Based on the energy method, the dynamic model of an arbitrary triangular plate with elastically restrained boundary conditions is constructed. Regardless of the boundary conditions, each of the displacement components of the plate are expanded invariantly as an improve Fourier series, which is composed of a standard Fourier series and closed-form auxiliary function. All the expansion coefficients are treated as the generalized coordinate and determined using the Rayleigh-Ritz method. The accuracy of the proposed improved Fourier series solutions is validated by finite element method (FEM) results, and excellent accuracy is demonstrated. Investigation on vibration of the triangular-triangular plate combination structure shows the extensive applicability of present method for more complex plate.
