The natural vibration of a symmetric cross-ply laminated composite conical-plate shell

The feasibility of using the transfer matrix method to analyze a composite laminated conical-plate shell is explored theoretically. With the vibration theory and the transfer matrix method combined, the dynamic characteristics of a symmetric cross-ply laminated conical shell with an annular plate at the top end are investigated in detail. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrixes and joining matrix are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth order Runge–Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix and the joining matrix can compose the matrix of entire structure. The frequency equations, mode shape and force vector are formulated in terms of the elements of the structural matrices. The 3D finite element numerical simulation has validated the present formulas of natural frequencies and mode shapes. The conclusions illustrate that this investigation will provide an important foundation for the advanced development of the laminated composite combination shells.