MODELLING OF ACOUSTIC POWER RADIATION FROM MOBILE SCREW COMPRESSORS
|
|
- Homer Lloyd
- 5 years ago
- Views:
Transcription
1 11 th International Conference on Viration Prolems Z. Dimitrovová et.al. (eds.) Lison, Portugal, 9 12 Septemer 213 MODELLING OF ACOUSTIC POWER RADIATION FROM MOBILE SCREW COMPRESSORS Jan Dupal* 1, Jan Vimmr 1, Ondřej Bulík 1, Michal Hajžman 1 1 European Centre of Excellence NTIS - The New Technologies for Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Repulic dupal@kme.zcu.cz jvimmr@kme.zcu.cz oulik@kme.zcu.cz mhajzman@kme.zcu.cz Keywords: Screw Compressor, Viro-Acoustics, Helmholtz Equation, Finite Element Method. Astract. The method for a numerical solution of the viro-acoustic prolem in a moile screw compressor is proposed and the in-house 3D finite element (FE) solver is developed. In order to reduce the complexity of the prolem, an attention is paid to the numerical solution of the acoustic pressure field in the compressor cavity interacting with linear elastic compressor housing. Propagation of acoustic pressure in the cavity is mathematically descried y Helmholtz equation in the amplitude form and is induced y periodically varying surface velocity of the compressor engine which can e determined experimentally. Numerical solution of Helmholtz equation for acoustic pressure amplitude distiution inside the cavity with regards to prescried oundary conditions is performed using FE method on unstructured tetrahedral grid. For the FE discretisation of the elastic compressor housing (modelled as a thin metal plate), a six-noded thin flat shell triangular finite element with 18 DOF ased on the Kirchhoff plate theory was developed and implemented. The resulting strong coupled system of linear algeraic equations descriing the viro-acoustic prolem, i.e. the prolem of interaction etween the air inside the cavity and the screw compressor housing, is solved numerically y well-known algorithms implemented in Matla. The developed 3D FE solver is verified against the approximate analytical solution of a specially designed enchmark test case. A construction of the enchmark test analytical solution is also presented in the paper. The verified FE solver is applied to viro-acoustic prolem of the simplified model of a screw compressor and its numerical results, i.e. distriution of the acoustic pressure amplitudes in the cavity and asolute values of the compressor housing deflection amplitudes, are discussed.
2 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman 1 INTRODUCTION Considering customer requirements and the necessity to satisfy hygienic standards, the producers of moile screw compressors are compelled to minimise the emitted acoustic power and the related noise. The ongoing research is focused on a proposal of a suitale and efficient method and its implementation within an in-house computational software for the numerical solution of the acoustic power radiation from screw compressors. The knowledge from computational results will e used to alter the moile screw compressor design so that the total emitted acoustic power is significantly decreased. The solution of the aove stated goals represents a complex prolem. This paper is primarily focused on the numerical solution for the viro-acoustic prolem of the simplified model of the moile screw-compressor. Main attention is paid to the acoustic pressure distriution [1, 2, 3, 4] in the compressor cavity interacting with the linear elastic housing of the screw compressor. It is assumed that the propagation of the acoustic pressure in the cavity is induced y periodically varying surface velocity of the compressor engine, which is known a priori (e.g. experimentally measured). Since the periodic function can e expressed in the form of Fourier series, the prolem can e solved for a single frequency value and with regards to linearity of the prolem the gloal solution can e derived using a superposition of the harmonic solutions. Based on this assumption, the acoustic pressure p (x, t) and the acoustic velocity v (x, t) can e expressed in the complex harmonic form p (x, t) = p(x)e iωt and v (x, t) = v(x)e iωt, respectively, where ω is an angular frequency of compressor engine movement. The method used for numerical solution of the viro-acoustic prolem is implemented into a newly developed 3D finite element (FE) solver in Matla. The FE solver is verified ased on the approximate analytical solution of a specially designed enchmark test case. Furthermore the FE solver is applied to the viro-acoustic prolem in the simplified model of a screw compressor and its numerical results, i.e. distriution of the acoustic pressure amplitudes in the cavity and asolute values of the compressor housing deflection amplitudes, are discussed. 2 PROBLEM FORMULATION In the following, the computational domain is divided into two regions, the compressor cavity Ω R 3 and the elastic compressor housing Ω R 3, as displayed in Figure 1. The cavity domain Ω is ounded y the oundary Ω = Γ in Γ out Γ w Γ t where Γ in, Γ out and Γ w denote the inlet, the outlet and the rigid walls of the computational domain, respectively. The elastic housing Ω is ounded y oundary Ω = Γ f Γ u Γ t where Γ f denotes the oundary with prescried force loads and Γ u denotes the oundary with prescried displacement field. Figure 1: Computational domain The interface etween the two interacting domains, i.e. etween the cavity Ω and the housing Ω, (Ω Ω) R 3. is denoted as Γ t. In the cavity domain Ω, the distriution of acoustic pressure p(x) is descried y the Helmholtz equation in the amplitude form [2, 4, 5] k 2 p + p = (1) where k = ω is the wave numer, c is the speed of sound and ω is the angular frequency of the c engine motion. The weak solution of the Helmholtz equation is given as 2
