Fundamental frequency of vibrations of a rectangular plate with a free, straight corner cut-out

Abstract

An approximate solution of the title problem is obtained by using the Ritz method. It is assumed that the edges of the rectangular plate are elastically restrianed against rotation and that translation is prevented. The displacement amplitude is approximated in terms of a polynomial co-ordinate function which identically satisfies the prescribed boundary conditions along the orthogonal edges but not along the corner cut-out. The analytical predictions are in reasonably good agreement with experimental results performed on a rigidly clamped square plate.