Vibration Analysis of Free Rectangular Plates Constrained by Translational Edge Springs

This paper aims to present comprehensive lists of accurate natural frequencies of isotropic thin free rectangular plates constrained only by translational springs distributed uniformly on the edges. Analytical and numerical approaches are employed to study the free vibration of the plates. The first approach is an extension of Ritz method, and second approach is the finite element method coded by the author. Numerical examples cover rectangular plates from totally free plate to totally simply supported on all edges. Convergence and comparison studies are made to establish accuracy of these solutions. Nine numerical examples are presented in terms of different of elastic constraints, and the lowest six frequency parameters are provided in the examples with different aspect ratios.