Free vibration analysis of moderately thick composite materials arbitrary triangular plates under multi-points support boundary conditions

Abstract

ABSTRACT In this research, free vibration characteristics of moderately thick composite materials arbitrary triangular plates under multi-points support boundary conditions are analyzed by an improved Fourier series method. After constructing the model, the triangular region is mapped to the unit square region. The boundary conditions are simulated by five types of artificial virtual springs. In the study, in order to remove the jump or disconnect phenomenon on the boundary, all allowable displacement functions are expressed by the improved Fourier series. Combined with the chain derivative rule, energy equations are established based on the first-order shear deformation theory. Finally, the Rayleigh-Ritz technique is adopted to solve unknown coefficients. The most innovative point of the paper is to pay attention to the special multi-points support boundary conditions and combine it with the coordinate transformation of any shape triangle. The purpose of this study is to simulate actual engineering structures more accurately by studying the free vibration of triangular structure under multi-points support. It is proved that the method has higher accuracy by comparing with the finite elemet method. This method can conveniently receive the free vibration characteristics of moderately thick composite materials arbitrary triangular plates under the multi-points support boundary conditions. In addition, according to the parametric study, geometrical parameters, material properties and external boundary conditions of the structure can all affect its free vibration characteristics, which can be used as a reference for the research in this field.