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Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method

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Abstract

The mathematical modelling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to investigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.

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Authors and Affiliations

  1. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Xiaodong Yang, Shaowen Wang & Wei Zhang

  2. Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing, 100176, China

    Zhaohong Qin

  3. Department of Engineering Mechanics, Shenyang Aerospace University, Shenyang, 110136, China

    Tianzhi Yang

Authors
  1. Xiaodong Yang
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  2. Shaowen Wang
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  3. Wei Zhang
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  4. Zhaohong Qin
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  5. Tianzhi Yang
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Corresponding author

Correspondence to Xiaodong Yang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11672007, 11402028, 11322214, and 11290152), the Beijing Natural Science Foundation (No. 3172003), and the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University (No.VCAME201601)

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Yang, X., Wang, S., Zhang, W. et al. Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method. Appl. Math. Mech.-Engl. Ed. 38, 1425–1438 (2017). https://doi.org/10.1007/s10483-017-2249-6

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  • DOI: https://doi.org/10.1007/s10483-017-2249-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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