Vibrations of cantilevered skewed trapezoidal and triangular plates with corner stress singularities

Abstract

In a recent companion paper, the efficacy of admissible corner functions used in conjunction with mathematically complete polynomials has been demonstrated in an exhaustive amount of Ritz convergence tables apropos to cantilevered skew parallelogram plates. The present work extends the method to include skewed plates having trapezoidal and triangular planforms, and is the first known vibrational study encompassing the effect of bending stress singularities at the reentrant corner of such plates. Extensive and accurate nondimensional frequency tables and graphical charts are presented for a series of trapezoidal plates showing the effect of aspect ratio, chord ratio and skew angle. The importance of using admissible corner functions in skew trapezoidal plate vibrations is found to increase as the skew angle increases and as the aspect ratio and chord ratio decreases. Some theoretical and experimental data heretofore published for delta and skewed triangular cantilevered plates are compared with results obtained using the present method. No previous theoretical results for skewed trapezoidal cantilevered plates are known to exist.