3 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman Ω k 2 ϕ p dω Ω ϕ p dω + Ω ϕ p ds = (2) n where ϕ(x) is a well chosen test function. The momentum conservation law for the inviscid fluid yields [2, 4] p n = iωϱ av n (3) where i is the imaginary unit, ϱ a is the air density and v n = n v is the normal component of the acoustic velocity. The oundary condition v n = is prescried at the rigid wall oundary Γ w which yields Γ w ϕ p ds = n Γ w ϕ i ωϱ a v n ds =. The normal velocity v n at the anechoic outlet Γ out is given as v n = p/(ϱ a c) [1, 4] which yields Γ out ϕ p ds = n Γ w ϕ i ω p ds. For c the inlet oundary Γ in (i.e. the engine surface), the surface acoustic velocity v n is prescried. The interface Γ t etween the cavity and elastic housing holds Γ t ϕ p ds = n Γ t ϕ i ωϱ a v n ds, where the normal component of the acoustic velocity v n is an unknown velocity resulting from the interaction etween the acoustic environment in the cavity and the elastic housing of the screw compressor. The solution in the housing domain Ω is ased on the principle of virtual work (PVW) in the following form δε T σ d Ω = ϱ h δu T ü d Ω + p δu T n ds (4) Γ t Ω Ω where ε = [ε x, ε y, ε z, γ yz, γ xz, γ xy ] T is the strain vector, σ = [σ x, σ y, σ z, τ yz, τ xz, τ xy ] T is the stress vector, u = [u, v, w] T is the displacement vector and ϱ h is the material density of the housing. The surface integrals over the oundary Γ u with prescried zero displacements and Γ f with prescried zero loads are equal to zero and are therefore omitted from Eq FINITE ELEMENT METHOD DISCRETISATION The finite element discretisation of the cavity domain Ω R 3 is carried out for an unstructured tetrahedral mesh, a sample tetrahedral element is shown in Figure 2(left). The amplitudes of the acoustic pressure and the acoustic velocity are approximated linearly as p(ξ, η, ζ) = Φ(ξ, η, ζ)x e S 1 e p e, v ν (ξ, η, ζ) = Φ(ξ, η, ζ)x e S 1 e v e ν, ν {x, y, z}, (5) where Φ(ξ, η, ζ) = [1, ξ, η, ζ], p e = [p 1, p 2, p 3, p 4 ] T is the vector of the acoustic pressure amplitudes at each node of the finite element, Figure 2(left), and vν e = [v ν1, v ν2, v ν3, v ν4 ] T, ν {x, y, z} is the vector of ν-th components of the acoustic velocity amplitudes at each node of the finite element. The matrices S e and X e are of the following form S e = 1 x 1 y 1 z 1 1 x 2 y 2 z 2 1 x 3 y 3 z 3 1 x 4 y 4 z 4, X e = 1 x 1 y 1 z 1 x 2 ȳ 2 z 2 x 3 ȳ 3 z 3 x 4 ȳ 4 z 4, (6) while x i = x i x 1, ȳ i = y i y 1, z i = z i z 1 for i = 2, 3, 4. The test function ϕ(ξ, η, ζ) is approximated linearly, similarly to the amplitudes of the acoustic pressure and the acoustic 3
4 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman Figure 2: Tetrahedral finite element Ω e (left) and normalised finite element Ω e (right). velocity. Sustituting the approximations of the test function and of the acoustic pressure and velocity amplitudes, Eq. 5, into the weak solution given y Eq. 2 and taking the oundary integrals into consideration, we otain a system of linear algeraic equations ω 2 J e c 2 S T e X T e A X e S 1 e } {{ } H e 1 p e 6 J e S T e X T e L T D T e D e LX e S 1 e } {{ } G e p e (7) iω J ej c S T e X T e ÃjX e S 1 e p e iωϱ a Jej S T e X T e A j T e P v e = iωϱ h J }{{}}{{} ej S T e X T e A j T e P }{{} F C t e e C in e where the matrices H e and G e are computed for all inner elements of the cavity domain Ω and the matrices F e, C t e and C in e are computed for the oundary elements at the oundaries Γ out, Γ [ ] t T Φ and Γ in, respectively, see Figure 1. The matrix L = T, ΦT, ΦT ξ η ζ, the matrices De and T e are of the following form ȳ 3 z 4 z 3 ȳ 4 z 2 ȳ 4 ȳ 2 z 4 ȳ 2 z 3 z 2 ȳ 3 X e S 1 e D e = z 3 x 4 x 3 z 4 x 2 z 4 z 2 x 4 z 2 x 3 x 2 z 3, T e = X e S 1 e, (8) x 3 ȳ 4 ȳ 3 x 4 ȳ 2 x 4 x 2 ȳ 4 x 2 ȳ 3 ȳ 2 x 3 X e S 1 e P is the permutation matrix that changes the sequence of the FE parameters, J e = det J e where J e = x 2 ȳ 3 z 4 x 2 ȳ 4 z 3 x 3 ȳ 2 z 4 + x 3 ȳ 4 z 2 + x 4 ȳ 2 z 3 x 4 ȳ 3 z 2, Jej expresses twice the area of 1 1 ξ 1 ξ η each face of tetrahedral element, A = Φ T (ξ, η, ζ)φ(ξ, η, ζ) dζ dη dξ, the matrices à j, j = 1, 2, 3, 4 are otained from the integration of the product of ase functions Φ(ξ, η, ζ) over each face of the normalised tetrahedral element, Figure 2(right), and the matrices A j, j = 1, 2, 3, 4 are otained from the integration of the product of ase function matrices for the test function and for the normal velocity over each face of the normalised tetrahedral element. After dividing Eq. 7 y the term ( iω) and after assemling the gloal matrices, the following equation is otained ( 1 iωh + 1 ) iω G + F p + C t v t = C in v in (9) ϱ a where v in is the vector of prescried acoustic velocity amplitudes in the element nodes located at the engine surface Γ in and v t is the vector of unknown acoustic velocity amplitudes in the element nodes located at the interface Γ t. v e 4
5 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman Figure 3: Six-noded thin flat shell triangular finite element Ω e efore (left) and after (right) transformation. For the FE discretisation of the housing domain Ω R 3, a new 6-noded thin flat shell triangular finite element with 18 degrees of freedom (DOF) was developed, see Figure 3(left). This thin flat shell element is ased on the Kirchhoff plate theory. Each corner node i, j and k contains three displacements û, ˆv, ŵ and two rotations ŵˆx, ŵŷ. The mid-side nodes l, m and n store the information aout normal derivatives of deflection ŵ n (l), ŵ n (m), ŵ n (n), where the sense of rotation is determined y the sign of difference of numers of the corresponding edge corner nodes, see Figure 3(left). Applying the PVW Eq. 4, the equation of motion for a housing element in the amplitude form is otained with regards to a local coordinate system (ˆx, ŷ, ẑ) of the element as iωm e v h e + B e v h e + 1 iω K ev h e + Q e p e =, (1) where M e and K e are the derived mass and stiffness matrices of the 6-noded thin flat shell triangular finite element, B e = βk e is the proportional-damping matrix and ve h is the vector of velocity amplitudes for the nodes located in the housing of the screw compressor. The matrix Q e expresses the distriution of acoustic pressure amplitudes at the element Ω e. In order to assemly the gloal matrices of mass M, stiffness K and proportional-damping B and the gloal loading vector Qp, it is necessary to perform a transformation of all matrices and vectors from the local coordinate system of the element (ˆx, ŷ, ẑ) to the gloal coordinate system (x, y, z). This way, two rotations ŵˆx, ŵŷ at each corner node i, j and k of the element are transformed into three rotations ϕ, ϑ, ψ in the gloal coordinate system (x, y, z), while the rotations in the mid-side nodes l, m and n are not transformed, i.e. ŵ n (l) sgn(j i) α (l) sgn(j i), ŵ n (m) sgn(k j) α (m) sgn(k j) and ŵ n (n) sgn(k i) α (n) sgn(k i). The displacements û, ˆv, ŵ in the corner nodes i, j and k of the element are transformed into displacements u, v, w. Using this transformation the otained finite element has 21 DOF, as shown in Figure 3(right). The resulting matrix equation descriing the motion of the compressor s housing in the gloal coordinate system (x, y, z) yields iωmv h + Bv h + 1 iω Kvh + Qp =. (11) The vector of acoustic velocity amplitudes v h can e divided into the suvector of velocity amplitudes v t of compressor housing nodes at the interface Γ t and into the suvector of velocity amplitudes v Ω of the other nodes inside the compressor housing domain Ω. Thus the coefficient 5
