Nonlinear Multi-modal Structural/acoustic Interaction between a Composite Plate Vibration and the Induced Pressure

摘要

This study aims to develop a mixed finite element and classical formulation for the nonlinear multimodal structural acoustic interaction of a composite plate backed by a three dimensional cavity. The formulation is developed by adopting the nonlinear finite element modal reduction method for the two-dimensional plate and the classical solution for the three-dimensional acoustic cavity, respectively. The main advantages of the adopted approach are as follows. 1) There is no need to update the nonlinear matrices; 2) the sizes of the nonlinear matrices can be reduced drastically; and 3) the acoustic pressure that acts on the plate can be obtained from the classical solution of the three-dimensional wave equation (i.e., no boundary element is required). Hence, the proposed approach can avoid the numerical error induced from the coupling between the two dimensional finite elements and three dimensional boundary elements. The frequency ratios for the fundamental modes of the structural-acoustic system at various plate vibration amplitudes, the contribution of each linear mode to the overall plate vibration, and the effect of air cavity depth on the frequency ratios are also studied.