Solution of clamped rectangular plate problems

摘要

In this brief note, we present an efficient scheme for determining very accurate solutions to the clamped rectangular plate problem. The method is based upon the classical double cosine series expansion and an exploitation of the Sherman-Morrison-Woodbury formula. If the cosine expansion involves M terms and N terms in the two plate axes directions, then the classical method for this problem involves solving a system of (MN) × (MN) equations. Our proposal reduces the problem down to a system of well-conditioned N × N equations (or M×M when M