Infinite systems for a biharmonic problem in a rectangle

Abstract

This paper addresses a general analytical method based upon Mellin's transforms technique of investigating asymptotic behaviour of infinite systems of linear algebraic equations occurring in some basic two–dimensional biharmonic problems in a rectangular domain. The object of this paper is to prove the advantages of the asymptotic analysis when studying the concrete problems of an equilibrium of an elastic rectangle, creeping flow of viscous fluid set up in a rectangular cavity by tangential velocities applied along its walls, and bending of a clamped thin rectangular plate by a normal load at one surface. The method is illustrated by several numerical examples; the rapidity of convergence and the accuracy of results are studied.