because acoustic short circuit effects are not considered in this function. As one example, the peak at 55 Hz in the LPM or PVV functions is not as much developed as in the ERP function. The structural mode shape belonging to this peak defines atorsional vibration, i.e. quadrupole so- 836

5 ACTA ACUSTICA UNITED WITH ACUSTICA lution. Such amode shape is well known to have lowradiation efficiency. The LPM and PVV solutions give higher values than the BEM reference solution in the frequency range up to approximately 80 Hz. Above this frequency they seem to normally underestimate the sound power. This is supposedly due to the Rayleigh integral assumption, which is quite contrary to the tub like shape of the floor panel. If we compare the LPM and the PVV functions, they show high discrepancy in the frequency range from 130 Hz to 180 Hz. The interaction between the discrete sources on the surface (i.e. the elements), which is only included in the LPM value, affects the sound power significantly in this frequency range. The error for LPM, PVV and ERP compared to the BEM solution is plotted in Figure 3. If the BE solution is understood as the reference solution, the lumped parameter model becomes highly interesting due to its efficient computation and good agreement. One has to admit and consequently be aware of the fact, that there is no error estimate for the applied plain radiator assumption yet. However, the ERP and PVV can be computed even faster, but the implemented approximative assumptions can lead to questionable results. It is suggested to use both values (P VV and P ERP )incombination to qualitatively estimate the radiated sound power,in particular to identify resonance peaks and to distinguish between resonances with lowand with high radiation efficiency Δ P in [db] PERP PBEM PVV PBEM PLP M PBEM f in Hz Figure 3. Floor panel: absolute error of sound power estimates in terms of frequency. 4. Radiating diesel engine The second example investigates the sound radiation of a diesel engine. Herein, the sound power solutions of the BEM, the lumped parameter model and the ERP approximation are compared. Again, the finemesh of the structure is directly used for the fluid. The fluid surface model contains nodes and constant elements. The problem is solvefor the frequency range up to 3000 Hz. The model is presented in Figure 4. In what follows, we consider one case of realistic excitation and further cases of artificial excitations using the entire engine as an elementary radiator, i.e. monopole or dipole source. The excitation of the acoustic field is applied by defining the particle velocity over the surface at each investigated frequency Realistic excitation The particle velocity distribution over the engine s surface for a certain operations condition was computed and provided by the AVL/ACC Graz (Austria). In Figure 4, the geometry mesh of the surface is shown. Originally, the particle velocity was given on the mesh of linear continuous elements. The piecewise constant particle velocity data which is used for our simulations can be understood as an average of the normal velocity on each element. To provide the reader with avivid impression and a comparison of the level distributions of the particle velocity, the sound pressure and the sound intensity, these data Figure 4. Diesel engine: boundary element model. are visualized for two specified frequencies, i.e. 503 Hz, cf. Figure 5, and 2196 Hz, cf. Figure 6. It can be realized at the lower frequency of503 Hz that the intensity contribution does not match with the velocity contribution. At 2196 Hz, the contributions show less differences. This means that the intensity is dominated by the velocity contribution. The same effect is revealed by the sound power spectrum in Figure 7. There, the ERP values agree with the BEM solution better and better the higher the frequencies are. The differences between the ERP and LPM solutions with respect to the BEM reference are shown in Figure 8. Actually, it is quite surprising that the simple approximations of ERP and LPM catch the behaviour of the reference solution with this accuracy, not only in the high frequency range. Even in the lower frequencyrange, the difference of approximate solutions and reference are a couple of decibel. However, peaks and valleys in the curves are found at the same frequencies. 837

6 ACTA ACUSTICA UNITED WITH ACUSTICA Figure 5. Diesel engine: surface distribution of particle velocity, sound pressure and sound intensity at 503 Hz Engine as an elementary radiator According to the Rayleigh integral assumptions the engine can not be understood as a plain radiator. Although we can simply model the engine as a cuboid by six half space plains it is questionable to explain the good agreement between the LPM and the BE solutions. Therefore, two simple cases of the engine s surface vibrations are investigated. Firstly, we exercise a harmonically pulsating vibration of the engine, i.e. a constant unit particle velocity is applied to all elements. This is similar to a monopole radiation. The resulting sound power levels are shown in Figure 9. The second case investigates the harmonic rigid body translation of the engine which can be interpreted as 838 a dipole source. Furthermore, we divide this case into two subcases which comprise two directions of motion. These are the two horizontal directions x and y, cf. Figure 4. We assume a unit vibration amplitude of the rigid body motion. Figures 10 and 11 show the resulting sound power levels. In all cases, the ERP estimation yields a constant sound power level. It provides a good approximation for higher frequencies. At low frequencies the ERP approximate is not able to represent the acoustic elimination effects. However, the LPM fails to give a good estimation of the radiated sound power for the entire frequency range. This is caused by the incorrect calculation of the distances Rµν between the source and receiver elements. Again, this is

7 ACTA ACUSTICA UNITED WITH ACUSTICA Figure 6. Diesel engine: surface distribution of particle velocity, sound pressure and sound intensity at 2196 Hz. due to the violation of the Rayleigh integral presumption. For concave fluid boundaries such as for the engine model, this problem can be avoided by the visibility test. This test checks the visibility between source and receiver point. Unfortunately, the test becomes quite expensive for large scale models [31]. (It is only required once, though.) When carrying out the visibility check, only the elements which have an unobstructed connection to each other are considered for the summations. This means, that each of the six sides of the cuboid like engine is separately investigated and then summed up to the overall radiated sound power value. Alternatively, an effective distance could be calculated via the periphery of the engine. This means, that the distance of the sound wave around the obstacle is taken into account. However, it is assumed that such an additional algorithm will be computationally inefficient and, thus, destroying the efficiency impact of the LPM compared to the MLFMA. 5. Interpretation of the results According to piecewise constant elements of the radiating surface, the previously presented sound power approximations can be reformulated in the following way, cf. [29] P = Ne $ Ne $ µ=1 ν=1 Pµν = Ne $ µ=1 Pµµ + 2 N e 1 $ Ne $ Pµν. (21) µ=1 ν=µ+1 839

