A Method for Solving Problems of Vibration, Deflection and Buckling of Rectangular Plates with Clamped or Supported Edges

Abstract

The problem of a rectangular plate with clamped or supported edges is treated in this paper by means of the undetermined multiplier method in the calculus of variations. The amplitude or the displacement of the plate is expressed by the double Fourier series, then by the orthogonality of the trigonometric functions, numerical calculations become very simple and many types of problems-natural and forced vibrations, statical deflections, bucklings and others-can be easily solved through the unifled and systematic procedures of calculations.