Free in-plane vibration analysis of rectangular plates with elastic support normal to the boundaries

The superposition method is employed to analyze the effects of elastic edge support on the in-plane free vibration frequencies and mode shapes of rectangular plates. The elastic edge support is considered to be uniformly distributed along the plate edges and symmetrically distributed with respect to the plate central axes. In addition, exact solutions are also obtained for a family of simply supported plates whose eigenvalues constitute upper limits for those of the elastically supported plates. An array of highly accurate eigenvalues for the completely free plate is also computed in order to provide lower limit eigenvalues. Eigenvalues are computed and tabulated for elastically supported plates of various aspect ratios and dimensionless elastic support coefficients.