A condensed transfer function method as a tool for solving vibroacoustic problems

Abstract

Substructuring approaches are nowadays widely used to predict numerically the vibroacoustic behavior of complex mechanical systems. Some of these methods are based on admittance or mobility frequency transfer functions at the coupling interfaces. They have already been used intensively to couple subsystems linked by point contacts and enable to solve problems at higher frequency while saving computation costs. In the case of subsystems coupled along lines, a Condensed Transfer Function method is developed in the present paper. The admittances on the coupling line are condensed in order to reduce the number of coupling forces evaluated. Three variants are presented, where the transfer functions are condensed using three different functions. After describing the principle of the CTF method, simple structures will be given as test cases for validation.

Keywords

Vibroacoustic sub-structuring admittance numerical analysis

Get full access to this article

View all access options for this article.

References

Hurty

. Dynamic analysis of structural systems using component modes. AIAA J 1965; 3: 678–685.

Bampton

MCC

Craig

Jr . Coupling of substructures for dynamic analyses. AIAA J 1968; 6: 1313–1319.

Gladwell

GML

. Branch mode analysis of vibrating systems. J Sound Vib 1964; 1: 41–59.

MacNeal

. A hybrid method of component mode synthesis. Comput Struct 1971; 1: 581–601.

Tournour

Atalla

Chiello

. Validation, performance, convergence and application of free interface component mode synthesis. Comput Struct 2001; 79: 1861–1876.

O’Hara

. Mechanical impedance and mobility concepts. J Acoust Soc Am 1967; 41: 1180–1184.

Hixson

. Mechanical impedance. Shock and vibration handbook. Mc Graw Hill Book Co., New York 1976, pp. 10–1.

Petersson

Plunt

. On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure, part i: theoretical background and basic experimental studies. J Sound Vib 1982; 82: 517–529.

Petersson

Plunt

. On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure, part ii: procedures for the estimation of mobilities. J Sound Vib 1982; 82: 531–540.

10.

Ouisse

Maxit

Cacciolati

. Patch transfer functions as a tool to couple linear acoustic problems. J Vib Acoust 2005; 127: 458–466.

11.

Chazot

J-D

Guyader

J-L

. Prediction of transmission loss of double panels with a patch-mobility method. J Acoust Soc Am 2007; 121: 267–278.

12.

Aucejo

Maxit

Totaro

. Convergence acceleration using the residual shape technique when solving structure–acoustic coupling with the patch transfer functions method. Comput Struct 2010; 88: 728–736.

13.

Maxit

Aucejo

Guyader

J-L

. Improving the patch transfer function approach for fluid-structure modelling in heavy fluid. J Vib Acoust 2012; 134: 051011–051011.

14.

Veronesi G, Albert C, Nijman E, et al. Patch transfer function approach for analysis of coupled vibro-acoustic problems involving porous materials. SAE technical paper no. 2014-01-2092, 2014.

15.

Boucher M, Pluymers B and Desmet W. Coupled (vibro)-acoustic problems using geometrical acoustics and patch transfer functions. In: ICSV22, Florence, Italy, 2015.

16.

Meyer V, Maxit L, Guyader J-L, et al. A condensed transfer function method as a tool for solving vibroacoustic problems. J Mech Eng Sci 2016; 230: 928–938.

17.

Firestone

. The mobility method of computing the vibration of linear mechanical and acoustical systems: mechanical-electrical analogies. J Appl Phys 1938; 9: 373–387.

18.

Rubin

. Mechanical immittance-and transmission-matrix concepts. J Acoust Soc Am 1967; 41: 1171–1179.

19.

Fahy

Gardonio

. Sound and structural vibration: radiation, transmission and response, Cambridge: Academic press, 2007.

20.

Mindlin

. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics 1951; 18: 31–38.

21.

Rubin

. Improved component-mode representation for structural dynamic analysis. AIAA J 1975; 13: 995–1006.

22.

Fornberg

. A practical guide to pseudospectral methods 1998; vol. 1.. Cambridge: Cambridge University press.

23.

Nelson

Yoon

S-H

. Estimation of acoustic source strength by inverse methods: part I, conditioning of the inverse problem. J Sound Vib 2000; 233: 639–664.

24.

Maxit

Ginoux

J-M

. Prediction of the vibro-acoustic behavior of a submerged shell non periodically stiffened by internal frames. J Acoust Soc Am 2010; 128: 137–151.