A DECOUPLED VIBRO-ACOUSTIC EXTENSION OF NASTRAN

Transcription

1 Twelfth International Congress on Sound and Vibration A DECOUPLED VIBRO-ACOUSTIC EXTENSION OF NASTRAN Philippe JEAN and Hugo SIWIAK Centre Scientifique et Technique du Bâtiment 24 rue Joseph Fourier F St Martin d Hères, France jean@cstb.fr Abstract A decoupled model for sound transmission problems has been derived. The structure is modelled by NASTRAN, thus allowing the consideration of complex partitions. The acoustical part of the problem is based on the GRIM approach, where the Green functions for a blocked structure can be computed by different means such as modal approaches, BEM or geometrical models. Numerical and experimental validations are presented. INTRODUCTION The computation of sound transmission between two rooms can be called a large problem since one is usually interested in a wide frequency range extending from 50 to 5000 Hz. Partitions range from very simple (plain concrete wall) to complex structures (bricks, hollow core slabs, steel frame lightweight partitions). Frequency, material and size parameters lead to large ka numbers. Fortunately, numeric tools such has finite elements, which rely heavily on the power of computers, can now handle vibration problems for such structures up to relatively high frequencies (1000 to 2000 Hz and higher is quite feasible). The acoustical part of the problem concerns large volumes having a high modal density and for which several approaches can be employed: Finite elements, BEM, modal approaches, geometrical models etc. Solving the fully coupled problem is quite possible [1] but is computationally expensive. Comparisons made at CSTB between modal approaches based on coupled 1

2 and decoupled models have lead to identical results in the case of sound transmission between two rooms. Coupling is however necessary for small volumes such air gaps between double glazings [2]. Other simpler approaches based on energy concepts have not been considered to be suitable due to the lower frequency components important in sound transmission problems in buildings but could be considered for the highest frequency range as a faster alternative to the method here presented. An other reason to use a decoupled approach lies in our wish to benefit from the advantage of the fine structural description which one can expect from FEM. Adapting a separate acoustical prolongation to commercial codes such as NASTRAN is simple, as will be showed, if a decoupled approach is employed. The whole numerical project which aims at the development of a numeric tool to complete the testing facilities at CSTB near Paris has been named LAVANDE (LAboratoire de Vibro-Acoustique Numérique DEcouplée) THE GRIM APPROACH The GRIM acronym stands for Green Ray Integral Method [2,3-5]. This approach is based on a Rayleigh-like integral expression of the acoustic pressure P P ( M ) = jωρ V ( Q) G ( M, Q) ds( Q) (1) S V V where S V is the radiating surface V its velocity. G V is the Green function in the receiving space, computed for a rigid structure but keeping all other boundaries unmodified. This integral is exact and it is a coupled expression between velocity and acoustical pressure. However, in most cases the velocity is little affected by the pressure in the receiver domain and (1) can be used as a direct expression assuming that V is known independently of P. When the receiving domain is a volume, (1) is employed at a discrete number of points reproducing the standard measuring procedure for sound insulation or impact noise in laboratories. Assuming a diffuse field will allow for the computation of radiated acoustic power. If the structure is baffled, (1) is incorporated in the classical radiation integral to give * Wr Re( j V ( Q) V ( M ) G( M, Q) ds ds) SR S V = ρω (2) The computation of the velocity is made by NASTRAN. Two types of computations are considered: i) impact noise, in which case NASTRAN only requires exiting forces to reproduce the standard tapping machine, ii) sound insulation where a precomputation of the sound field must be done prior to the use of NASTRAN; again the incident pressure field is computed in a decoupled manner and the incident acoustic power is computed by averaging the sound pressure at selected positions in 2

3 accordance with measuring standards. As already mentioned, several means of computing incident and radiated pressure fields can be employed. Results here presented have been obtained by using the computer program GAIA [5] based on a decoupled modal approach for both structures and volumes. ADAPTING NASTRAN Although NASTRAN includes acoustic elements, these are employed only for small volumes within the partition. Computations for double glazings have been compared with success with computations made either with FEM/BEM and coupled analytical modal approaches. In the examples here presented for sound transmission problems the adopted procedure is the following: 1) the sound pressure is computed with GAIA resulting in the acoustic power incident on the structure and in a pressure field spectrum file (PRESS) defined on a regular grid on the partition. 2) a first PATRAN/NASTRAN meshing/computation is made for a point-like mechanical excitation, the result being an ASCII file (one.bdf) which is the input file to NASTRAN 3) an interface program (modif_bdf) has been written to include the PRESS file into the file (one.bdf ) as a distributed pressure excitation spectrum; this results in a new (two.bdf) file. In order to facilitate the parametric study of a given situation the modif_bdf program can do several modifications to the input data to NASTRAN, such as modifying the boundary conditions which can become time consuming through PATRAN (the pre processor to NASTRAN). 4) NASTRAN is run; the output is an ASCII file (file.f06) of very large dimensions which contains the velocity field spectra at chosen nodes, usually only the radiating nodes. 5) a pos-treatment program (vit_nastran) has been written to extract the velocities from radiating nodes and store them into a compact binary file (file.vit) of reduced size compared to the (file.f06) file 6) GAIA is run a second time with the velocities input from the (file.vit) file, thus bypassing the structural modal computation included in GAIA. Pressures and radiated power are computed according to the previous description. The sound reduction index is then obtained from the ratio between incident and radiated acoustic powers. VALIDATION Analytical validation of the decoupled approach has been obtained by comparing fully coupled and decoupled modal computations. GAIA giving only analytical solutions for thin plates without shear effects but with several basic boundary conditions, the first validations of the proposed numerical scheme has been made 3

