Free vibration of arbitrary-shaped laminated triangular thin plates with elastic boundary conditions

Abstract

Abstract This paper studies the free vibration of arbitrary shaped laminated triangular thin plates based on a modified Fourier series method. An arbitrary shaped triangular plate is mapped into a right-angled isosceles triangular plate with unit length by the coordinate transformation. By padding another right–angled isosceles triangular plate which is near zero thickness on the plate after transformation. The displacement functions are then generally expressed as the combinations of Fourier cosine series and supplementary functions introduced to eliminate the discontinuous or jumping phenomenon in the boundaries. The classical thin plate elasticity theory is employed to construct the energy expressions of the plate. The Rayleigh-Ritz method is used in the present method to obtain all the unknown series expansion coefficients. A number of results are presented to verify the convergence and accuracy of current solution method to laminated triangular thin plates with arbitrary shapes, different material parameters and different boundary conditions. Additionally, some new results are given as the benchmark for future research, which are based on the various boundary conditions and geometric dimensions.