Abstract
This paper communicates the first comprehensive analytical study of the title problem. The Ritz method with admissible functions in the form of Legendre polynomials is used, and is shown to provide rapid convergence and highly economic eigensolutions for a given problem. The robustness of the method is demonstrated, and proof is given of its validity at extreme skew angles. Chladni figures are presented for the first six modes of plates with three different aspect ratios and six different skew angles, making a total of 108 cases. (Additional results can be inferred for two more plate aspect ratios, thus raising the total number of Chladni figures to 180.) Outstanding agreement is obtained between all the analytically derived nodal patterns from this work and the experimental work of other investigators. The dependence of frequency on the skew angle, the aspect ratio and the Poisson ratio is also investigated, and extensive results are presented in diagrammatic and graphical format.
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