4 using plate finite elements without shear effects. Figure 1 shows such a comparison of radiated power for a clamped 16 cm concrete plate. Computing the plate response with GAIA and with NASTRAN gives very similar results. Also showed on these graphs, the results with NASTRAN using plate elements with shear and CHEXA volume elements show that the results are significantly different. The shear effects in the wall can not be ignored. In the following results the CHEXA elements are used. Figure 1. Sound reduction index of a 16 cm concrete wall placed between two rooms. 4 computations for the structure: modal, FEM with no and with shear, CHEXA elements Impact noise Measurements have been carried out at the LABE, in the testing facilities at CSTB near Paris. Impact noise and sound insulation measurements have been carried out. The objective of these measurements was to validate the GAIA/NASTRAN calculations. It rapidly appeared that the computations of Ln were strongly dependent on the material input data and on the chosen boundary conditions. In addition to the Ln measurements input mobilities have been measured and used in a calibration step. Figure 2 reports the comparison between two measurements and computations with two modelling of the boundary conditions: either simply supported or by trying to model the particular technique used at the LABE to fix the plate through plaster peripheral bedding. Agreement with measurements are rather good although a detailed analysis of the input mobility has showed that agreement due to the imperfect modelling of the boundary conditions can still be improved. 4

5 Figure 2. Simply supported or peripheral bedding. 2 measurements, computations with 3 boundary conditions (SS,CP,CP1). Sound transmission The measuring of sound reduction indices is made with a different facility. The source room is moveable and is pressed against the fixed receiving room + moveable wall as showed in figures 3a and 3b. The sealing of the wall is made by means of injected plaster. Tested wall Fixed receiving volume Plaster sealing of wall Moving source volume 5

6 Plaster Sealing Rubber seams External box: mobile External box: b Source room Wall to be measured External box: fixed Springs Internal box: fixed Rubber seam Receiving room Figure 3. testing facility for the measuring of sound reduction index. The technique employed for assembling the wall between two volumes (one fixed and one mobile) with the use of injected plaster bedding is numerically complex. Therefore, an important effort has been put into the modelling of the boundary conditions. Figure 4 shows several boundary conditions with zero displacement imposed (red nodes) at different locations depending on whether the seams are assumed to be free to move or blocked.. Figure 4. Modelling of boundary conditions in NASTRAN. Red nodes are blocked. Figure 5 shows the resultant input mobilities. The best agreement is obtained for the case CP3. Figure 5. Input mobilities for three different NASTRAN boundary conditions. Measurement NASTRAN Figure 6 shows a comparison of the input mobility measured and computed with different modelling hypothesis for the Young s modulus and the internal loss factor. 6

7 Input mobility Figure 6. Comparison of measured ( ) and computed input mobility. Left graph: effect of Young s modulus (28 and 23 GPa). Right graph, E=23 GPa: effect of internal loss factor (5 % and function of frequency). The recovery of the first three resonances is achieved if a Young s modulus of 23 GPa and a measured loss factor spectrum -obtained from the measured structural reverberation time- are used as inputs. Next, Figure 7a(left graph) shows the level difference between the structure s velocity and the incident power. The agreement is very satisfactory. Figure 7b(right graph) represents the sound reduction index. The coloured results correspond to 3 different computations where the volume employed for acoustic pressure averaging and the walls absorption are varied. The computed values tend to be lower than the measured ones (3 sets of measurements). The good agreement observed in the previous results (mobilities and LV-LWinc) tends to show that the computation of radiated pressure is overestimated whereas for impact noise (Ln in Figure 3) the radiated pressure was rather underestimated in the higher frequency range. Theses aspects should be further investigated in a close future. Figure 7a. Difference of plate s velocity level and radiated power level. Figure 7b. Sound reduction index measured ( ) or computed ( ). 7

8 CONCLUSIONS The use of numerical schemes to complete traditional laboratory measurements of impact noise and sound reduction indices can be achieved with reasonable cost by means of a commercial finite code completed with a decoupled modal approach for both source and receiver rooms. Such approaches have been undertaken by other authors [6] and need a preliminary calibration process in order, first to qualify the measuring conditions, principally in terms of boundary conditions and rooms description, and second to tune the material properties from mobility measurements. Such precautions are essential for low frequency recovery which are essential for the estimation of db(a) values. At present more complex bodies are being investigated, principally hollow core slabs where the proposed method will be compared against measurements prior to parametric studies and product optimisation. It must be finally stresses that numerical simulation is not developed with the hope of replacing all experimental testing but it is strongly believed by the authors that it can form a useful tool whenever relative effects are sought such as needed for product optimisation. REFERENCES [1] L. Gagliardini, J. Roland, J.L. Guyader. Journal of Sound and Vibration 145, The use of a functional basis to calculate acoustic transmission between rooms (1991). [2] P. Jean and J.-F. Rondeau A model for the calculation of noise transmission inside dwellings. Application to aircraft noise. Applied Acoustics 65, (2004). [3] P. Jean Coupling integral and geometrical representations for vibro-acoustical problems. Journal of Sound and Vibration, 224, (1999) [4] P. Jean, J. Roland. Application of the Green Ray Integral Method (GRIM) to sound transmission problems Building Acoustics, 8, (2001) [5] P. Jean and J.-F. Rondeau. A simple decoupled modal calculation of sound transmission between volumes. Acta Acustica, 88, , (2002) [6] J. Brunskop and P. Davidson. Sound transmission of structures; a finite element approach with simplified room description. Submitted to Acta Acustica. 8