Free vibration analysis of rectangular cantilever plates with symmetrically distributed lateral point supports

Abstract This paper provides, for the first time, a long awaited analytically exact highly reliable solution to the title problem by the exploitation of Gorman's superposition techniques. Eigenvalues for a large number of plate aspect ratios are provided, as well as some modal shapes for both symmetric and antisymmetric vibration modes. The effects of point constraints on the free vibration frequencies of the cantilever plate are also briefly discussed. Although not shown, the numerical results have been rigorously tested, as discussed later in the paper.