Accurate natural frequencies of skewed cantilevered thin plates are determined using the Ritz method. The present work is the first known vibrational study of the effects of stress singularities at the reentrant corner of skewed plates. In conjunction with classical thin plate theory, the Ritz trial space of assumed transverse displacement functions consists of algebraic polynomials, which are mathematically complete, and corner functions, which account for the singular behaviour of bending stresses at the reentrant corner. The corner functions were derived approximately four decades ago to study the nature of the stress singularities which occur at sharp interior corners or crack tips of typical plane elasticity and plate bending problems. Accurate non‐dimensional frequencies are calculated for thin plates having various side ratios and arbitrary degrees of skewness. Detailed numerical studies show that augmenting the Ritz trial space of polynomials with corner functions, having a co‐ordinate origin at the reentrant corner, enhances the convergence of the upper‐bound frequencies. The importance of using corner functions in skew plate vibrations is found to increase as the skew angle increases and as the side ratio decreases. Results obtained using the present method are compared with those obtained by other investigators using both theoretical and experimental methods.
|Number of pages||16|
|Journal||International Journal for Numerical Methods in Engineering|
|State||Published - Aug 15 1992|