Minimum stiffness location of point support for control of fundamental natural frequency of rectangular plate by Rayleigh–Ritz method

The Rayleigh–Ritz method is employed to determine the minimum stiffness location of the elastic point support for raising the fundamental natural frequency of a rectangular plate to the second frequency of the unsupported plate, which usually is the upper limit of the first frequency for a single support. Based on the optimal design of the support position, the minimum stiffness can be obtained numerically by solving a characteristic eigenvalue sub-problem. In the Rayleigh–Ritz procedure the boundary characteristic orthogonal polynomials are used for the admissible functions. Several typical examples of plate structures with the additional point supports are analyzed in detail, and the results prove that the proposed method is very effective in the solution to the optimal design of the supports. It will be shown that elastic supports can be designed like rigid ones for the purpose of increasing the fundamental natural frequency of a rectangular plate.