General time-dependent analysis with the frequency-domain hybrid boundary element method

Abstract

The paper presents an attempt to consolidate a formulation for the general analysis of the dynamic response of elastic systems. Based on the mode-superposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second order differential equations, which may be integrated by means of standard procedures. The first motivation for these theoretical developments is the hybrid boundary element method, a generalization of T. H. H. Pian's previous achievements for finite elements which, requiring only boundary integrals, yields a stiffness matrix for arbitrary domain shapes and any number of degrees of freedom. The method is also an extension of a formulation introduced by J. S. Przemieniecki, for the free vibration analysis of bar and beam elements based on a power series of frequencies, that handles constrained and unconstrained structures, non-homogeneous initial conditions given as nodal values as well as prescribed domain fields (including rigid body movement), forced time-dependent displacements, and general domain forces (other than inertial forces).