Analysis of acoustic wave propagation in composite laminates via a spectral element method

Abstract

AbstractThe analysis of the acoustic or elastic wave propagation phenomena in the time‐domain is computationally expensive. An often‐cited rule of thumb is to use at least ten nodes per wavelength if using quadratic shape functions, and even more nodes are necessary in order to achieve highly accurate numerical results. For large‐scale problems, this results in a large system of linear algebraic equations, which must be solved for several thousands of time‐steps. This requires a vast amount of the computing time. In this paper, a spectral element method (SEM), which is a variant of the finite element method (FEM) by using high‐order shape functions with non‐equidistant node distributions, is presented in order to investigate the acoustic wave propagation problems taking the fluid‐structure interaction into account with a minimum of required degrees of freedoms (DOFs). Hence, the computing time for solving the system of linear algebraic equations is reduced while maintaining a high accuracy. The element matrices are computed using the Lobatto quadrature method, which results in a diagonal element mass matrix. For fluid‐structure interaction problems in acoustics, a non‐symmetric sparse mass matrix is obtained. By using an explicit time‐integration scheme only the mass matrix becomes the coefficient matrix of the linear system and, due to its high sparsity, the solution process is very efficient. In this work, the SEM is implemented and applied for the analysis of the transient behavior of the laminated composite structures excited by acoustic waves. Numerical examples are presented and discussed to show the efficiency of the SEM in the time‐domain for applications in acoustic wave propagation problems considering the fluid‐structure interaction.