Free vibration of shear-deformable general triangular plates

An analysis of free vibration of shear-deformable general triangular plates with arbitrary combinations of boundary conditions is presented. The Reissner-Mindlin plate theory is used to incorporate shear deformation effects in the analysis. The triangular plate is first mapped onto a basic square plate. The Rayleigh-Ritz method with an admissible displacement function expressed as a product of a two-dimensional simple polynomial and a basic function is then used to obtain the governing eigenvalue equation. The basic function is chosen as the product of boundary expressions of the basic square plate, each raised to an appropriate power to satisfy the various geometric boundary conditions of the actual triangular plate. Gaussian quadrature is used for numerical evaluation of stiffness and mass matrices. The natural frequencies of general triangular Mindlin plates with different combinations of free, simply supported and clamped conditions are determined. Wherever possible, the results are verified by comparison with existing published solutions. A comprehensive parametric study of natural frequencies of general triangular plates with all three edges clamped is presented graphically. No previous results are known to exist for general triangular Mindlin plates having arbitrary combinations of boundary conditions. (C) 1997 Academic Press Limited.