Improved non-dimensional dynamic influence function method for vibration analysis of arbitrarily shaped plates with simply supported edges

Abstract

An analytical method for free vibration analysis of arbitrarily shaped plates with simply supported edges is presented using the non-dimensional dynamic influence function (NDIF) method, which was introduced by the author. A major difficulty in the theoretical formulation of the proposed method is to analytically measure the values of diagonal elements of the system matrix that gives the eigenvalues and mode shapes of the plate of interest. In addition, particular attentions are given to remove the spurious eigenvalues of the plate. Various case studies show that the proposed method yields very accurate eigenvalues and mode shapes compared with other analytical and numerical methods in spite of its theoretical simplicity.