Frequency splitting of parametric excitation vibration of rotating periodic structures

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (21) : 253-262.

GAO Peng1, WEI Zhenhang1, WANG Shiyu1,2,3

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Abstract

Rotationally periodic structures are widely used in mechanical engineering fields, where parametric vibration is a common form of vibration. A time-varying partial differential elastic dynamic model is proposed by using the time-spatial symmetry of the periodic structures. The mathematical model of ordinary differential multi-freedom parametric vibration is obtained by using Galerkin method and modal orthogonality, based on which the vibration behaviors of the rotationally periodic structures induced by the time-varying stiffness excitation are examined. In order to study the frequency splitting of the parametric vibration, the modulation feedback principle is employed to analyze the dynamic response for different feedback types, and the relationships between parameter combinations, including the time-varying stiffness number and wavenumber, and frequency splitting are revealed. In addition, the excitation frequencies for corresponding to the parametric instability for different feedback types are predicted. Finally, the parametric instability regions and the response frequencies for different feedback types are verified by the Floquét theory and the Runge-Kutta method, respectively.

Key words

rotationally periodic structures / parametric vibrations / time-varying stiffness / modulation feedback / frequency splitting

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GAO Peng1, WEI Zhenhang1, WANG Shiyu1, 2, 3. Frequency splitting of parametric excitation vibration of rotating periodic structures[J]. Journal of Vibration and Shock, 2024, 43(21): 253-262

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