The effectiveness of the Galerkin method (or the Rayleigh-Ritz method) is well known due to its simplicity and its fast convergent properties when using complete set of orthogonal functions (Galerkin functions) in the vibration of rectangular plates. However, since all Galerkin functions are required to satisfy at least the essential boundary conditions, it is restricted to global analysis when the boundary conditions are given. No element matrices have been generated by the Galerkin method because the boundary conditions are still unknown. On the other hand, the convergence of the finite element method is not as good as the Galerkin method in terms of computational counts in vibration analysis. A new method is introduced to form the dynamic stiffness matrix by means of orthogonal Galerkin functions.

We demonstrate the power of the method by calculating the natural modes of a non-uniform rectangular plate of 65536x256 kinds of boundary conditions in a single program.

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