6 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman matrices M, B, K can e divided into dedicated locks and Eqs. (9), (11) can e rewritten as ( 1 ϱ a iωh+ 1 G+F) C t p C in v in iω iωm 11 +B K iω 11 iωm 12 +B K iω 12 v Ω =. (12) Q iωm 21 +B K iω 21 iωm 22 +B K iω 22 v t The resulting strong coupled system of linear algeraic equations descriing the viro-acoustic prolem, i.e. the prolem of interaction etween the air inside the cavity Ω and the elastic housing Ω, is solved numerically y well-known algorithms implemented in Matla. 4 ANALYTICAL SOLUTION OF THE VIBRO-ACOUSTIC PROBLEM In order to verify the method descried aove and to validate numerical results of the developed solver, a enchmark test case, which can e solved analytically, is suggested. For simplicity, a rectangular cavity domain Ω R 2 with dimensions a is considered. The amplitude of normal velocity vn in (x) = A sin 2πx is prescried at the oundary Γ in at the ottom of the cavity domain and normal velocity v n = is prescried at the rigid side walls Γ w. At the top of the cavity, there is a simple supported elastic eam Ω R 1. Between the cavity and the elastic eam, there is the interface oundary Γ t. The test setup is displayed in Figure 4. It is possile to find an approximate analytic solution of this simple viro-acoustic prolem descriing the distriution of the acoustic pressure amplitudes in domain Ω and the deflection amplitudes in domain Ω. Figure 4: Computational domains Ω R 2 and Ω R 1 for the enchmark test case. In this case, the weak solution of Eq. 1 for acoustic pressure amplitudes is a ω 2 c ϕ p dydx 2 a ϕ p dydx + Γ in Γ w Γ t ϕ p ds = (13) n where ϕ = ϕ(x, y) are well-chosen test functions. It is assumed, that the solution for the amplitude of the acoustic pressure can e approximated y finite series p(x, y) = k=1 l=1 ( a kl sin kπx sin lπy a + kl cos kπx sin lπy a + (14) +c kl sin kπx cos lπy a + d kl cos kπx cos lπy a where N is a numer of considered harmonics in x and y directions. With regards to Eq. 3, the following conditions are applied at the rigid wall oundary Γ w p n = iωϱ av n = = p p (, y) = (, y) =. (15) x x Thus the a kl and c kl terms must e excluded from Eq. 14. The final form of the approximate solution for the acoustic pressure amplitudes is then 6 )
7 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman p(x, y) = k=1 kl cos kπx l=1 sin lπy a } {{ } ϕ kl (x,y) +d kl cos kπx cos lπy a } {{ } ϕ kl (x,y). (16) Due to the fact that Eq. 1 is of second order, the oundary conditions p are unstale and the n solution must e from a function space where a ϕ kl(x, y) dydx = a ϕ kl (x, y) dydx =, which are the functions with null mean values. The function in Eq. 16 meets this requirement. The oundary integral over Γ w from Eq. 13 is omitted with regards to Eq. 15. The velocity v n at the oundary Γ in is prescried. Thus the term p is given according to Eq. 3. At the interface Γ n t, the velocity v n is identical for oth the cavity domain Ω and the elastic eam Ω. The amplitude of the elastic eam deflection is assumed to e the harmonic function w(x) = j=1 which yields the amplitude of velocity of the eam v(x) = iω j=1 α j sin jπx (17) α j sin jπx. (18) In the following, the Galerkin method is applied. The estimated aproximate solution Eq. 16 is sustituted into Eq. 13 and the functions ϕ kl (x, y), ϕ kl (x, y) respectively, are applied as the test functions. This yield to two systems of N 2 algeraic equations for unknown coefficients kl and d kl, k, l = 1,..., N. Due to the fact that ϕ kl (x, ) = ϕ kl (x, a) = the first system holds ω 2 c 2 a The second system is given as ω 2 c 2 a ϕ kl (x, y)p(x, y) dydx ϕ kl(x, y)p(x, y) dydx +ω 2 ϱ a cos lπ j=1 a a 2j α j π j 2 k 2 jk = i ω A ϕ kl (x, y) p(x, y) dydx =. (19) ϕ kl(x, y) p(x, y) dydx + (2) [ ] 4 π(4 k 2 ) 2k where jk = 1 for (j k) even and jk = for (j k) odd. When considering the ortogonality of functions ϕ kl (x, y) and ϕ kl (x, y), Eqs. (19-2) ecome significantly simplified. The solution for the elastic eam Ω R 1 is given elow. With regards to Eq. 16, the acoustic pressure amplitude that is acting on the eam can e expressed in the form p(x, a) = k=1 l=1 d kl cos kπx cos lπ. (21) The amplitude form of the elastic eam equation of motion can e written as EI 4 w x 4 ω2 ϱ h S 2 w = p(x, a) (22) t2 7
8 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman where I = h3 and S =.1 h. After sustituting Eq. 17 and Eq. 21 into Eq. 22, consequent 12 multiplication y the term sin jπx, j = 1,..., N and after integration over domain Ω (i.e. for x ; ), the following system of equations is derived ) α j (EI j4 π 4 ω 2 ϱ 2 4 h S = k=1 d kl cos lπ 2j π j 2 k jk. (23) 2 Systems of Eqs. (19), (2) and (23) form a system of 2N 2 + N linear algeraic equations for 2N 2 + N unknown coefficients kl, d kl and α j where j, k, l = 1,..., N. The system can e written in a lock form A 11 A 12 A 21 A 22 A 23 A 32 A 33 l=1 d α = c 2 (24) where vectors, d and α include unknown coefficients kl, d kl and α j, respectively. Sustituting coefficients kl, d kl and α j into Eqs. (16-18) yields the solution for the acoustic pressure amplitudes in the cavity and for amplitudes of elastic eam deflections and velocities. 5 ANALYTICAL AND NUMERICAL RESULTS First, results of the approximate analytical solution for the enchmark test case of section 4 are presented and a comparison with numerical results of the in-house developed 3D FE solver is provided. In order to test the performance of the new thin flat shell triangular element, the 2D-1D enchmark test case (rectangular cavity and elastic eam) is numerically solved as a 3D- 2D case (cuoidal cavity and elastic plate), Figure 5(right) and the numerical results from the central plane section are compared to the aproximate analytical solution. Both the analytical and the numerical solution of the viro-acoustic prolem is provided for the cavity domain with dimensions a = 1 m, = 2 m and the amplitude A =.1 m s 1 of the prescried normal velocity at oundary Γ in, Figure 4. In the numerical model, the third dimension is given as z =.1 m. The air density is ϱ a = kg m 3 and the speed of sound is c = 34 m s 1. The elastic eam with thickness h =.1 m, density ϱ h = 78 kg m 3, Young modulus E = Pa and Poisson ratio µ =.3 is applied. The angular frequency ω = 5 rad s 1 and proportional damping coefficient β = are considered. Comparison of analytically and numerically computed asolute values of elastic eam/plate deflection amplitudes is provided in Figure 5(left). A minor