Free Vibration of Orthotropic Cantilever Plates with Point Supports

The method of superposition is used to achieve a free-vibration analysis of orthotropic cantilever plates resting on point supports. In the initial development of the analysis it is assumed that the supports are symmetrically distributed about the plate centerline running normal to the clamped edge. Delineation is then made between modes that are symmetric, or antisymmetric, with respect to this centerline. It is shown how a small modification to the theory permits the obtaining of solutions for the case where supports are located at the plate outer corners. Modifications required to handle the case where support points do not have a symmetric distribution are also described. Free-vibration eigenvalues are provided for square plates with a pair of symmetrically distributed support points and various combinations of orthotropic property ratios. The problem under study is one that may occur, for example, in cantilevered mezzanine floors in buildings. It is expected that the tabulated eigenvalues will also provide useful reference points for other researchers. This appears to be the first analytical-type solution developed for this realistic industrial problem.