New method for predicting the free vibration characteristics of composite laminates based on generalized cell and spectral-Tchebychev methods

This paper presents a new method for analyzing the free vibration characteristics of composite laminates under arbitrary boundary conditions by integrating the generalized method of cells (GMC) and the Two-Dimensional Spectral-Tchebychev (2D-ST) method. First, a meso-macro correlation matrix is constructed based on the GMC, and the macroscopic performance parameters of the composite laminates are predicted. Then, virtual boundary springs are introduced to simulate the arbitrary boundary conditions, and the energy equation of the laminate is derived based on the first-order shear deformation theory (FSDT) and Hamilton's principle. Furthermore, an approximate displacement function of the laminate is derived by using the 2D-ST Tchebychev polynomials, and the Gauss-Lobatto points are selected for meshless discretization of the structure to obtain the discretized characteristic equation, which is solved to obtain the free vibration frequency of the laminate. Based on Matlab programming, the free vibration frequencies of the laminate under different conditions are calculated, and the convergence, accuracy and computational efficiency of the calculation method are discussed, and the effects of boundary conditions, stacking angle, geometrical parameters, and material parameters on the free vibration frequencies of the laminate are analyzed. The numerical results show that the method has the advantages of fast convergence, high accuracy and high efficiency, and the method can be convenient and fast for parametric studies. Highlights: The free vibration characteristics of composite laminates are studied. Combining generalized cell method with spectral-Tchebychev method. The method has the characteristics of fast convergence, high accuracy and high efficiency. A parametric study is conducted on the free vibration of laminated panels.