Accurate frequencies and mode shapes for moderately thick, cantilevered, skew plates

Abstract

Accurate free vibration frequencies and mode shapes are presented for complete sets of moderately thick, cantilevered skew plates of triangular, trapezoidal and parallelogram shape. These accurate results are obtained by using the Ritz method applied to the Mindlin plate theory. Two sets of functions are employed simultaneously for each of the three dependent variables: transverse displacement (w) and bending rotations (phi(x) and phi(y)). One set is the widely used algebraic polynomials. The other is the set of corner functions which provide the proper stress singularities in the reentrant clamped-free corner, and accelerates the convergence of the solutions. The extensive frequencies presented are exact to the four digits shown. Corresponding mode shapes are also shown, by means of nodal patterns, most of which are novel in the published literature.