A unified scaled boundary finite element method for transient two-dimensional vibro-acoustic analysis of plate-like structures

This paper develops a unified and efficient simulation technique based on the scaled boundary finite element method (SBFEM) for transient structural-acoustic problems in two dimensions. The structural component can be an assembly of thin to moderately thick unidirectional plates. Each of them is treated as a plane strain problem and the principle of virtual work involving the inertial contribution is applied to derive the scaled boundary finite element equation. Only the longitudinal dimension is discretized with line elements and the solution through the thickness is expressed analytically as a Padé expansion. A variable transformation process together with certain structural assumptions leads to the static stiffness and mass matrices. The acoustic field can be a semi-infinite region, which is first divided by an artificial boundary into a near field and an exterior domain. The former is analyzed using the improved continued-fraction approach and the latter is modeled by the improved doubly-asymptotic open boundary. These formulations are based on velocity potential and established consistently in the SBFEM framework. High-order spectral elements are employed for both the structural and acoustic domains, to which independent discretization schemes are applied. Numerical examples are presented to demonstrate the excellent performances of the proposed technique.