Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions

In this study, free vibration analysis of moderately thick symmetrically laminated general trapezoidal plates with various combinations of boundary conditions is investigated. The governing partial differential equations and boundary conditions for trapezoidal plate are obtained using first order shear deformation theory (FSDT) together with proper transformation from Cartesian system into trapezoidal coordinates. Generalized differential quadrature (GDQ) method is then employed to obtain solutions for the governing equations. Results of the GDQ method are compared and validated with available results in the literature which show accuracy and fast rate of convergence of the method. Effect of various parameters such as geometry, thickness, boundary condition and lay-up configuration on the natural frequency of trapezoidal and skew plates is investigated through several examples. It is also shown that the method can be used for analysis of triangular plates as special case of trapezoidal geometry with the same performance and convergence.