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research-article

Free vibrations and energy transfer analysis of the vibrating piezoelectric gyroscope based on the linear and nonlinear decoupling methods

[+] Author and Article Information
Wei Li

Pingleyuan 100, Chaoyang Dist, Beijing, 100124 China webbli@163.com

Xiao-Dong Yang

#100, Pingleyuan Chaoyang District Beijing, 100124 China jxdyang@163.com

Wei Zhang

Foundation Building 606, Pingleyuan 100#, Chaoyang District Beijing, 100124 China sandyzhang0@163.com

Yuan Ren

Bayi Road, Huairou Dist Beijing, 101416 China renyuan_823@aliyun.com

Tianzhi Yang

Weijin 92, Nankai Dist Tianjin, 300072 China yangtz@tju.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received August 25, 2018; final manuscript received February 26, 2019; published online xx xx, xxxx. Assoc. Editor: Miao Yu.

ASME doi:10.1115/1.4043062 History: Received August 25, 2018; Accepted February 28, 2019

Abstract

The present research is concerned with the free vibrations and energy transfer of a vibrating gyroscope, which is composed of a flexible beam with surrounded piezoelectric films in a rotating space. The governing equations involve nonlinear curvature and rotary inertia of an in-extensional rotating piezoelectric beam are obtained by using the transformation of two Euler angles and extended Hamilton principle. The gyroscopic effect due to the rotating angular speed is investigated in the frame of complex modes based on the invariant manifold method. The effects of angular speed, initial values and electrical resistance to the nonlinear natural frequencies of a rotating piezoelectric beam are studied by both linear and nonlinear decoupling methods. The results reveal that the rotation causes one nonlinear frequency to bifurcate into a pair of frequencies: one forward and one backward nonlinear frequencies. The variation of the frequency with the angular speed is used to measure the angular speed. Finally, the energy transfer due to nonlinear coupling under 1:1 internal resonance condition and the energy transfer due to the linear gyroscopic decoupling are investigated.

Copyright © 2019 by ASME
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