Characterizing the vibration of an elastically point supported rectangular plate using eigensensitivity analysis

Abstract

Normalized frequencies are computed for a rectangular, isotropic plate resting on elastic supports. The normalized frequencies are determined using eigensensitivity analysis, which approximates the eigenparameters in a Mauclarin series, yielding an approximate closed-form expression. One benefit of the approximate closed-form expression is its computational efficiency and yet another is its application of re-analysis. Accuracy of the approximate expression is assessed by comparing results with the widely used Rayleigh–Ritz method using orthogonal polynomials and beam shape functions in both approaches. Consideration for a variety of edge conditions is given through a combination of simply supported, clamped and free boundary conditions. Results indicate that the accuracy of higher frequencies computed by the sensitivity approach is highly dependent upon choice of basis function.