FREE-VIBRATION OF ORTHOTROPIC CANTILEVER PLATES WITH POINT SUPPORTS

The method of superposition is used to achieve a free-vibration analys is of orthotropic cantilever plates resting on point supports. In the initial development of the analysis it is assumed that the supports ar e symmetrically distributed about the plate centerline running normal to the clamped edge. Delineation is then made between modes that are s ymmetric, or antisymmetric, with respect to this centerline. It is sho wn how a small modification to the theory permits the obtaining of sol utions for the case where supports are located at the plate outer corn ers. 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 symmetricall y distributed support points and various combinations of orthotropic p roperty ratios. The problem under study is one that may occur, for exa mple, in cantilevered mezzanine floors in buildings. It is expected th at the tabulated eigenvalues will also provide useful reference points for other researchers. This appears to be the first analytical-type s olution developed for this realistic industrial problem.