Nonlinear acoustic radiation induced by in-plane vibration of hyperelastic rubber-like plates subject to dynamic loads

Abstract

This work is concerned with numerical studies on nonlinear vibration and acoustic radiation behaviors of hyperelastic plates made of rubber material. Considering both the geometric and material nonlinearity of the rubber material, structural model of the hyperelastic plate is developed based on the nonlinear finite element method and the Mooney-Rivlin constitutive model. Acoustic waves in an inviscid and compressible fluid perturbed by the in-plane vibrations of the hyperelastic plate are governed by a set of first-order linearized partial differential equations. A fourth-order dispersion-relation-preserving (DRP) finite difference scheme is utilized to compute numerical solutions of the acoustic pressure responses. The structural-acoustic interface between the hyperelastic plate and exterior fluid is constructed through a robust ghost-cell sharp-interface immersed boundary method (IBM) of high numerical stability such that the compatibility conditions on the interface can be satisfied implicitly, although the structural Lagrangian meshes of the rubber plate and the fluid Eulerian grids are not matched. Several numerical examples are designed to check the effectiveness, convergence, and availability of the numerical structural-acoustic coupling model. Based on the numerical model, nonlinear vibro-acoustics response behaviors of the hyperelastic rubber plate subject to uniform dynamic loads are analyzed. Relevance between the in-plane vibrations of the plate and the spatial distribution of the acoustic pressure in exterior fluid is revealed. Effects of the excitation frequency and amplitude of the external loads on the nonlinear vibro-acoustics behaviors of the hyperelastic plate are discussed. Radiation directivity patterns of the fundamental and high-order components show significant differences, and may change dramatically against the excitation frequency and amplitude. In addition, the influences of the geometric and material nonlinearity of the hyperelastic plate on the higher-order vibro-acoustics responses are evaluated.