deviations of the two solutions can e oserved. These are likely caused y a limited numer of harmonic functions respected in the approximate analytical solution (the provided solution refers to N = 8). For higher numer of harmonics the prolem ecomes ill-conditioned. This is actually an advantage of numerical solution y means of FE method. Figure 5(right) displays a complete numerical solution of the viro-acoustic prolem. Both distriution of acoustic pressure amplitudes in the cavity domain and asolute values of deflection amplitudes at elastic plate. For completeness, there is a comparison of acoustic pressure amplitudes in the cavity as computed using approximate analytical solution, Figure 6(left), and numerically, Figure 6(right), showing a good agreement of the two solutions. The second case studied numerically is a simplified model of moile screw compressor. The compressor cavity is represented y a cuoidal computational domain geometry with dimensions mm as depicted in Figure 7(top-left). The cavity ottom is rigid and corresponds to the oundary Γ w. All other walls of the cuoidal domain form the interface 8
9 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman Figure 5: Benchmark test case: comparison of analytical (red) and numerical (lue) solution of asolute values of elastic eam/plate deflection amplitudes (left) and numerical solution of distriution of acoustic pressure amplitudes in cavity and of asolute values of deflection amplitudes at elastic plate (right). Figure 6: Benchmark test case: distriution of acoustic pressure amplitudes in cavity - approximate analytical solution (left) and numerical results (right). oundary Γ t etween the compressor cavity and elastic housing. The elastic compressor housing is made of a thin metal plate with thickness h =.1 m and density ϱ h = 78 kg m 3. The compressor engine ody is modelled as a small lock attached to the rigid ottom and its surface represents the Γ in oundary. The engine lock dimensions are mm and the prescried amplitudes of normal velocity v n are equal to.2249 m s 1. The following two parameters are selected: angular frequency of compressor engine motion ω = 2 rad s 1 and the coefficient of proportional damping β =. All other parameter values are identical to values from the previous enchmark test case. In Figure 7(right), the resulting distriution of the acoustic pressure amplitudes in the cavity of the simplified model of the screw compressor as solved y the implemented 3D FE solver is shown. Figure 7(ottom-left) displays asolute values of deflection amplitudes at compressor housing in a direction that is normal to the compressor housing surface. The numerical results of a viro-acoustic prolem solved for a real geometry of the computational domain prepared according to the technical drawings provided y compressor producer and consisting of the engine ody, the inner cavity and compressor housing will e presented during the conference ICOVP CONCLUSIONS The in-house 3D FE solver for viro-acoustic analysis of screw compressors has een developed and the new 6-noded flat shell triangular finite element with 18 DOF implemented. Correctness of the proposed method and of the implemented solver has een verified using the enchmark test case, for which the analytical solution has een derived. First numerical results of viro-acoustic analysis have een presented for a simplified screw compressor model. In 9
10 Jan Dupal, Jan Vimmr, Ondřej Bulík, Michal Hajžman Figure 7: Simplified screw compressor model: computational domain geometry (top-left), numerical solution of asolute values of deflection amplitudes at compressor housing (ottom-let) and numerical solution of distriution of acoustic pressure amplitudes in compressor cavity (right). order to quantify the total emitted acoustic power, the numerical solution in amplitude form has to e performed for all angular frequencies of periodically varying surface velocity of the compressor engine. Then the total emitted acoustic power is a superposition of all particular solutions. In the near future, the solution of compressor housing virations that are kinematically excited y the rotating parts of the screw compressor will e addressed and superimposed to the housing virations caused y the acoustic pressure field. The results of this numerical analysis will enale modifications of the present moile screw compressor design which will lead to significant decrease in the total emitted acoustic power. 7 ACKNOWLEDGEMENTS This work was supported y the project TA21565 of the Technology Agency of the Czech Repulic. An assistance of Lior Loovský and Alena Jonášová during the preparation of the manuscript is also acknowledged. REFERENCES [1] L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of acoustics. John Wiley & Sons, Inc., Forth eddition, 2. [2] S. Temkin, Elements of acoustics. Acoustical Society of America, 21. [3] P.M. Morse, K.U. Ingard, Theoretical acoustics. Princeton University Press, New Jersey, [4] R. Matas, J. Kňourek, J. Voldřich, Influence of the terminal muffler geometry with three chamers and two tailpipes topology on its attenuation characteristics. Applied and Computational Mechanics, 3, , 29. [5] A. Bermúdez, P. Gamallo, R. Rodríguez, Finite element methods in local active control of sound. SIAM Journal on Control and Optimization, 43, , 24. 1
Homework 6: Energy methods, Implementing FEA.
EN75: Advanced Mechanics of Solids Homework 6: Energy methods, Implementing FEA. School of Engineering Brown University. The figure shows a eam with clamped ends sujected to a point force at its center.
More informationSIMILARITY METHODS IN ELASTO-PLASTIC BEAM BENDING
Similarity methods in elasto-plastic eam ending XIII International Conference on Computational Plasticity Fundamentals and Applications COMPLAS XIII E Oñate, DRJ Owen, D Peric and M Chiumenti (Eds) SIMILARIT
More informationExact Free Vibration of Webs Moving Axially at High Speed
Eact Free Viration of Wes Moving Aially at High Speed S. HATAMI *, M. AZHARI, MM. SAADATPOUR, P. MEMARZADEH *Department of Engineering, Yasouj University, Yasouj Department of Civil Engineering, Isfahan
More informationME 323 Examination #2
ME 33 Eamination # SOUTION Novemer 14, 17 ROEM NO. 1 3 points ma. The cantilever eam D of the ending stiffness is sujected to a concentrated moment M at C. The eam is also supported y a roller at. Using
More informationDavid A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan
Session: ENG 03-091 Deflection Solutions for Edge Stiffened Plates David A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan david.pape@cmich.edu Angela J.
