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

doi:10.1007/s10483-017-2249-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (10): 1425-1438.doi: https://doi.org/10.1007/s10483-017-2249-6

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

Xiaodong YANG¹, Shaowen WANG¹, Wei ZHANG¹, Zhaohong QIN², Tianzhi YANG³

1. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China;
2. Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing 100176, China;
3. Department of Engineering Mechanics, Shenyang Aerospace University, Shenyang 110136, China Abstract

Received:2017-03-19 Revised:2017-04-17 Online:2017-10-01 Published:2017-10-01
Contact: Xiaodong YANG E-mail:jxdyang@163.com
Supported by:
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)

Abstract

Abstract:

The mathematical modeling 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.

Key words: fuzzy-stochastic finite element, equations of interval numbers, perturbation theory, power series method, gyroscopic coupling, natural frequency, rotating Timoshenko beam

2010 MSC Number:

74S70
35C11

Xiaodong YANG, Shaowen WANG, Wei ZHANG, Zhaohong QIN, Tianzhi YANG. Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1425-1438.

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References

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

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