Z Zagadnień Wartości Własnych Płyt Pierścieniowych

In this paper is solved the problem of the free vibration of uniform isotropic ring plate having a discontinuously varying thickness along the radii. It was assumed that the plate is resting on a two-parameter elastic base of the Winkler or Leontiev-Vlasov type. Moreover, it is assumed that the plate is under the load of forces acting in its plane. Solution of the problem is obtained by of the method of transfer matrix. The plate means is divided into a finite number of concentric rings. Assuming that the thickness of each ring is constant the solution of the differentiel equation is obtained using the development of the surface of bending into an infinite single trigonometrical series. Next, the general integral of the equation is determined by seeking the solution infinite power series. On the basis of the solution obtained for in the form of an are formed (formula 2.30). Subsequently, from the elements each ring, the transfer matrices R of this matrix, depending on the boundary conditions on the edges of the plate, the equations of frequency are built up. The results of numerical calculations for two numerical examples are given.