Influence of corner stress singularities and nonstructural mass on the vibrations of cantilevered skewed trapezoidal plates

This work examines the combined influences of re-entrant corner stress singularities and nonstructural mass on the natural frequencies of cantilevered, skewed trapezoidal plates. Using the Ritz method in conjunction with classical thin plate theory, the vibratory transverse displacements are assumed as mathematically complete polynomials and admissible corner functions, which account for the singular bending stress behavior at the re-entrant corner. Detailed numerical studies show that the convergence of upper-bound frequencies of skewed trapezoids with nonstructural mass is enhanced when the oft-used Ritz trial space of polynomials is augmented by admissible corner functions. To close an apparent void in the plate vibration data base, accurate nondimensional frequencies are calculated for thin, isotropic trapezoidal plates (including parallelogram and triangular ones as special cases). An extensive amount of frequency data is reported which summarize the combined effects of geometrical parameters such as skew angle and chord ratio, and of dynamical system parameters such as mass ratio, and the nonstructural mass position. The results obtained by the present method are compared with those obtained by alternative theoretical approaches.