An efficient scaled boundary finite element method for transient vibro-acoustic analysis of plates and shells

Abstract

This paper develops an efficient modeling technique based on the scaled boundary finite element method (SBFEM) for transient vibro-acoustic analysis of plates and shells. For simulating the structural dynamic behaviors, a novel shell formulation based on three-dimensional linear elastic theory is presented where only the bottom surface of the shell is discretized with finite elements while the solution along the thickness is expressed analytically as a Padé expansion. A new scaling idea named normal scaling strategy is introduced to enable the formulation to be applicable to geometrically arbitrary shells. The acoustic field is assumed to be infinite and first truncated by a spherical surface into an interior finite region and an exterior unbounded region. The former is further split into a number of bounded subdomains which are analyzed by the improved continued-fraction approach while the latter is simulated by the improved high-order doubly-asymptotic open boundary. These formulations are consistently constructed within the SBFEM framework. The structural and acoustic domains are discretized independently and a simple and reliable coupling scheme is devised. The Bathe time integration method is employed to perform the transient analysis. Numerical examples are presented to demonstrate the validity and performance of the proposed methodology.