More informationVIBRATION 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 informationSolving Homogeneous Trees of Sturm-Liouville Equations using an Infinite Order Determinant Method
Paper Civil-Comp Press, Proceedings of the Eleventh International Conference on Computational Structures Technology,.H.V. Topping, Editor), Civil-Comp Press, Stirlingshire, Scotland Solving Homogeneous
More informationPREDICTION OF ACOUSTIC NATURAL FREQUENCIES FOR TWO DIMENSIONAL SIMPLIFIED AIRCRAFT CABIN BY IMPEDANCE MOBILITY COMPACT MATRIX (IMCM) APPROACH
PREDICION OF ACOUSIC NAURAL FREQUENCIES FOR WO DIMENSIONAL SIMPLIFIED AIRCRAF CABIN BY IMPEDANCE MOBILIY COMPAC MARIX (IMCM) APPROACH Veerabhadra REDDY 1 ; Venkatesham B 2 1 Department of Mechanical and
More informationSpectral methods for fuzzy structural dynamics: modal vs direct approach
Spectral methods for fuzzy structural dynamics: modal vs direct approach S Adhikari Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Wales, UK IUTAM Symposium
More informationComposite Plates Under Concentrated Load on One Edge and Uniform Load on the Opposite Edge
Mechanics of Advanced Materials and Structures, 7:96, Copyright Taylor & Francis Group, LLC ISSN: 57-69 print / 57-65 online DOI:.8/5769955658 Composite Plates Under Concentrated Load on One Edge and Uniform
More informationBasic Equations of Elasticity
A Basic Equations of Elasticity A.1 STRESS The state of stress at any point in a loaded bo is defined completely in terms of the nine components of stress: σ xx,σ yy,σ zz,σ xy,σ yx,σ yz,σ zy,σ zx,andσ
More informationIMPROVING 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 informationTransmission Loss of a Dissipative Muffler with Perforated Central Pipe
Transmission Loss of a Dissipative Muffler with Perforated Central Pipe 1 Introduction This example problem demonstrates Coustyx ability to model a dissipative muffler with a perforated central pipe. A
More informationIntegral Equation Method for Ring-Core Residual Stress Measurement
Integral quation Method for Ring-Core Residual Stress Measurement Adam Civín, Miloš Vlk & Petr Navrátil 3 Astract: The ring-core method is the semi-destructive experimental method used for evaluation of
More informationAnalytical Mechanics: Elastic Deformation
Analytical Mechanics: Elastic Deformation Shinichi Hirai Dept. Robotics, Ritsumeikan Univ. Shinichi Hirai (Dept. Robotics, Ritsumeikan Univ.) Analytical Mechanics: Elastic Deformation 1 / 60 Agenda Agenda
More informationSound Power Of Hermetic Compressors Using Vibration Measurements
Purdue University Purdue e-pus International Compressor Engineering Conference chool of Mechanical Engineering 00 ound Power Of Hermetic Compressors Using Viration Measurements L. Gavric CETIM M. Darpas
More informationBuckling Behavior of Long Symmetrically Laminated Plates Subjected to Shear and Linearly Varying Axial Edge Loads
NASA Technical Paper 3659 Buckling Behavior of Long Symmetrically Laminated Plates Sujected to Shear and Linearly Varying Axial Edge Loads Michael P. Nemeth Langley Research Center Hampton, Virginia National
More informationEFFECTS 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 informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 2, 2011
Volume, No, 11 Copyright 1 All rights reserved Integrated Pulishing Association REVIEW ARTICLE ISSN 976 459 Analysis of free virations of VISCO elastic square plate of variale thickness with temperature
More informationMuffler 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 informationThe Finite Element Method
The Finite Element Method 3D Problems Heat Transfer and Elasticity Read: Chapter 14 CONTENTS Finite element models of 3-D Heat Transfer Finite element model of 3-D Elasticity Typical 3-D Finite Elements
More informationME FINITE ELEMENT ANALYSIS FORMULAS
ME 2353 - FINITE ELEMENT ANALYSIS FORMULAS UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE PROBLEMS 01. Global Equation for Force Vector, {F} = [K] {u} {F} = Global Force Vector [K] = Global Stiffness
More informationLASER GENERATED THERMOELASTIC WAVES IN AN ANISOTROPIC INFINITE PLATE
LASER GENERATED THERMOELASTIC WAVES IN AN ANISOTROPIC INFINITE PLATE H. M. Al-Qahtani and S. K. Datta University of Colorado Boulder CO 839-7 ABSTRACT. An analysis of the propagation of thermoelastic waves
More informationSound Propagation through Media. Nachiketa Tiwari Indian Institute of Technology Kanpur
Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur LECTURE-13 WAVE PROPAGATION IN SOLIDS Longitudinal Vibrations In Thin Plates Unlike 3-D solids, thin plates have surfaces
More informationAn indirect Trefftz method for the steady state dynamic analysis of coupled vibro acoustic systems
An indirect Trefftz method for the steady state dynamic analysis of coupled vibro acoustic systems W. Desmet, P. Sas, D. Vandepitte K.U. Leuven, Department of Mechanical Engineering, Division PMA Celestijnenlaan
More informationMath 216 Second Midterm 28 March, 2013
Math 26 Second Midterm 28 March, 23 This sample exam is provided to serve as one component of your studying for this exam in this course. Please note that it is not guaranteed to cover the material that
More informationIn-plane free vibration analysis of combined ring-beam structural systems by wave propagation
In-plane free viration analysis of comined ring-eam structural systems y wave propagation Benjamin Chouvion, Colin Fox, Stewart Mcwilliam, Atanas Popov To cite this version: Benjamin Chouvion, Colin Fox,
More informationUpper-bound limit analysis based on the natural element method
Acta Mechanica Sinica (2012) 28(5):1398 1415 DOI 10.1007/s10409-012-0149-9 RESEARCH PAPER Upper-ound limit analysis ased on the natural element method Shu-Tao Zhou Ying-Hua Liu Received: 14 Novemer 2011
More informationIN-PLANE VIBRATIONS OF PINNED-FIXED HETEROGENEOUS CURVED BEAMS UNDER A CONCENTRATED FORCE
5th International Conference on "Advanced Composite Materials Engineering" COMAT 4 6-7 OCTOBER 4, Braşov, Romania IN-PLANE VIBRATIONS OF PINNED-FIXED HETEROGENEOUS CURVED BEAMS UNDER A CONCENTRATED FORCE
More informationTECHNISCHE UNIVERSITEIT EINDHOVEN Department of Biomedical Engineering, section Cardiovascular Biomechanics
TECHNISCHE UNIVERSITEIT EINDHOVEN Department of Biomedical Engineering, section Cardiovascular Biomechanics Exam Cardiovascular Fluid Mechanics (8W9) page 1/4 Monday March 1, 8, 14-17 hour Maximum score
More information3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1
Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is
More informationNONLINEAR STRUCTURAL DYNAMICS USING FE METHODS
NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS Nonlinear Structural Dynamics Using FE Methods emphasizes fundamental mechanics principles and outlines a modern approach to understanding structural dynamics.