8 ACTA ACUSTICA UNITED WITH ACUSTICA Figure 7. Diesel engine: sound power in terms of frequency for realistic loadcase. Figure 8. Diesel engine: sound power difference between LPM / ERP and reference solution in terms of frequency. Figure 9. Diesel engine as a monopole radiator: sound power in terms of frequency. Figure 10. Diesel engine vibrating as a rigid body in x direction: sound power in terms of frequency. This means that each of the N e constant elements acts as an acoustical monopole source (i.e. apiston) providing the partial sound power, i.e. the sound power por- Figure 11. Diesel engine vibrating as arigid body in y direction: sound power in terms of frequency. tion P µν.the portions can be distinguished into independently radiating sources P µµ and the interaction between the sources P µν (µ = ν). Due to reciprocity, the interaction matrix with entries P µν is symmetric. In general, each portion P µν can be determined by P µν = 1 2 fc f S µ σ µν v µ v ν, (22) where σ µν represents the radiation efficiency ofthe portion. Following the derivation of the presented methods, the radiation efficiency can be written as σ µν = z µν Sν general, f c f S µ σ µν = δ µν for ERP, σ µν = k2 S ν sin(kr µν ) for LPM and 2π kr µν σ µν = k2 S ν 2π for volume velocity. (23) Note that σ µν is indeed dimensionless but generally non symmetric in all formulations. It can be transformed into asymmetric form σ µν by multiplying with S µ as σ µν = S µ σ µν for all formulations. The ERP neglects all the interaction between the sources but each source portion P µ µ has aradiation efficiency of 1.In the method using the volume velocity (PVV), all interactions are considered but have aconstant frequency dependent radiation efficiency. The LPM radiation efficiencyadditionally contains information about the distance between the single sources. Thus, the PVV will give questionable results for higher frequencies, since the interaction efficiencywill vanish much faster with the distance between the sources than modeled by the method. Despite of this, the PVV will provide a good approximation of the average sound power value in the lower frequency range, what can not be interpreted from the ERP function. The partial radiation efficiency is illustrated in Figure 12 schematically. Another important fact can be found in the dependency of the approximative methods on the used mesh refinement. The equivalent radiated power and the sound power value provided by the volume velocity are independent on the element size, if the refinement provides no additional 840

9 ACTA ACUSTICA UNITED WITH ACUSTICA Table I. Overview onthe three sound power approximations. Method estimated time mesh refinement frequencyrange ERP O(N e ) no effect no prediction available PVV O(N e ) no effect low frequencies LPM O(Ne 2 ) convergence for finer mesh low/mid frequency range ERP PVV LPM σ σ µµ =1 σ σ µ ν σ µµ = k 2 S ν 2π R µν µ ν σ µµ = k 2 S ν 2π R µν µ ν Figure 12. Radiation efficiencyofthe three approximation methods (schematic visualization). information but subdivision of elemental data. This means if the genuine mesh is refined by subdividing the elements, i.e. no additional information for velocity contribution is created, the ERP and the PVV will each provide the results of the coarser mesh again. The LPM depends on the mesh refinement since it shows convergence behavior for finer meshes in this case. The radiation efficiency, cf. Figure 12, in terms of R µν can be approximated more accurately for finer meshes. If the sound power is estimated from avery coarse mesh, the ERP or PVV solution can provide sufficient results. R µν R R R on the structural vibration. Consequently, the coupling between the structure and the fluid is modeled unidirectionally. To determine the sound power, the velocity distribution on the structure s surface acts as input information of the acoustic field. The particle velocity is approximated by piecewise constant interpolation. Two ofthe methods, the ERP and the PVV, require evaluation of asingle summation of order O(N e )ofthe velocity distribution over the N e constant elements only. Since therefore these methods are computationally very fast, theycan be used in combination to estimate the sound radiation in the lower frequency mainly in aqualitative manner. The lumped parameter model contains a double summation of order O(N 2 e )overall N e elements since the interaction between the discretized piston sources is considered. This model is based on the Rayleigh integral but even may provide acceptable results if the Rayleigh integral assumption is violated. The LPM will mostly fail if the structural vibration contains rigid body motion or if no phase information is included in the velocity distribution. The general statements about the estimated computation time, the dependency on mesh refinement and the recommended frequencyrange of the approximation methods are compiled in Table I. It was shown in this article that these approximation methods can be successfully used for realistic problems. An expensive and highly detailed boundary element computation wascarried out to provide areference solution for the investigated examples. Acknowledgments These investigations were extracted from the research project P 579. The research project P 579 " Minimum sound emission of steel plates" was carried out by the Institut für Festkörpermechanik with technical and scientific support by the FOSTA Research Association for Steel Application, Düsseldorf (Germany), with funds of the Stiftung Stahlanwendungsforschung, Essen (Germany). Wefurther thank the Audi AG Ingolstadt (Germany) and AVL/ACC in Graz (Austria). The computation was run on the SGI Orig0 at the Zentrum für Hochleistungsrechnen of the Technische Universität Dresden. 6. Conclusions The presented sound power approximations have in common that the acoustic field is not solved to estimate the radiated sound power of astructural component. It was presumed in these methods that the acoustic field has no effect References [1] G. H. Koopmann, J. B. Fahnline (eds.): Designing quiet structures: A sound power minimization approach. Academic Press, San Diego, London, [2] S. Marburg: Developments in structural acoustic optimization for passive noise control. Archives of Computational 841

