Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields

doi:10.1007/s10483-022-2904-9

Abstract

Abstract: Composite cylindrical shells, as key components, are widely employed in large rotating machines. However, due to the frequency bifurcations and dense frequency spectra caused by rotation, the nonlinear vibration usually has the behavior of complex multiple internal resonances. In addition, the varying temperature fields make the responses of the system further difficult to obtain. Therefore, the multiple internal resonances of composite cylindrical shells with porosities induced by rotation with varying temperature fields are studied in this paper. Three different types of the temperature fields, the Coriolis forces, and the centrifugal force are considered here. The Hamilton principle and the modified Donnell nonlinear shell theory are used to obtain the equilibrium equations of the system, which are transformed into the ordinary differential equations (ODEs) by the multi-mode Galerkin technique. Thereafter, the pseudo-arclength continuation method, which can identify the regions of instability, is introduced to obtain the numerical results. The detailed parametric analysis of the rotating composite shells is performed. Multiple internal resonances caused by the interaction between backward and forward wave modes and the energy transfer phenomenon are detected. Besides, the nonlinear amplitude-frequency response curves are different under different temperature fields.

Key words: multiple internal resonances, rotation effect, nonlinear temperature variation, multi-mode Galerkin technique, pseudo-arclength continuation method, coupled effect

2010 MSC Number:

74H45

Yunfei LIU, Jun WANG, Jiaxin HU, Zhaoye QIN, Fulei CHU. Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1543-1554.

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