Abstract
Free in-plane vibration of rectangular plates undergoing plane stress deformation is investigated through Ritz discretization of the Rayleigh quotient. Of particular interest is the manner in which the plate's natural frequencies and coupled longitudinal–lateral vibration modes evolve as its length-to-width aspect ratio is varied. Vibration modes are grouped into families or classes based on (1) common asymptotic behavior of natural frequency loci with increasing aspect ratio, (2) reflective symmetry of the displacement field about the plate's centerline, and (3) the presence of nodal points on or off the plate's centerline. The applicability of the traditional strength-of-materials bending and longitudinal vibration models for predicting the lower in-plane modes is also discussed, and the range of aspect ratios for which those simpler models provide acceptable accuracy is quantified. In-plane twisting and higher order modes having nodal points off the plate's centerline are not predicted by those traditional theories, and these are also discussed in several parameter studies.
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