FREE-VIBRATION ANALYSIS OF RIGHT TRIANGULAR PLATES WITH VARIABLE THICKNESS

An approximate method for analyzing the free vibration of right triangular plates with arbitrary variable thickness and various boundary conditions is proposed. In this paper, a right triangular plate is considered as a kind of rectangular plate with non-uniform thickness. Therefore, the free-vibration characteristics of any right triangular plate are obtained by analyzing the equivalent rectangular plate with non-uniform thickness. The approximate method is based on the Green function of an equivalent rectangular plate. The Green function of a rectangular plate with arbitrary variable thickness is obtained as a discrete-form solution for deflection of the plate with a concentrated load. By applying the Green function, the free-vibration problem of plate is translated into the eigenvalue problem of matrix.