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 is obtained by using the transformation of two Euler angles and the 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.
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August 2019
Research-Article
Free Vibrations and Energy Transfer Analysis of the Vibrating Piezoelectric Gyroscope Based on the Linear and Nonlinear Decoupling Methods
Wei Li,
Wei Li
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: webbli@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: webbli@163.com
Search for other works by this author on:
Xiao-Dong Yang,
Xiao-Dong Yang
1
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: jxdyang@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: jxdyang@163.com
1Corresponding author.
Search for other works by this author on:
Wei Zhang,
Wei Zhang
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: sandyzhang0@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: sandyzhang0@163.com
Search for other works by this author on:
Yuan Ren,
Yuan Ren
Department of Aeronautical and Astronautical Science,
Beijing 101416,
e-mail: renyuan_823@aliyun.com
Aerospace Engineering University
,Beijing 101416,
China
e-mail: renyuan_823@aliyun.com
Search for other works by this author on:
Tianzhi Yang
Tianzhi Yang
Search for other works by this author on:
Wei Li
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: webbli@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: webbli@163.com
Xiao-Dong Yang
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: jxdyang@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: jxdyang@163.com
Wei Zhang
Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing 100124,
e-mail: sandyzhang0@163.com
College of Mechanical Engineering,
Beijing University of Technology
,Beijing 100124,
China
e-mail: sandyzhang0@163.com
Yuan Ren
Department of Aeronautical and Astronautical Science,
Beijing 101416,
e-mail: renyuan_823@aliyun.com
Aerospace Engineering University
,Beijing 101416,
China
e-mail: renyuan_823@aliyun.com
Tianzhi Yang
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 May 10, 2019. Assoc. Editor: Miao Yu.
J. Vib. Acoust. Aug 2019, 141(4): 041015 (11 pages)
Published Online: May 10, 2019
Article history
Received:
August 25, 2018
Revision Received:
February 26, 2019
Accepted:
February 28, 2019
Citation
Li, W., Yang, X., Zhang, W., Ren, Y., and Yang, T. (May 10, 2019). "Free Vibrations and Energy Transfer Analysis of the Vibrating Piezoelectric Gyroscope Based on the Linear and Nonlinear Decoupling Methods." ASME. J. Vib. Acoust. August 2019; 141(4): 041015. https://doi.org/10.1115/1.4043062
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