An efficient SBFEM-based approach for transient exterior vibro-acoustic analysis of power-law functionally graded shells

Abstract

An efficient approach for transient exterior vibro-acoustic analysis of power-law functionally graded (FG) shells is developed using the scaled boundary finite element method. In the structural formulation, a shell element is treated as a three-dimensional continuum and its middle surface is represented with a quadrilateral spectral element. Along the thickness, the middle surface is scaled and the displacements are approximated using a quadratic Lagrange interpolation. The assumed natural strain method is applied to treat numerical locking and the integral along the thickness is performed analytically. In the acoustic formulation, velocity potential acts as the basic unknown. An infinite fluid is truncated by a spherical surface. The exterior field is simulated through the improved doubly asymptotic open boundary while the interior region is split into subdomains with their impedance evaluated by the improved continued-fraction method. The structure and fluid are discretized independently. The collocation procedure is utilized to perform the data transfer across the nonconforming interface. A high-order implicit time integration scheme is applied to solve the coupled system of equations. Numerical examples demonstrate that the proposed approach is stable, accurate and highly efficient. The effects of the geometric and material parameters on the vibro-acoustic behaviors of FG shells are systematically studied.