Free Vibration Analysis of Anisotropic Right Triangular Plates

概要

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An approximate method is used for analyzing the free vibration problem of isotropic and anisotropic right triangular plates with various aspect-ratios and variable thickness.In this paper, a right triangular plate is considered as a kind of equivalent rectangular plate with point supports. Therefore, the free vibration characteristics of any triangular plate can be obtained by analyzing the equivalent rectangular plate. The differential equations of the equivalent rectangular plate with point supports are established based on the first-order shear deformation theory. By transforming the differential equations into integral equations and using numerical integration, the solutions of the partial differential equation can be obtained in discrete form. The Green function, which is the discrete solution for the deflection, is introduced to obtain the characteristic equation of the free vibration. Frequencies and mode shapes are shown for some triangular plates with various aspect-ratio and variable thickness. The effects of boundary conditions and the fibre orientation on the frequency parameters are considered. The efficiency and accuracy of the numerical solutions by the present method are investigated.