An Orthogonality relation for a class of problems with high-order boundary conditions; Applications in sound-structure interaction

Abstract

A new orthogonality relation, involving eigenfunctions and their derivatives, for the general class of problems involving a scalar wave equation and high-order boundary conditions is presented. It discusses the procedure for incorporating the necessary edge conditions. Via two specific examples from structural acoustics, both of which have exact solutions obtainable by other techniques, it is shown that the orthogonality relations allows mode matching to follow through in the same manner as for simpler boundary conditions.