Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates

An examination of the accuracy and convergence behaviors of polynomial basis function differential quadrature (PDQ) and harmonic basis function differential quadrature (HDQ) for free vibration analysis of variable thickness thick skew plates will be carried out. The plate governing equations are based on the first-order shear deformation theory including the effects of rotary inertia. Arbitrary thickness variations will be assumed yielding a system of equations with nonlinear spatial dependent coefficients. Differential quadrature (DQ) analogs of the equations are obtained by transforming the governing equations and boundary conditions into the computational domains. Studies are carried out to examine the effects of different types of boundary conditions, skew angles, and thickness-to-length ratios for thin as well as moderately thick plates. The thickness is simulated by bilinear or nonlinear functions. The results are compared with those of other numerical schemes. It is concluded that both PDQ and HDQ yield accurate solutions for natural frequencies both at low and high modes of vibration. Some new results are presented for skew plates with bilinearly varying thickness and for different sets of boundary conditions, which can be used as benchmarks for future works.