Vibration analysis of simply supported plates of general shape with internal point and line supports using the Galerkin method

A numerical technique is developed for the dynamic analysis of arbitrary quadrilateral-shaped plates with internal supports. The procedure uses the Galerkin method in conjunction with natural coordinates in order to represent general plates. The method is programmed, and several numerical examples are presented to illustrate the accuracy and validity of the method. Natural frequencies of trapezoidal, rhombic, skew, rectangular and square plates with intermediate line supports are obtained, and the results, where possible, are compared with established solutions presented in the literature.