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Frequency analysis of rotating truncated conical shells using the Haar wavelet method. (English) Zbl 1480.70008

Summary: 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.

MSC:

70E15 Free motion of a rigid body
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65T60 Numerical methods for wavelets
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