10 ACTA ACUSTICA UNITED WITH ACUSTICA Methods in Engineering. State of the art reviews 9 (2002) [3] L. Cremers, P. Guisset, L. Meulewaeter, M. Tournour: Acomputer-aided engineering method for predicting the acoustic signature of vibrating structures using discrete models. Great Britain Patent No. GB , [4] S. Marburg, H.-J. Hardtke, R. Schmidt, D. Pawandenat: An application of the concept of acoustic influence coefficients for the optimization of avehicle roof. Engineering Analysis with Boundary Elements 20 (1997) [5] J. Dong, K. K. Choi, N.-H. Kim: Design optimization of structural-acoustic problems using fea-bea with adjoint variable method. ASME Journal of Mechanical Design 126 (2004) [6] S. P. Crane, K. A. Cunefare, S. P. Engelstad, E. A. Powell: Comparison of design optimization formulations for minimization of noise transmission in acylinder. Journal of Aircraft 34 (1997) [7] K. A. Cunefare, S. P. Crane, S. P. Engelstad, E. A. Powell: Design minimization of noise in stiffened cylinders due to tonal external excitation. Journal of Aircraft 36 (1999) [8] S. P. Engelstad, K. A. Cunefare, E. A. Powell, V. Biesel: Stiffener shape design to minimize interior noise. Journal of Aircraft 37 (2000) [9] S. Marburg, B. Nolte (eds.): Computational acoustics of noise propagation in fluids. Finite and boundary element methods. Springer, Berlin, Heidelberg, [10] R. D. Ciskowski, C. A. Brebbia (eds.): Boundary elements in acoustics. Computational Mechanics Publications and Elsevier Applied Science, Southampton, Boston, [11] S. M. Kirkup: The boundary element method in acoustics. Integrated Sound Software, Heptonstall, [12] O. v. Estorff (ed.): Boundary element in acoustics: Advances and applications. WIT Press, Southampton, [13] T. W. Wu (ed.): Boundary element in acoustics: Fundamentals and computer codes. WIT Press, Southampton, [14] I. Harari, T. J. R. Hughes: Acost comparison of boundary element and finite element methods for problems of timeharmonic acoustics. Computer Methods in Applied Mechanics and Engineering 97 (1992) [15] I. Harari, K. Grosh, T. J. R. Hughes, M. Malhotra, P. M. Pinsky, J. R. Stewart, L. L. Thompson: Recent development in finite element methods for structural acoustics. Archives of Computational Methods in Engineering 3 (1996) [16] S. Schneider: Application of fast methods for acoustic scattering and radiation problems. Journal of Computational Acoustics 11 (2003) [17] S. Marburg, S. Schneider: Performance of iterative solvers for acoustic problems. Part I: Solvers and effect of diagonal preconditioning. Engineering Analysis with Boundary Elements 27 (2003) [18] S. Schneider, S. Marburg: Performance of iterative solvers for acoustic problems. Part II: Acceleration by ilu-type preconditioner. Engineering Analysis with Boundary Elements 27 (2003) [19] T. Sakuma, Y. Yasuda: Fast multipole boundary element method for large-scale steady-state sound field analysis. Part I: Setup and validation. Acustica united with Acta Acustica 88 (2002) [20] T. Sakuma, Y. Yasuda: Fast multipole boundary element method for large-scale steady-state sound field analysis. Part II: Examination of numerical items. Acustica united with Acta Acustica 89 (2003) [21] M. Fischer, U. Gauger, L. Gaul: A multipole galerkin boundary element method for acoustics. Engineering Analysis with Boundary Elements 28 (2004) [22] M. Fischer, L. Gaul: Fast bem-fem mortar coupling for acoustic-structure interaction. International Journal for Numerical Methods in Engineering 62 (2005) [23] N. A. Gumerov, R. Duraiswami: Computation of scattering from nspheres using multipole reexpansion. Journal of the Acoustical Society of America 112 (2002) [24] N. A. Gumerov, R. Duraiswami: Computation of scattering from clusters of spheres using the fast multipole method. Journal of the Acoustical Society of America 117 (2005) [25] J. B. Fahnline, G. H. Koopmann: Lumped parameter model for the acoustic power output from avibrating structure. Journal of the Acoustical Society of America 100 (1996) [26] J. B. Fahnline, G. H. Koopmann: Numerical implementation of the lumped parameter model for the acoustic power output from a vibrating structure. Journal of the Acoustical Society of America 102 (1997) [27] G. Hübner, J. Messner, E. Meynerts: Schalleistungsbestimmung mit der Direkten Finite Elemente Methode (Sound power estimation using the Direct Finite Element Method). In: Volume Fb 479 of Schriftenreihe der Bundesanstalt für Arbeitsmedizin (Forschung). Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, Dortmund, Berlin, [28] G. Hübner: Eine Betrachtung zur Physik der Schallabstrahlung (A contribution on the physics of sound radiation). Acustica 75 (1991) [29] G. Hübner, A. Gerlach: Schalleistungsbestimmung mit der DFEM (Sound power estimation using the DFEM). In: Volume Fb 846 of Schriftenreihe der Bundesanstalt für Arbeitsmedizin (Forschung). Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, Dortmund, Berlin, [30] D. Fritze, S. Marburg, H.-J. Hardtke: Reducing radiated sound power of plates and shallow shells by local modification of geometry. Acta Acustica united with Acustica 89 (2003) [31] D. W. Herrin, T. W. Wu, A. F. Seybert: Practical issues regarding the use of the finite and boundary element methods for acoustics. Building Acoustics 10 (2003) [32] D. W. Herrin, F. Martinus, T. W. Wu, A. F. Seybert: An assessment of the high frequency boundary element and Rayleigh integral approximations. Applied Acoustics 67 (2006) [33] S. Marburg: Six boundary elements per wavelength. Is that enough? Journal of Computational Acoustics 10 (2002) [34] S. Marburg, S. Schneider: Influence of element types on numeric error for acoustic boundary elements. Journal of Computational Acoustics 11 (2003) [35] A. J. Burton, G. F. Miller: The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society of London 323 (1971) [36] S. Marburg, S. Amini: Cat s eye radiation with boundary elements: Comparative study on treatment of irregular frequencies. Journal of Computational Acoustics 13 (2005) [37] B. Nolte, I. Schäfer, J. Ehrlich, M. Ochmann, R. Burgschweiger, S.Marburg: Numerical methods for wave scattering phenomena by means of different boundary integral formulations. Journal of Computational Acoustics 15 (2007)

New Developments of Frequency Domain Acoustic Methods in LS-DYNA

New Developments of Frequency Domain Acoustic Methods in LS-DYNA 11 th International LS-DYNA Users Conference Simulation (2) New Developments of Frequency Domain Acoustic Methods in LS-DYNA Yun Huang 1, Mhamed Souli 2, Rongfeng Liu 3 1 Livermore Software Technology

More information

Efficient boundary element analysis of periodic sound scatterers

Efficient boundary element analysis of periodic sound scatterers Boundary Element and Meshless Methods in Acoustics and Vibrations: Paper ICA2016-418 Efficient boundary element analysis of periodic sound scatterers M. Karimi, P. Croaker, N. Kessissoglou 1 School of

More information

Fast Multipole BEM for Structural Acoustics Simulation

Fast Multipole BEM for Structural Acoustics Simulation Fast Boundary Element Methods in Industrial Applications Fast Multipole BEM for Structural Acoustics Simulation Matthias Fischer and Lothar Gaul Institut A für Mechanik, Universität Stuttgart, Germany

More information

11 Discretization Requirements: How many Elements per Wavelength are Necessary?

11 Discretization Requirements: How many Elements per Wavelength are Necessary? 11 Discretization Requirements: How many Elements per Wavelength are Necessary? Steffen Marburg Institut für Festkörpermechanik, Technische Universität Dresden, 01062 Dresden, Germany marburg@ifkm.mw.tu-dresden.de

More information

FastBEM Acoustics. Verification Manual , Advanced CAE Research, LLC (ACR) Cincinnati, Ohio, USA All Rights Reserved

FastBEM Acoustics. Verification Manual , Advanced CAE Research, LLC (ACR) Cincinnati, Ohio, USA All Rights Reserved FastBEM Acoustics Verification Manual 2007-2017, Advanced CAE Research, LLC (ACR) Cincinnati, Ohio, USA All Rights Reserved www.fastbem.com Copyright 2007-2017, Advanced CAE Research, LLC, All Rights Reserved

More information

Muffler Transmission Loss Simple Expansion Chamber

Muffler Transmission Loss Simple Expansion Chamber Muffler Transmission Loss Simple Expansion Chamber 1 Introduction The main objectives of this Demo Model are Demonstrate the ability of Coustyx to model a muffler using Indirect model and solve the acoustics

More information

TRANSMISSION LOSS OF EXTRUDED ALUMINIUM PANELS WITH ORTHOTROPIC CORES

TRANSMISSION LOSS OF EXTRUDED ALUMINIUM PANELS WITH ORTHOTROPIC CORES TRANSMISSION LOSS OF EXTRUDED ALUMINIUM PANELS WITH ORTHOTROPIC CORES PACS REFERENCE: 43.40-Rj RADIATION FROM VIBRATING STRUCTURES INTO FLUID MEDIA Names of the authors: Kohrs, Torsten; Petersson, Björn

More information

Simulation of Acoustic and Vibro-Acoustic Problems in LS-DYNA using Boundary Element Method

Simulation of Acoustic and Vibro-Acoustic Problems in LS-DYNA using Boundary Element Method 10 th International LS-DYNA Users Conference Simulation Technolog (2) Simulation of Acoustic and Vibro-Acoustic Problems in LS-DYNA using Boundar Element Method Yun Huang Livermore Software Technolog Corporation

