The natural vibration of a conical shell with an annular end plate

In this paper, natural frequencies and mode shapes for a conical shell with an annular end plate or a round end plate are investigated in detail by combining the vibration theory with the transfer matrix method. The governing equations of vibration for this structure are expressed in terms of a matrix differential equation, and a novel recurrence formula method that can close in on analytical solution of transfer matrix is presented. Once the transfer matrix of single component has been determined, and the product of each component matrix and the joining matrix can obtain entire structure matrix. The frequency equations and mode shape functions are represented in terms of the elements of the structural transfer matrices. The 3D finite element numerical simulations have verified the present formulas of natural frequencies and mode shapes. The conclusions show that the transfer matrix method can accurately obtain natural vibration characteristics of the conical shell with an annular end plate.