THE QUESTION OF CALCULATING EIGENFREQUENCIES AND MODES OF FREE RECTANGULAR PLATES

Abstract

The problem of determining the natural frequencies and natural modes of free oscillations of the free rectangular isotropic plate is one of the difficult tasks and has both theoretical and practical importance. Mathematically, the problem is to find the eigenvalues and eigenfunctions of the free oscillations of the plate, whose decision shall be subject only to the dynamic boundary conditions. Having widespread variational methods allow for this to determine practically only the lowest natural frequencies and the corresponding own forms of free oscillations. In this connection it is interesting to Edman method, which allows for this problem is relatively easy to calculate the eigenvalues and eigenfunctions of any room. However, in the method of Edman found hidden features not examined by the author of the method. The article presents the results of a study of these issues and discuss ways to incorporate them into the numerical implementation of the method.