More information

Learning Acoustics through the Boundary Element Method: An Inexpensive Graphical Interface and Associated Tutorials

Learning Acoustics through the Boundary Element Method: An Inexpensive Graphical Interface and Associated Tutorials Learning Acoustics through the Boundary Element Method: An Inexpensive Graphical Interface and Associated Tutorials ABSTRACT Laura A. Brooks, Rick C. Morgans, Colin H. Hansen School of Mechanical Engineering,

More information

Calculation of sound radiation in infinite domain using a meshless method

Calculation of sound radiation in infinite domain using a meshless method PROCEEDINGS of the 22 nd International Congress on Acoustics Structural Acoustics and Vibration: Paper ICA2016-41 Calculation of sound radiation in infinite domain using a meshless method Shaowei Wu (a),

More information

Virtual Prototyping of Electrodynamic Loudspeakers by Utilizing a Finite Element Method

Virtual Prototyping of Electrodynamic Loudspeakers by Utilizing a Finite Element Method Virtual Prototyping of Electrodynamic Loudspeakers by Utilizing a Finite Element Method R. Lerch a, M. Kaltenbacher a and M. Meiler b a Univ. Erlangen-Nuremberg, Dept. of Sensor Technology, Paul-Gordan-Str.

More information

This is the author s version of a work that was submitted/accepted for publication in the following source:

This is the author s version of a work that was submitted/accepted for publication in the following source: This is the author s version of a work that was submitted/accepted for publication in the following source: Lin, Tian Ran & Pan, Jie (29) Sound radiation characteristics of a box-type structure. Journal

More information

Sound radiation and sound insulation

Sound radiation and sound insulation 11.1 Sound radiation and sound insulation We actually do not need this chapter You have learned everything you need to know: When waves propagating from one medium to the next it is the change of impedance

More information

Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods

Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods Bearbeitet von Steffen Marburg, Bodo Nolte 1. Auflage 2008. Buch. xiii, 578 S. Hardcover ISBN 978 3 540 77447

More information

Factors Affecting the Accuracy of Numerical Simulation of Radiation from Loudspeaker Drive Units. P.C.Macey PACSYS Limited

Factors Affecting the Accuracy of Numerical Simulation of Radiation from Loudspeaker Drive Units. P.C.Macey PACSYS Limited Factors Affecting the Accuracy of Numerical Simulation of Radiation from Loudspeaker Drive Units P.C.Macey PACSYS Limited Presented at ALMA European Symposium Frankfurt, Germany 4 th April 2009 Loudspeaker

More information

TOPOLOGY OPTIMIZATION APPROACH OF DAMPING TREATMENT IN CABIN ACOUSTIC DESIGN

TOPOLOGY OPTIMIZATION APPROACH OF DAMPING TREATMENT IN CABIN ACOUSTIC DESIGN TOPOLOGY OPTIMIZATION APPROACH OF DAMPING TREATMENT IN CABIN ACOUSTIC DESIGN Jianrun Zhang, Beibei Sun, Xi Lu Southeast University, School of Mechanical Engineering, Nanjing, Jiangsu, China 211189 email:

More information

ACOUSTIC RADIATION BY SET OF L-JOINTED VIBRATING PLATES

ACOUSTIC RADIATION BY SET OF L-JOINTED VIBRATING PLATES Molecular and Quantum Acoustics vol. 26, (2005) 183 ACOUSTIC RADIATION BY SET OF L-JOINTED VIBRATING PLATES Marek S. KOZIEŃ (*), Jerzy WICIAK (**) (*) Cracow University of Technology, Institute of Applied

More information

NUMERICAL MODELLING OF RUBBER VIBRATION ISOLATORS

NUMERICAL MODELLING OF RUBBER VIBRATION ISOLATORS NUMERICAL MODELLING OF RUBBER VIBRATION ISOLATORS Clemens A.J. Beijers and André de Boer University of Twente P.O. Box 7, 75 AE Enschede, The Netherlands email: c.a.j.beijers@utwente.nl Abstract An important

More information

VIBRATION ENERGY FLOW IN WELDED CONNECTION OF PLATES. 1. Introduction

VIBRATION ENERGY FLOW IN WELDED CONNECTION OF PLATES. 1. Introduction ARCHIVES OF ACOUSTICS 31, 4 (Supplement), 53 58 (2006) VIBRATION ENERGY FLOW IN WELDED CONNECTION OF PLATES J. CIEŚLIK, W. BOCHNIAK AGH University of Science and Technology Department of Robotics and Mechatronics

More information

Hybrid boundary element formulation in acoustics

Hybrid boundary element formulation in acoustics Hybrid boundary element formulation in acoustics L. Gaul, M. Wagner Institute A of Mechanics, University of Stuttgart, Germany. Abstract A symmetric hybrid boundary element method in the frequency domain

More information

Application of LS-DYNA to NVH Solutions in the Automotive Industry

Application of LS-DYNA to NVH Solutions in the Automotive Industry 14 th International LS-DYNA Users Conference Session: Simulation Application of LS-DYNA to NVH Solutions in the Automotive Industry Prasanna S. Kondapalli, Tyler Jankowiak BASF Corp., Wyandotte, MI, U.S.A

More information

Fan Noise Control by Enclosure Modification

Fan Noise Control by Enclosure Modification Fan Noise Control by Enclosure Modification Moohyung Lee a, J. Stuart Bolton b, Taewook Yoo c, Hiroto Ido d, Kenichi Seki e a,b,c Ray W. Herrick Laboratories, Purdue University 14 South Intramural Drive,

More information

The influence of Boundary Conditions on Sound Insulation

The influence of Boundary Conditions on Sound Insulation The influence of Boundary Conditions on Sound Insulation Master s Thesis in the Master s programme in Sound and Vibration CHRISTOFFER JANCO Department of Civil and Environmental Engineering Division of

More information

PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS

PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS PLEASURE VESSEL VIBRATION AND NOISE FINITE ELEMENT ANALYSIS 1 Macchiavello, Sergio *, 2 Tonelli, Angelo 1 D Appolonia S.p.A., Italy, 2 Rina Services S.p.A., Italy KEYWORDS pleasure vessel, vibration analysis,

More information

Analogy Electromagnetism - Acoustics: Validation and Application to Local Impedance Active Control for Sound Absorption

Analogy Electromagnetism - Acoustics: Validation and Application to Local Impedance Active Control for Sound Absorption Analogy Electromagnetism - Acoustics: Validation and Application to Local Impedance Active Control for Sound Absorption L. Nicolas CEGELY - UPRESA CNRS 5005 - Ecole Centrale de Lyon BP63-693 Ecully cedex

More information

Sound radiation from the open end of pipes and ducts in the presence of mean flow

Sound radiation from the open end of pipes and ducts in the presence of mean flow Sound radiation from the open end of pipes and ducts in the presence of mean flow Ray Kirby (1), Wenbo Duan (2) (1) Centre for Audio, Acoustics and Vibration, University of Technology Sydney, Sydney, Australia

More information

Vibration Generations Mechanisms: Flow Induced

Vibration Generations Mechanisms: Flow Induced Vibration Generations Mechanisms: Flow Induced Introduction That sound and vibration generation and flow are correlated is apparent from a range of phenomena that we can observe around us. A noteworthy

More information

Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition

Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition Fluid Structure Interaction and Moving Boundary Problems IV 63 Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition K.-H. Jeong, G.-M. Lee, T.-W. Kim & J.-I.

