Bem analysis of free vibration problems using polynomial particular integrals

Abstract

The development of a boundary element method for free vibration analysis using particular solutions is discussed. The formulation presented is based on treating the forcing function, in the governing differential equation, as an initially unknown distributed body force within the domain. The volume integral due to this body force is then eliminated by approximating the inertia force by global interpolation and polynomial function representations and finding particular solutions for the governing, inhomogeneous equations. The resulting non-symmetric system matrix is solved by using a modified Arnoldi's algorithm that takes advantage of the special structure of the substructured boundary element method. The techniques described here are embedded in a computer program GPBEST, and the numerical examples arc solved by using this computer code.