More informationPlanar Rigid Body Kinematics Homework
Chapter 2: Planar Rigid ody Kinematics Homework Chapter 2 Planar Rigid ody Kinematics Homework Freeform c 2018 2-1 Chapter 2: Planar Rigid ody Kinematics Homework 2-2 Freeform c 2018 Chapter 2: Planar
More informationStochastic 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 informationJEPPIAAR ENGINEERING COLLEGE
JEPPIAAR ENGINEERING COLLEGE Jeppiaar Nagar, Rajiv Gandhi Salai 600 119 DEPARTMENT OFMECHANICAL ENGINEERING QUESTION BANK VI SEMESTER ME6603 FINITE ELEMENT ANALYSIS Regulation 013 SUBJECT YEAR /SEM: III
More informationP = ρ{ g a } + µ 2 V II. FLUID STATICS
II. FLUID STATICS From a force analysis on a triangular fluid element at rest, the following three concepts are easily developed: For a continuous, hydrostatic, shear free fluid: 1. Pressure is constant
More informationDynamic response of foundations on threedimensional layered soil using the scaled boundary finite element method
IOP Conference Series: Materials Science and ngineering Dynamic response of foundations on threedimensional layered soil using the scaled oundary finite element method To cite this article: Carolin irk
More informationGREEN FUNCTION MATRICES FOR ELASTICALLY RESTRAINED HETEROGENEOUS CURVED BEAMS
The th International Conference on Mechanics of Solids, Acoustics and Virations & The 6 th International Conference on "Advanced Composite Materials Engineering" ICMSAV6& COMAT6 Brasov, ROMANIA, -5 Novemer
More informationdw 2 3(w) x 4 x 4 =L x 3 x 1 =0 x 2 El #1 El #2 El #3 Potential energy of element 3: Total potential energy Potential energy of element 1:
MAE 44 & CIV 44 Introduction to Finite Elements Reading assignment: ecture notes, ogan. Summary: Pro. Suvranu De Finite element ormulation or D elasticity using the Rayleigh-Ritz Principle Stiness matri
More informationTransfer-matrix-based approach for an eigenvalue problem of a coupled rectangular cavity
ransfer-matrix-based approach for an eigenvalue problem of a coupled rectangular cavity Hiroyuki IWAMOO ; Nobuo ANAKA Seikei University, Japan okyo Metropolitan University, Japan ABSRAC his study concerns
More informationNew 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 informationNONLINEAR CONTINUUM FORMULATIONS CONTENTS
NONLINEAR CONTINUUM FORMULATIONS CONTENTS Introduction to nonlinear continuum mechanics Descriptions of motion Measures of stresses and strains Updated and Total Lagrangian formulations Continuum shell
More informationActive Impact Sound Isolation with Floating Floors. Gonçalo Fernandes Lopes
Active Impact Sound Isolation with Floating Floors Gonçalo Fernandes Lopes Outubro 009 Active impact sound isolation with floating floors Abstract The users of buildings are, nowadays, highly demanding
More informationCritical loss factor in 2-DOF in-series system with hysteretic friction and its use for vibration control
Critical loss factor in -DOF in-series system with hysteretic friction and its use for vibration control Roman Vinokur Acvibrela, Woodland Hills, CA Email: romanv99@aol.com Although the classical theory
More informationModel Reduction & Interface Modeling in Dynamic Substructuring
Model Reduction & Interface Modeling in Dynamic Sustructuring Application to a multi-megawatt wind turine MSc. Thesis Author: Supervisor Siemens: Supervisor TU Delft: P.L.C. van der Valk Ir. S.N. Voormeeren
More informationABHELSINKI UNIVERSITY OF TECHNOLOGY
ABHELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D HELSINKI A posteriori error analysis for the Morley plate element Jarkko Niiranen Department of Structural
More informationNumerical Model of the Insertion Loss Promoted by the Enclosure of a Sound Source
Numerical Model of the Insertion Loss Promoted by the Enclosure of a Sound Source Gil F. Greco* 1, Bernardo H. Murta 1, Iam H. Souza 1, Tiago B. Romero 1, Paulo H. Mareze 1, Arcanjo Lenzi 2 and Júlio A.
