A coupled finite element/equivalent source formulation for transient structural-acoustic problems

Abstract

Recent research suggests that instability problems that occur in the time domain boundary element formulations are manifestations of nonuniqueness difficulties, and that remedies similar to those used in frequency domain formulations can address the difficulties and improve solution stability. For frequency domain equivalent source formulations, the difficulties can be addressed by combining simple and dipole sources together to form “tripole sources”. The basic goals of the current research are to develop an analogous equivalent source formulation for transient acoustic boundary value problems and to combine it with structural finite element analyses to solve transient coupled structural-acoustic problems. A brief description of the equivalent source formulation is given along with several validation cases for acoustic boundary value problems, including one with a closed boundary surface where nonexistence difficulties should occur. The formulation requires convolution summations, which are independent of each other and a brief discussion is given of how the computations can be parallelized. A brief description is also given of the coupled finite element/equivalent source formulation for transient structural-acoustic boundary value problems. Several examples are given to validate the formulation and to demonstrate that the tripole source formulation for the equivalent sources is more stable than the simple source version.