Computation of the time-history response of dynamic problems using the boundary element method and modal techniques

Abstract

The boundary element method in combination with modal techniques is used to calculate the response of transient excited structures in the time domain numerically. If the system matrices of a structure are evaluated with a fundamental solution in the frequency domain these matrices become functions of frequency which normally cannot be expressed analytically. The associated eigenvalue problem therefore is non-linear and difficult to solve. For simplification a series expansion formula for the fundamental solution is used in different frequency ranges. Then the eigenvalue problem can be linearized and solved by direct or iterative methods. By using the orthogonal properties of the eigenfunctions, the normal modes of the dynamic problem can be uncoupled as is well known in vibration analysis. That way the transient response of a dynamic excited system in the time domain can be determined without difficulties. Displacements and stresses at different points of the structure are the result. Difficulties in the formulation of time-dependent problems using the boundary element method can be avoided. There is no problem in considering modal damping factors, for general damping characteristics the associated fundamental solutions have to be found. Several examples are studied in the paper to illustrate how the new method can be applied. Copyright © 1999 John Wiley & Sons, Ltd.