A unified power series method for vibration analysis of composite laminate conical, cylindrical shell and annular plate

Abstract In this article, the power series method is adopted to investigate the free vibration characteristics of the composite laminated conical, cylindrical shell, and annular plate with arbitrary boundary conditions by the wave based matrix. By the first-order shear deformation shell theory, the governing equation of the composite laminated structure is established. The displacement and moment variables are transformed as the power series function form. Through the introduction of the boundary conditions and the continuous condition between the adjacent segments, the total matrix of the composite structure is established. Searching the zero locations of the total matrix determinant by the bisection method, the natural frequencies of the composite laminated structure under arbitrary boundary conditions are obtained. To further verify the correctness of the solutions by the presented method, some numerical examples are established. From the comparison of the solutions by the presented method and the results in some reported literature and experimental studies, the calculation accuracy is verified. Furthermore, the effect of the geometric parameters and material constants, such are elastic restrained spring stiffness constants, the angle between the shell surface and axis, length to the radius ratios, and modulus ratios, on the free vibration characteristics of the composite laminated structure, have been discussed. The advantage of the presented method is high calculation accuracy, simple matrix assembly, and convenient replacement of boundary conditions. Furthermore, some new numerical solutions are presented in this paper to provide the basic foundation for subsequent research.