Free vibration analysis of composite conical shells using Walsh series method

Abstract

As a typical structure of underwater vehicles, the vibration characteristics of the conical shell are of great significance to the selection of structural design parameters. This paper aims at the free vibration of composite conical shells with general boundary conditions by presenting a simple yet efficient solution based on the Walsh series (WS). The theoretical model is formulated on the basis of the first-order shear deformation shell theory. Elastic boundary conditions are equivalent by introducing weight parameters at boundary positions. The governing differential equation and boundary equation are obtained directly by the Hamilton principle, and decomposed by separating variables. Then Walsh series (WS) is applied for the axial direction and the Fourier series is assumed with respect to the circumferential direction. The unknown constants generated during integration can be determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. By solving these algebraic equations, then natural frequencies and mode shapes of the composite conical shells are obtained. Compared with the existing solutions, the accuracy and reliability of the proposed method are verified. The effects of geometric and material parameters on the natural frequencies of composite conical shells are studied.