Three-dimensional vibrations of cantilevered right triangular plates

Abstract

The first known three-dimensional continuum vibration solutions for cantilevered right triangular plates with variable thickness are obtained using the Ritz method. Assumed displacement functions are in the form of algebraic polynomials, which satisfy the fixed face conditions exactly, and which are mathematically complete. Reasonably accurate natural frequencies are calculated for low aspect ratio, right triangular thin plates having arbitrary values of thickness taper ratios in the spanwise direction. Detailed numerical studies show that a three-dimensional analysis is essential to monitoring coupled-mode sensitivities in the variation of non-dimensional natural frequencies with increasing thickness taper ratio. Upper bound results, obtained using the present method, are compared with those obtained by other investigators using ordinary beam theories, two-dimensional finite element and finite difference procedures, and experimental methods. This unified comparison of upper and lower bound solutions is presented here with the aim of “bracketing” the exact analytical solution of the subject problem.