Free vibration analysis of rectangular plates with variable thickness

An approximate method for analyzing the free vibration of thin and moderately thick rectangular plates with arbitrary variable thickness is proposed. The approximate method is based on the Green function of a 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. The discrete form solution is obtained at each discrete point equally distributed on the plate. It is shown that the numerical solution for the Green function has good convergency and accuracy. By applying the Green function, the free vibration problem of the plate is translated into the eigenvalue problem of the matrix. The convergency and accuracy of the numerical solutions for the natural frequency parameter calculated by the proposed method are investigated, and the frequency parameters and their modes of free vibration are shown for some rectangular plates. (C) 1998 Academic Press.