More information

EFFECTS OF PERMEABILITY ON SOUND ABSORPTION AND SOUND INSULATION PERFORMANCE OF ACOUSTIC CEILING PANELS

EFFECTS OF PERMEABILITY ON SOUND ABSORPTION AND SOUND INSULATION PERFORMANCE OF ACOUSTIC CEILING PANELS EFFECTS OF PERMEABILITY ON SOUND ABSORPTION AND SOUND INSULATION PERFORMANCE OF ACOUSTIC CEILING PANELS Kento Hashitsume and Daiji Takahashi Graduate School of Engineering, Kyoto University email: kento.hashitsume.ku@gmail.com

More information

IMPROVING THE ACOUSTIC PERFORMANCE OF EXPANSION CHAMBERS BY USING MICROPERFORATED PANEL ABSORBERS

IMPROVING THE ACOUSTIC PERFORMANCE OF EXPANSION CHAMBERS BY USING MICROPERFORATED PANEL ABSORBERS Proceedings of COBEM 007 Copyright 007 by ABCM 9th International Congress of Mechanical Engineering November 5-9, 007, Brasília, DF IMPROVING THE ACOUSTIC PERFORMANCE OF EXPANSION CHAMBERS BY USING MICROPERFORATED

More information

Extension of acoustic holography to cover higher frequencies. Jørgen Hald, Brüel & Kjær SVM A/S, Denmark

Extension of acoustic holography to cover higher frequencies. Jørgen Hald, Brüel & Kjær SVM A/S, Denmark Extension of acoustic holography to cover higher frequencies Jørgen Hald, Brüel & Kjær SVM A/S, Denmark 1 1 Introduction Near-field Acoustical Holography (NAH) is based on performing D spatial Discrete

More information

Acoustics Analysis of Speaker ANSYS, Inc. November 28, 2014

Acoustics Analysis of Speaker ANSYS, Inc. November 28, 2014 Acoustics Analysis of Speaker 1 Introduction ANSYS 14.0 offers many enhancements in the area of acoustics. In this presentation, an example speaker analysis will be shown to highlight some of the acoustics

More information

On determination of microphone response and other parameters by a hybrid experimental and numerical method

On determination of microphone response and other parameters by a hybrid experimental and numerical method On determination of microphone response and other parameters by a hybrid experimental and numerical method S. Barrera-Figueroa a, F. Jacobsen b and K. Rasmussen a a Danish Fundamental Metrology, Matematiktorvet

More information

Vibration analysis of concrete bridges during a train pass-by using various models

Vibration analysis of concrete bridges during a train pass-by using various models Journal of Physics: Conference Series PAPER OPEN ACCESS Vibration analysis of concrete bridges during a train pass-by using various models To cite this article: Qi Li et al 2016 J. Phys.: Conf. Ser. 744

More information

LOUDSPEAKER ROCKING MODES MODELLING AND ROOT CAUSE ANALYSIS. William Cardenas and Wolfgang Klippel. Presented by Stefan Irrgang. KLIPPEL GmbH.

LOUDSPEAKER ROCKING MODES MODELLING AND ROOT CAUSE ANALYSIS. William Cardenas and Wolfgang Klippel. Presented by Stefan Irrgang. KLIPPEL GmbH. LOUDSPEAKER ROCKING MODES MODELLING AND ROOT CAUSE ANALYSIS William Cardenas and Wolfgang Klippel Presented by Stefan Irrgang KLIPPEL GmbH Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis,

More information

Stochastic structural dynamic analysis with random damping parameters

Stochastic structural dynamic analysis with random damping parameters Stochastic structural dynamic analysis with random damping parameters K. Sepahvand 1, F. Saati Khosroshahi, C. A. Geweth and S. Marburg Chair of Vibroacoustics of Vehicles and Machines Department of Mechanical

More information

Vibro-Acoustic Modelling of Hermetic Reciprocating Compressors

Vibro-Acoustic Modelling of Hermetic Reciprocating Compressors Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1998 Vibro-Acoustic Modelling of Hermetic Reciprocating Compressors L. Gavric CETIM Follow

More information

Active Structural Acoustic Control of. Ribbed Plates using a Weighted Sum of Spatial Gradients.

Active Structural Acoustic Control of. Ribbed Plates using a Weighted Sum of Spatial Gradients. Active Structural Acoustic Control of Ribbed Plates using a Weighted Sum of Spatial Gradients. William R. Johnson, Daniel R. Hendricks, and Jonathan D. Blotter Department of Mechanical Engineering, Brigham

More information

Finite element study of the vibroacoustic response of a structure, excited by a turbulent boundary layer

Finite element study of the vibroacoustic response of a structure, excited by a turbulent boundary layer Finite element study of the vibroacoustic response of a structure, excited by a turbulent boundary layer A. Clement 1, C. Leblond 2, C. Audoly 3 and J.-A. Astolfi 4 1,4 Institut de Recherche de l Ecole

More information

Nuclear models: Collective Nuclear Models (part 2)

Nuclear models: Collective Nuclear Models (part 2) Lecture 4 Nuclear models: Collective Nuclear Models (part 2) WS2012/13: Introduction to Nuclear and Particle Physics,, Part I 1 Reminder : cf. Lecture 3 Collective excitations of nuclei The single-particle

More information

An eigenvalue method using multiple frequency data for inverse scattering problems

An eigenvalue method using multiple frequency data for inverse scattering problems An eigenvalue method using multiple frequency data for inverse scattering problems Jiguang Sun Abstract Dirichlet and transmission eigenvalues have important applications in qualitative methods in inverse

More information

Acoustic performance of industrial mufflers with CAE modeling and simulation

Acoustic performance of industrial mufflers with CAE modeling and simulation csnak, 214 Int. J. Nav. Archit. Ocean Eng. (214) 6:935~946 http://dx.doi.org/1.2478/ijnaoe-213-223 pissn: 292-6782, eissn: 292-679 Acoustic performance of industrial mufflers with CAE modeling and simulation

More information

A 3 D finite element model for sound transmission through a double plate system with isotropic elastic porous materials

A 3 D finite element model for sound transmission through a double plate system with isotropic elastic porous materials Acoustics and Vibrations Group Université de Sherbrooke, QC CANADA Département génie mécanique Université de Sherbrooke Sherbrooke, QC CANADA Tel.: (819) 821-7157 Fax: (819) 821-7163 A 3 D finite element

More information

A coupled BEM and FEM for the interior transmission problem

A coupled BEM and FEM for the interior transmission problem A coupled BEM and FEM for the interior transmission problem George C. Hsiao, Liwei Xu, Fengshan Liu, Jiguang Sun Abstract The interior transmission problem (ITP) is a boundary value problem arising in

More information

Titelmasterformat durch Klicken bearbeiten

Titelmasterformat durch Klicken bearbeiten Titelmasterformat durch Klicken bearbeiten Vibration and Acoustics for Electric Drive Development Presenter: Jens Otto, CADFEM GmbH Developer: Dr. Jürgen Wibbeler, Dr. Martin Hanke, CADFEM GmbH 4th CADFEM

More information

Graduate School of Engineering, Kyoto University, Kyoto daigaku-katsura, Nishikyo-ku, Kyoto, Japan.

