Frequency analysis of rotating truncated conical shells using the Haar wavelet method

Abstract

• We extend the Haar wavelet method to vibration analysis of rotating conical shells. • We simplify the solution process in this method for non-rotating shells. • Effects of different parameters on the vibration characteristics are investigated. • Critical rotating speed only occurs for the forward wave with mode n = 1. In this study, we present an analysis of the frequency characteristics of rotating truncated conical shells using the Haar wavelet method. Based on the Love first-approximation theory, the governing equations are formulated by considering the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation. The displacement field is expressed as the Haar wavelet series in the axial direction and trigonometric functions in the circumferential direction. By considering the boundary conditions, the eigenvalue equation is obtained to determine the vibration behaviors of rotating conical shells. To validate the current analysis, the results obtained by the proposed method are compared with those reported previously, where the agreement is very good. Finally, we investigate the effects of the geometrical parameters, rotation speed, and boundary conditions on the vibration characteristics of rotating conical shells and the results are presented.