More informationExact Shape Functions for Timoshenko Beam Element
IOSR Journal of Computer Engineering (IOSR-JCE) e-iss: 78-66,p-ISS: 78-877, Volume 9, Issue, Ver. IV (May - June 7), PP - www.iosrjournals.org Exact Shape Functions for Timoshenko Beam Element Sri Tudjono,
More informationOPTIMAL DESIGN IN VIBRO-ACOUSTIC PROBLEMS INVOLVING PERFORATED PLATES
11 th International Conference on Vibration Problems Z. Dimitrovová et.al. (eds.) Lisbon Portugal 9 12 September 2013 OPTIMAL DESIGN IN VIBRO-ACOUSTIC PROBLEMS INVOLVING PERFORATED PLATES Eduard Rohan
More informationNatural vibration frequency of classic MEMS structures
Natural vibration frequency of classic MEMS structures Zacarias E. Fabrim PGCIMAT, UFRGS, Porto Alegre, RS, Brazil Wang Chong, Manoel Martín Pérez Reimbold DeTec, UNIJUI, Ijuí, RS, Brazil Abstract This
More informationEffects of mass layer dimension on a finite quartz crystal microbalance
University of Neraska - Lincoln DigitalCommons@University of Neraska - Lincoln Mechanical & Materials Engineering Faculty Pulications Mechanical & Materials Engineering, Department of Summer 8-2011 Effects
More informationCIV-E1060 Engineering Computation and Simulation Examination, December 12, 2017 / Niiranen
CIV-E16 Engineering Computation and Simulation Examination, December 12, 217 / Niiranen This examination consists of 3 problems rated by the standard scale 1...6. Problem 1 Let us consider a long and tall
More informationInternational Journal of Scientific & Engineering Research, Volume 5, Issue 7, July-2014 ISSN
ISSN 2229-5518 692 In literature, finite element formulation uses beam element or plate element for structural modelling which has a limitation on transverse displacement. Atkinson and Manrique [1] studied
More informationPosterior Covariance vs. Analysis Error Covariance in Data Assimilation
Posterior Covariance vs. Analysis Error Covariance in Data Assimilation F.-X. Le Dimet(1), I. Gejadze(2), V. Shutyaev(3) (1) Université de Grenole (2)University of Strathclyde, Glasgow, UK (3) Institute
More informationTransient vibration analysis of a completely free plate using modes obtained by Gorman s Superposition Method
Transient vibration analysis of a completely free plate using modes obtained by Gorman s Superposition Method Y Mochida *, S Ilanko Department of Engineering, The University of Waikato, Te Whare Wananga
More informationFinite Elements for Elastic Shell Models in
Elastic s in Advisor: Matthias Heinkenschloss Computational and Applied Mathematics Rice University 13 April 2007 Outline Elasticity in Differential Geometry of Shell Geometry and Equations The Plate Model
More informationLEAST-SQUARES FINITE ELEMENT MODELS
LEAST-SQUARES FINITE ELEMENT MODELS General idea of the least-squares formulation applied to an abstract boundary-value problem Works of our group Application to Poisson s equation Application to flows
More informationRESEARCH REPORT IN MECHANICS
No. XX ISSN XXXX XXXX Oct. 8 Semi-analytical postuckling analysis of stiffened plates with a free edge y ars Bruak RESEARCH REPORT IN MECHANICS UNIVERSITY OF OSO DEPARTMENT OF MATHEMATICS MECHANICS DIVISION
More informationANALYTICAL AND EXPERIMENTAL ELASTIC BEHAVIOR OF TWILL WOVEN LAMINATE
ANALYTICAL AND EXPERIMENTAL ELASTIC BEHAVIOR OF TWILL WOVEN LAMINATE Pramod Chaphalkar and Ajit D. Kelkar Center for Composite Materials Research, Department of Mechanical Engineering North Carolina A
More informationSTRUCTURAL ANALYSIS OF A WESTFALL 2800 MIXER, BETA = 0.8 GFS R1. By Kimbal A. Hall, PE. Submitted to: WESTFALL MANUFACTURING COMPANY
STRUCTURAL ANALYSIS OF A WESTFALL 2800 MIXER, BETA = 0.8 GFS-411519-1R1 By Kimbal A. Hall, PE Submitted to: WESTFALL MANUFACTURING COMPANY OCTOBER 2011 ALDEN RESEARCH LABORATORY, INC. 30 Shrewsbury Street
More informationAcoustic radiation by means of an acoustic dynamic stiffness matrix in spherical coordinates
Acoustic radiation by means of an acoustic dynamic stiffness matrix in spherical coordinates Kauê Werner and Júlio A. Cordioli. Department of Mechanical Engineering Federal University of Santa Catarina
More informationA SHEAR LOCKING-FREE BEAM FINITE ELEMENT BASED ON THE MODIFIED TIMOSHENKO BEAM THEORY
Ivo Senjanović Nikola Vladimir Dae Seung Cho ISSN 333-4 eissn 849-39 A SHEAR LOCKING-FREE BEAM FINITE ELEMENT BASED ON THE MODIFIED TIMOSHENKO BEAM THEORY Summary UDC 534-6 An outline of the Timoshenko
More informationNon-linear and time-dependent material models in Mentat & MARC. Tutorial with Background and Exercises
Non-linear and time-dependent material models in Mentat & MARC Tutorial with Background and Exercises Eindhoven University of Technology Department of Mechanical Engineering Piet Schreurs July 7, 2009
More informationApplication of a novel method to identify multi-axis joint properties
Application of a novel method to identify multi-axis joint properties Scott Noll, Jason Dreyer, and Rajendra Singh The Ohio State University, 219 W. 19 th Avenue, Columbus, Ohio 4321 USA ABSTRACT This
More informationCOMPOSITE MATERIAL WITH NEGATIVE STIFFNESS INCLUSION FOR VIBRATION DAMPING: THE EFFECT OF A NONLINEAR BISTABLE ELEMENT
11 th International Conference on Vibration Problems Z. Dimitrovová et.al. (eds.) Lisbon, Portugal, 9 12 September 2013 COMPOSITE MATERIAL WITH NEGATIVE STIFFNESS INCLUSION FOR VIBRATION DAMPING: THE EFFECT
More information13.42 LECTURE 16: FROUDE KRYLOV EXCITATION FORCE SPRING 2003
13.42 LECURE 16: FROUDE KRYLOV EXCIAION FORCE SPRING 2003 c A. H. ECHE & M.S. RIANAFYLLOU 1. Radiation and Diffraction Potentials he total potential is a linear superposition of the incident, diffraction,
More informationNUMERICAL PREDICTION OF PERFORATED TUBE ACOUSTIC IMPEDANCE
NUMERICAL PREDICTION OF PERFORATED TUBE ACOUSTIC IMPEDANCE G. Pradeep, T. Thanigaivel Raja, D.Veerababu and B. Venkatesham Department of Mechanical and Aerospace Engineering, Indian Institute of Technology
More information3D Elasticity Theory
3D lasticity Theory Many structural analysis problems are analysed using the theory of elasticity in which Hooke s law is used to enforce proportionality between stress and strain at any deformation level.
More informationStudies of Sound Radiation From Beams with Acoustic Black Holes
Studies of Sound Radiation From Beams with Acoustic Black Holes Chenhui Zhao 1, M.G. Prasad 2 Stevens Institute of Technology Abstract: Recently, Acoustic Black Holes (), a new passive structural modification
More informationFig. 1. Circular fiber and interphase between the fiber and the matrix.
Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In
More informationSound Propagation through Media. Nachiketa Tiwari Indian Institute of Technology Kanpur
Sound Propagation through Media Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 14 Waves Propagation in Solids Overview Terminology: phasor, wave front, wave number, phase velocity, and
More informationTransmission Matrix Model of a Quarter-Wave-Tube with Gas Temperature Gradients
Transmission Matrix Model of a Quarter-Wave-Tube with Gas Temperature Gradients Carl Howard School of Mechanical Engineering, University of Adelaide, South Australia, Australia ABSTRACT A transmission
More informationBOUSSINESQ-TYPE MOMENTUM EQUATIONS SOLUTIONS FOR STEADY RAPIDLY VARIED FLOWS. Yebegaeshet T. Zerihun 1 and John D. Fenton 2
ADVANCES IN YDRO-SCIENCE AND ENGINEERING, VOLUME VI BOUSSINESQ-TYPE MOMENTUM EQUATIONS SOLUTIONS FOR STEADY RAPIDLY VARIED FLOWS Yeegaeshet T. Zerihun and John D. Fenton ABSTRACT The depth averaged Saint-Venant
More informationComputational Simulation of Dynamic Response of Vehicle Tatra T815 and the Ground
IOP Conference Series: Earth and Environmental Science PAPER OPEN ACCESS Computational Simulation of Dynamic Response of Vehicle Tatra T815 and the Ground To cite this article: Jozef Vlek and Veronika
More informationEffects of mass distribution and buoyancy on the sound radiation of a fluid loaded cylinder
Effects of mass distribution and buoyancy on the sound radiation of a fluid loaded cylinder Hongjian Wu, Herwig Peters, Roger Kinns and Nicole Kessissoglou School of Mechanical and Manufacturing, University
More informationASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR
ASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR M PRANESH And Ravi SINHA SUMMARY Tuned Mass Dampers (TMD) provide an effective technique for viration control of flexile
More informationinter.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: 7.0 VIBRATIONS OF FLAT
More informationA consistent dynamic finite element formulation for a pipe using Euler parameters
111 A consistent dynamic finite element formulation for a pipe using Euler parameters Ara Arabyan and Yaqun Jiang Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721,
More information19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 NUMERICAL SIMULATION OF THE ACOUSTIC WAVES PROPAGATION IN A STANDING WAVE TUBE
19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 27 NUMERICAL SIMULATION OF THE ACOUSTIC WAVES PROPAGATION IN A STANDING WAVE TUBE PACS: 43.2.Ks Juliá Sanchis, Ernesto 1 ; Segura Alcaraz,
More informationICSV14 Cairns Australia 9-12 July, 2007
ICSV14 Cairns Australia 9-1 July, 7 STUDY ON THE CHARACTERISTICS OF VIBRATION AND ACOUSTIC RADIATION OF DAMAGED STIFFENED PANELS Hong Ming 1, Guo Xin-yi, Liu Lian-hai 3 and Li Gen-tian 4 1 Department of
More informationSPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES
2010/2 PAGES 1 8 RECEIVED 21. 9. 2009 ACCEPTED 20. 1. 2010 Y. KOLEKOVÁ, M. PETRONIJEVIĆ, G. SCHMID SPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES ABSTRACT
More informationBHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I
BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I 635 8 54. Third Year M E C H A NICAL VI S E M ES TER QUE S T I ON B ANK Subject: ME 6 603 FIN I T E E LE ME N T A N A L YSIS UNI T - I INTRODUCTION
More informationarxiv:nlin/ v1 [nlin.si] 29 Jan 2007
Exact shock solution of a coupled system of delay differential equations: a car-following model Y Tutiya and M Kanai arxiv:nlin/0701055v1 [nlin.si] 29 Jan 2007 Graduate School of Mathematical Sciences
More informationImpedance correction for a branched duct in a thermoacoustic air-conditioner
20-22 November 2006, Christchurch, New ealand Impedance correction for a branched duct in a thermoacoustic air-conditioner Carl Howard School of Mechanical Engineering, The University of Adelaide, Adelaide,
More informationChapter 2. General concepts. 2.1 The Navier-Stokes equations
Chapter 2 General concepts 2.1 The Navier-Stokes equations The Navier-Stokes equations model the fluid mechanics. This set of differential equations describes the motion of a fluid. In the present work
More informationResearch Article Analysis Bending Solutions of Clamped Rectangular Thick Plate
Hindawi Mathematical Prolems in Engineering Volume 27, Article ID 7539276, 6 pages https://doi.org/.55/27/7539276 Research Article Analysis Bending Solutions of lamped Rectangular Thick Plate Yang Zhong
More informationEffect of effective length of the tube on transmission loss of reactive muffler
Effect of effective length of the tube on transmission loss of reactive muffler Gabriela Cristina Cândido da SILVA 1 ; Maria Alzira de Araújo NUNES 1 1 University of Brasilia, Brazil ABSTRACT Reactive
More informationSuperelements and Global-Local Analysis
10 Superelements and Gloal-Local Analysis 10 1 Chapter 10: SUPERELEMENTS AND GLOBAL-LOCAL ANALYSIS TABLE OF CONTENTS Page 10.1 Superelement Concept................. 10 3 10.1.1 Where Does the Idea Come
More informationTransmission 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 informationExperimental Modal Analysis of a Flat Plate Subjected To Vibration
American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-5, Issue-6, pp-30-37 www.ajer.org Research Paper Open Access
More informationON FLATNESS OF NONLINEAR IMPLICIT SYSTEMS
ON FLATNESS OF NONLINEAR IMPLICIT SYSTEMS Paulo Sergio Pereira da Silva, Simone Batista Escola Politécnica da USP Av. Luciano Gualerto trav. 03, 158 05508-900 Cidade Universitária São Paulo SP BRAZIL Escola
More informationEffect of Uniform Horizontal Magnetic Field on Thermal Instability in A Rotating Micropolar Fluid Saturating A Porous Medium
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue Ver. III (Jan. - Fe. 06), 5-65 www.iosrjournals.org Effect of Uniform Horizontal Magnetic Field on Thermal Instaility
More informationHydroelastic 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 informationSEG/New Orleans 2006 Annual Meeting. Non-orthogonal Riemannian wavefield extrapolation Jeff Shragge, Stanford University
Non-orthogonal Riemannian wavefield extrapolation Jeff Shragge, Stanford University SUMMARY Wavefield extrapolation is implemented in non-orthogonal Riemannian spaces. The key component is the development
More informationStatic & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering
Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition
More informationCHAPTER 5 SIMULATION OF A PAYLOAD FAIRING
CHAPTER 5 SIMULATION OF A PAYLOAD FAIRING In the preceding chapters, a model of a PZT actuator exciting a SS cylinder has been presented. The structural model is based on a modal expansion formulation
More informationSound radiation from nested cylindrical shells
Sound radiation from nested cylindrical shells Hongjian Wu 1 ; Herwig Peters 1 ; Nicole Kessissoglou 1 1 School of Mechanical and Manufacturing Engineering, UNSW Australia, Sydney NSW 252 ABSTRACT Fluid-loaded
More informationImproved 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 informationUNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES
UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES A Thesis by WOORAM KIM Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the
More informationPerformance comparison between hybridizable DG and classical DG methods for elastic waves simulation in harmonic domain
March 4-5, 2015 Performance comparison between hybridizable DG and classical DG methods for elastic waves simulation in harmonic domain M. Bonnasse-Gahot 1,2, H. Calandra 3, J. Diaz 1 and S. Lanteri 2
More information