Coupled Analysis of Acoustic Space and Thin-Plate Vibrations by a Lumped-Mass Model Using Raviart–Thomas Elements

Abstract

Suppression of noise and vibration in machine products is an important problem, and many methods have been studied. In particular, structural–acoustic coupled effects due to the weight reduction of machines cannot be ignored. In structural–acoustic coupled analysis, the finite-element method in which the acoustic space is described by sound pressure and the structure is described by displacement is often used. However, the eigenvalue analysis in that method takes a great deal of computational time because the mass and stiffness matrices are asymmetric. Instead, in this paper, we propose an efficient coupled analysis method for a three-dimensional acoustic space and a two-dimensional thin plate using a lumped-mass model. The proposed modeling method is derived systematically using Raviart–Thomas elements. In addition, we propose a coordinate transformation method that accelerates the calculations by reducing the number of degrees of freedom (DOF). In this way, a symmetric eigenvalue problem with no extra DOF is derived. The effectiveness of the proposed method is confirmed by numerical calculations. This analysis method is particularly effective for systems in which the acoustic space contributes to the majority of the DOF, since the acoustic space is sparse owing to the adoption of edge elements.