Analytical derivations for one-dimensional eigenproblems using dual boundary element method and multiple reciprocity method

Abstract

In this paper, MRM (multiple reciprocity method) and DBEM (dual boundary element method) are combined to solve one-dimensional eigenproblems. It is found that the hypersingular equation (LM method) for MRM provides an additional constraint to determine the eigenfunctions in case of failure using the singular equation (UT) method only. Also, augmented eigenvalues can be deleted by employing dual equations. The hypersingular equation of DBEM (LM equation) plays an important role in determining the eigenvalues and eigenmodes. Four numerical examples are given to verify the validity of the present formulation.