Graduate School of Engineering, Kyoto University, Kyoto daigaku-katsura, Nishikyo-ku, Kyoto, Japan. On relationship between contact surface rigidity and harmonic generation behavior in composite materials with mechanical nonlinearity at fiber-matrix interface (Singapore November 2017) N. Matsuda, K.

More information

Transactions on Modelling and Simulation vol 3, 1993 WIT Press, ISSN X

Transactions on Modelling and Simulation vol 3, 1993 WIT Press,  ISSN X Boundary element method in the development of vehicle body structures for better interior acoustics S. Kopuz, Y.S. Unliisoy, M. Qali kan Mechanical Engineering Department, Middle East Technical University,

More information

From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes

From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes Dylan Copeland 1, Ulrich Langer 2, and David Pusch 3 1 Institute of Computational Mathematics,

More information

Vibration damping in polygonal plates using the acoustic black hole effect: model based on the image source method

Vibration damping in polygonal plates using the acoustic black hole effect: model based on the image source method Vibration damping in polygonal plates using the acoustic black hole effect: model based on the image source method Jacques Cuenca a,b, Adrien Pelat a, François Gautier a a. Laboratoire d Acoustique de

More information

Transmission Matrix Model of a Quarter-Wave-Tube with Gas Temperature Gradients

Transmission Matrix Model of a Quarter-Wave-Tube with Gas Temperature Gradients Proceedings of Acoustics 2013 Victor Harbor Transmission Matrix Model of a Quarter-Wave-Tube with Gas Temperature Gradients Carl Howard School of Mechanical Engineering, University of Adelaide, South Australia,

More information

Computational Acoustics by Means of Finite and Boundary Elements for Woofers, Tweeters, Horns and Small Transducers

Computational Acoustics by Means of Finite and Boundary Elements for Woofers, Tweeters, Horns and Small Transducers Computational Acoustics by Means of Finite and Boundary Elements for Woofers, Tweeters, Horns and Small Transducers Alfred J. Svobodnik NAD - Numerical Analysis and Design GmbH & Co KG as@nadwork.at http://www.nadwork.at

More information

Natural frequency analysis of fluid-conveying pipes in the ADINA system

Natural frequency analysis of fluid-conveying pipes in the ADINA system Journal of Physics: Conference Series OPEN ACCESS Natural frequency analysis of fluid-conveying pipes in the ADINA system To cite this article: L Wang et al 2013 J. Phys.: Conf. Ser. 448 012014 View the

More information

Structural Optimization. for Acoustic Disciplines

Structural Optimization. for Acoustic Disciplines Optimization for Acoustic Disciplines 4. Norddeutschen Simulationsforum 26 May Hamburg, Germany Claus B.W. Pedersen (claus.pedersen@fe-design.com) Peter M. Clausen, Peter Allinger, Jens Harder FE-Design

More information

Prediction of the Sound Reduction Index: Application to Monomurs Walls

Prediction of the Sound Reduction Index: Application to Monomurs Walls paper ID: 15 /p.1 Prediction of the Sound Reduction Index: Application to Monomurs Walls Thomas Buzzi, Cécile Courné, André Moulinier, Alain Tisseyre TISSEYRE & ASSOCIES, www.planete-acoustique.com 16

More information

Improved Method of the Four-Pole Parameters for Calculating Transmission Loss on Acoustics Silence

Improved Method of the Four-Pole Parameters for Calculating Transmission Loss on Acoustics Silence 7659, England, UK Journal of Information and Computing Science Vol., No., 7, pp. 6-65 Improved Method of the Four-Pole Parameters for Calculating Transmission Loss on Acoustics Silence Jianliang Li +,

More information

MODELLING AND MEASUREMENT OF BACKSCATTERING FROM PARTIALLY WATER-FILLED CYLINDRICAL SHELLS

MODELLING AND MEASUREMENT OF BACKSCATTERING FROM PARTIALLY WATER-FILLED CYLINDRICAL SHELLS MODELLING AND MEASUREMENT OF BACKSCATTERING FROM PARTIALLY WATER-FILLED CYLINDRICAL SHELLS Victor Humphrey a, Lian Sheng Wang a and Nisabha Jayasundere b a Institute of Sound & Vibration Research, University

More information

The Corrected Expressions for the Four-Pole Transmission Matrix for a Duct with a Linear Temperature Gradient and an Exponential Temperature Profile

The Corrected Expressions for the Four-Pole Transmission Matrix for a Duct with a Linear Temperature Gradient and an Exponential Temperature Profile Open Journal of Acoustics, 03, 3, 6-66 http://dx.doi.org/0.436/oja.03.3300 Published Online September 03 (http://www.scirp.org/journal/oja) he Corrected Expressions for the Four-Pole ransmission Matrix

More information

Vibro-acoustic Analysis for Noise Reduction of Electric Machines

Vibro-acoustic Analysis for Noise Reduction of Electric Machines Vibro-acoustic Analysis for Noise Reduction of Electric Machines From Flux to OptiStruct Example : Synchronous Machine Flux 2D coupling to OptiStruct Patrick LOMBARD Application Team Manager Patrick.Lombard@cedrat.com

More information

Design of Partial Enclosures. D. W. Herrin, Ph.D., P.E. University of Kentucky Department of Mechanical Engineering

Design of Partial Enclosures. D. W. Herrin, Ph.D., P.E. University of Kentucky Department of Mechanical Engineering D. W. Herrin, Ph.D., P.E. Department of Mechanical Engineering Reference 1. Ver, I. L., and Beranek, L. L. (2005). Control Engineering: Principles and Applications. John Wiley and Sons. 2. Sharp, B. H.

