Analysis of Simply Supported Rectangular Kirchhoff Plates by the Finite Fourier Sine Transform Method

Abstract

In this work, the boundary value problem of simply supported rectangular Kirchhoff plates subjected to applied transverse loads is solved by the method of finite Fourier sine transform. The finite Fourier sine transform method was adopted as the analytical research tool due to the Dirchlet boundary conditions of the plate problem. Application of the finite Fourier sine transform to the fourth order governing partial differential equation of the Kirchhoff plate problem and the associated boundary conditions simplified the problem to an algebraic problem in the transform domain. The solution is obtained in the plate domain by inversion. The problem was solved for general distributed load p(x, y), point load applied at an arbitrary point on the plate, uniformly distributed patch load over the plate region x0 x  x1, y0 y  y1, and uniformly distributed load over the entire plate. The finite Fourier sine transform solutions obtained in each case were found to be identical solutions obtained with the Navier’s double trigonometrical series method as presented in Timoshenko and Woinowsky-Krieger. The finite Fourier sine transform method was found to yield exact solutions to the classical thin plate flexure problem for simply supported edges.