More information

FREQUENCY-DOMAIN RECONSTRUCTION OF THE POINT-SPREAD FUNCTION FOR MOVING SOURCES

FREQUENCY-DOMAIN RECONSTRUCTION OF THE POINT-SPREAD FUNCTION FOR MOVING SOURCES FREQUENCY-DOMAIN RECONSTRUCTION OF THE POINT-SPREAD FUNCTION FOR MOVING SOURCES Sébastien Guérin and Christian Weckmüller DLR, German Aerospace Center Institute of Propulsion Technology, Engine Acoustics

More information

Baryon spectroscopy with spatially improved quark sources

Baryon spectroscopy with spatially improved quark sources Baryon spectroscopy with spatially improved quark sources T. Burch,, D. Hierl, and A. Schäfer Institut für Theoretische Physik Universität Regensburg D-93040 Regensburg, Germany. E-mail: christian.hagen@physik.uni-regensburg.de

More information

Spherical Waves, Radiator Groups

Spherical Waves, Radiator Groups Waves, Radiator Groups ELEC-E5610 Acoustics and the Physics of Sound, Lecture 10 Archontis Politis Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering November

More information

Finite Element Method (FEM)

Finite Element Method (FEM) Finite Element Method (FEM) The finite element method (FEM) is the oldest numerical technique applied to engineering problems. FEM itself is not rigorous, but when combined with integral equation techniques

More information

Experimental Investigation of the Use of Equivalent Sources Model in Room Acoustics Simulations

Experimental Investigation of the Use of Equivalent Sources Model in Room Acoustics Simulations Purdue University Purdue e-pubs Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering 8-216 Experimental Investigation of the Use of Equivalent Sources Model in Room Acoustics

More information

Sound Radiation Of Cast Iron

Sound Radiation Of Cast Iron Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2002 Sound Radiation Of Cast Iron N. I. Dreiman Tecumseh Products Company Follow this and

More information

Noise impact of innovative barriers dedicated to freight trains in urban areas

Noise impact of innovative barriers dedicated to freight trains in urban areas Edinburgh, Scotland EURONOISE 9 October -8 Noise impact of innovative barriers dedicated to freight trains in urban areas Marine Baulac a Jérôme Defrance Philippe Jean Paris Est, CSTB, rue Joseph Fourier,

More information

1. How do error estimators for the Galerkin FEM depend on &, ft? 2. Can the classical Galerkin approach be improved towards a linear rule?

1. How do error estimators for the Galerkin FEM depend on &, ft? 2. Can the classical Galerkin approach be improved towards a linear rule? Reliability of finite element methods for the numerical computation of waves F. Ihlenburg*, I. Babuska*, S. Sauted "Institute for Physical Science and Technology, University of Maryland at College Park,

More information

Final Exam Solution Dynamics :45 12:15. Problem 1 Bateau

Final Exam Solution Dynamics :45 12:15. Problem 1 Bateau Final Exam Solution Dynamics 2 191157140 31-01-2013 8:45 12:15 Problem 1 Bateau Bateau is a trapeze act by Cirque du Soleil in which artists perform aerial maneuvers on a boat shaped structure. The boat

More information

Finite and Boundary Element Methods in Acoustics

Finite and Boundary Element Methods in Acoustics Finite and Boundary Element Methods in Acoustics W. Kreuzer, Z. Chen, H. Waubke Austrian Academy of Sciences, Acoustics Research Institute ARI meets NuHAG Kreuzer, Chen, Waubke (ARI) FEM-BEM-FMM ARI meets

More information

A Fast Regularized Boundary Integral Method for Practical Acoustic Problems

A Fast Regularized Boundary Integral Method for Practical Acoustic Problems Copyright 2013 Tech Science Press CMES, vol.91, no.6, pp.463-484, 2013 A Fast Regularized Boundary Integral Method for Practical Acoustic Problems Z.Y. Qian, Z.D. Han 1, and S.N. Atluri 1,2 Abstract: To

More information

In-situ measurements of the complex acoustic impedance of materials in vehicle interiors

In-situ measurements of the complex acoustic impedance of materials in vehicle interiors 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 In-situ measurements of the complex acoustic impedance of materials in vehicle interiors Leonardo Miranda Group Research/Vehicle Concepts,

More information

Proceedings of Meetings on Acoustics

Proceedings of Meetings on Acoustics Proceedings of Meetings on Acoustics Volume 9, 0 http://acousticalsociety.org/ ICA 0 Montreal Montreal, Canada - 7 June 0 Structural Acoustics and Vibration Session asa: History and Application of Constrained

More information

Dynamic Analysis on Vibration Isolation of Hypersonic Vehicle Internal Systems

Dynamic Analysis on Vibration Isolation of Hypersonic Vehicle Internal Systems International Journal of Engineering Research and Technology. ISSN 0974-3154 Volume 6, Number 1 (2013), pp. 55-60 International Research Publication House http://www.irphouse.com Dynamic Analysis on Vibration

More information

ALGEBRAIC FLUX CORRECTION FOR FINITE ELEMENT DISCRETIZATIONS OF COUPLED SYSTEMS

ALGEBRAIC FLUX CORRECTION FOR FINITE ELEMENT DISCRETIZATIONS OF COUPLED SYSTEMS Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2007 M. Papadrakakis, E. Oñate and B. Schrefler (Eds) c CIMNE, Barcelona, 2007 ALGEBRAIC FLUX CORRECTION

More information

Analysis of Geometrical Aspects of a Kelvin Probe

Analysis of Geometrical Aspects of a Kelvin Probe Analysis of Geometrical Aspects of a Kelvin Probe Stefan Ciba 1, Alexander Frey 2 and Ingo Kuehne* 1 1 Heilbronn University, Institute for Fast Mechatronic Systems (ISM), Kuenzelsau, Germany 2 University

More information

University of Kentucky

University of Kentucky Introduction David Herrin Wave Animation http://www.acs.psu.edu/drussell/demos/waves-intro/waves-intro.html 2 Wave Motion Some Basics Sound waves are pressure disturbances in fluids, such as air or hydraulic

More information

A hybrid finite element approach to modelling sound radiation. from circular and rectangular ducts.

A hybrid finite element approach to modelling sound radiation. from circular and rectangular ducts. A hybrid finite element approach to modelling sound radiation from circular and rectangular ducts. Wenbo Duan School of Engineering and Design, Mechanical Engineering, Brunel University, Uxbridge, Middlesex,

More information

Code_Aster. Finite elements in acoustics

Code_Aster. Finite elements in acoustics Titre : Éléments finis en acoustique Date : 03/06/2016 Page : 1/10 Finite elements in acoustics Summary: This document describes in low frequency stationary acoustics the equations used, the variational

More information

inter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering August 2000, Nice, FRANCE

inter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering August 2000, Nice, FRANCE Copyright SFA - InterNoise 2000 1 inter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering 27-30 August 2000, Nice, FRANCE I-INCE Classification: 3.4 LOW NOISE PANTOGRAPH

More information

BOUNDARY ELEMENT METHOD IN REFRACTIVE MEDIA

BOUNDARY ELEMENT METHOD IN REFRACTIVE MEDIA BOUDARY ELEMET METHOD I REFRACTIVE MEDIA David R. Bergman Exact Solution Scientific Consulting LLC, Morristown J, USA email: davidrbergman@essc-llc.com Boundary Element Method (BEM), an application of

More information

Solution Methods. Steady State Diffusion Equation. Lecture 04

Solution Methods. Steady State Diffusion Equation. Lecture 04 Solution Methods Steady State Diffusion Equation Lecture 04 1 Solution methods Focus on finite volume method. Background of finite volume method. Discretization example. General solution method. Convergence.

More information

On spherical-wave scattering by a spherical scatterer and related near-field inverse problems

On spherical-wave scattering by a spherical scatterer and related near-field inverse problems IMA Journal of Applied Mathematics (2001) 66, 539 549 On spherical-wave scattering by a spherical scatterer and related near-field inverse problems C. ATHANASIADIS Department of Mathematics, University

More information

Noise reduction applied to a decanter centrifuge

Noise reduction applied to a decanter centrifuge Noise reduction applied to a decanter centrifuge A.J. van Engelen DCT2009.069 Research report, research performed at University of Canterbury, New ealand New ealand Supervisor: Dr. J.R. Pearse University

More information

Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum

Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum Archives of Hydro-Engineering and Environmental Mechanics Vol. 56 (29), No. 3 4, pp. 121 137 IBW PAN, ISSN 1231 3726 Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum Dariusz

More information

INFLUENCE OF FILL EFFECT ON PAYLOAD IN A LARGE LAUNCH VEHICLE FAIRING

INFLUENCE OF FILL EFFECT ON PAYLOAD IN A LARGE LAUNCH VEHICLE FAIRING INFLUENCE OF FILL EFFECT ON PAYLOAD IN A LARGE LAUNCH VEHICLE FAIRING Zheng Ling State Key Laboratory of Mechanical Transmission, College of Automotive Engineering, Chongqing University, Chongqing email:

More information

ADVANCED SCANNING TECHNIQUES APPLIED TO VI- BRATIONS AND OPERATIONAL DEFLECTION SHAPES IN REAL MEASUREMENT SCENARIOS

ADVANCED SCANNING TECHNIQUES APPLIED TO VI- BRATIONS AND OPERATIONAL DEFLECTION SHAPES IN REAL MEASUREMENT SCENARIOS ADVANCED SCANNING TECHNIQUES APPLIED TO VI- BRATIONS AND OPERATIONAL DEFLECTION SHAPES IN REAL MEASUREMENT SCENARIOS Andrea Grosso Microflown Technologies, Arnhem - The Netherlands Lola García Microflown

More information

Multi Acoustic Prediction Program (MAPP tm ) Recent Results Perrin S. Meyer and John D. Meyer

Multi Acoustic Prediction Program (MAPP tm ) Recent Results Perrin S. Meyer and John D. Meyer Multi Acoustic Prediction Program (MAPP tm ) Recent Results Perrin S. Meyer and John D. Meyer Meyer Sound Laboratories Inc., Berkeley, California, USA Presented at the Institute of Acoustics (UK), Reproduced

More information

Sound Pressure Generated by a Bubble

Sound Pressure Generated by a Bubble Sound Pressure Generated by a Bubble Adrian Secord Dept. of Computer Science University of British Columbia ajsecord@cs.ubc.ca October 22, 2001 This report summarises the analytical expression for the

More information

Geometric nonlinear sensitivity analysis for nonparametric shape optimization with non-zero prescribed displacements

Geometric nonlinear sensitivity analysis for nonparametric shape optimization with non-zero prescribed displacements 0 th World Congress on Structural and Multidisciplinary Optimization May 9-24, 203, Orlando, Florida, USA Geometric nonlinear sensitivity analysis for nonparametric shape optimization with non-zero prescribed

More information

Proceedings of Meetings on Acoustics

Proceedings of Meetings on Acoustics Proceedings of Meetings on Acoustics Volume 19, 2013 http://acousticalsociety.org/ ICA 2013 Montreal Montreal, Canada 2-7 June 2013 Structural Acoustics and Vibration Session 2pSA: Memorial Session in

More information

Proceedings of Meetings on Acoustics

Proceedings of Meetings on Acoustics Proceedings of Meetings on Acoustics Volume 9, 23 http://acousticalsociety.org/ ICA 23 Montreal Montreal, Canada 2-7 June 23 Engineering Acoustics Session aea: Thermoacoustics I aea8. Computational fluid

More information

Ship structure dynamic analysis - effects of made assumptions on computation results

Ship structure dynamic analysis - effects of made assumptions on computation results Ship structure dynamic analysis - effects of made assumptions on computation results Lech Murawski Centrum Techniki Okrętowej S. A. (Ship Design and Research Centre) ABSTRACT The paper presents identification

More information

A simple formula for insertion loss prediction of large acoustical enclosures using statistical energy analysis method

A simple formula for insertion loss prediction of large acoustical enclosures using statistical energy analysis method csnak, 014 Int. J. Nav. Archit. Ocean Eng. (014) 6:894~903 http://dx.doi.org/10.478/ijnaoe-013-00 pissn: 09-678, eissn: 09-6790 A simple formula for insertion loss prediction of large acoustical enclosures

More information

VIBRATION RESPONSE OF AN ELECTRIC GENERATOR

VIBRATION RESPONSE OF AN ELECTRIC GENERATOR Research Report BVAL35-001083 Customer: TEKES/SMART VIBRATION RESPONSE OF AN ELECTRIC GENERATOR Paul Klinge, Antti Hynninen Espoo, Finland 27 December, 2001 1 (12) Title A B Work report Public research

More information

COMPARISON OF TWO METHODS TO SOLVE PRESSURES IN SMALL VOLUMES IN REAL-TIME SIMULATION OF A MOBILE DIRECTIONAL CONTROL VALVE

COMPARISON OF TWO METHODS TO SOLVE PRESSURES IN SMALL VOLUMES IN REAL-TIME SIMULATION OF A MOBILE DIRECTIONAL CONTROL VALVE COMPARISON OF TWO METHODS TO SOLVE PRESSURES IN SMALL VOLUMES IN REAL-TIME SIMULATION OF A MOBILE DIRECTIONAL CONTROL VALVE Rafael ÅMAN*, Heikki HANDROOS*, Pasi KORKEALAAKSO** and Asko ROUVINEN** * Laboratory

More information

Acoustic and Vibration Stability Analysis of Furnace System in Supercritical Boiler

Acoustic and Vibration Stability Analysis of Furnace System in Supercritical Boiler Acoustic and Vibration Stability Analysis of Furnace System in Supercritical Boiler Hyuk-Min Kwon 1 ; Chi-Hoon Cho 2 ; Heui-Won Kim 3 1,2,3 Advanced Technology Institute, Hyundai Heavy Industries, Co.,

More information

Absorption and scattering

Absorption and scattering Absorption and scattering When a beam of radiation goes through the atmosphere, it encounters gas molecules, aerosols, cloud droplets, and ice crystals. These objects perturb the radiation field. Part

More information

Acoustical contribution calculation and analysis of compressor shell based on acoustic transfer vector method

Acoustical contribution calculation and analysis of compressor shell based on acoustic transfer vector method IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Acoustical contribution calculation and analysis of compressor shell based on acoustic transfer vector method o cite this article:

More information

Exhaust noise a new measurement technology in duct

Exhaust noise a new measurement technology in duct Exhaust noise a new measurement technology in duct Mr Claes-Göran Johansson MSc,Sen. Scient. Acoustics ABB Corp.Research, Västerås Sweden, claes-goran.johansson@se.abb.com Mr Kari Saine MSc, Wärtsilä Finland

More information