Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

doi:10.1007/s10483-018-2322-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (5): 717-732.doi: https://doi.org/10.1007/s10483-018-2322-6

Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

Bo WANG

School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China

收稿日期:2017-03-28 修回日期:2017-11-13 出版日期:2018-05-01 发布日期:2018-05-01
通讯作者: Bo WANG,E-mail:b.wang@live.com E-mail:b.wang@live.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11202136, 11372195, 11502147, and 11602146)

Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

Bo WANG

School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China

Received:2017-03-28 Revised:2017-11-13 Online:2018-05-01 Published:2018-05-01
Contact: Bo WANG E-mail:b.wang@live.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11202136, 11372195, 11502147, and 11602146)

摘要/Abstract

摘要：

The dynamic stability of axially moving viscoelastic Rayleigh beams is presented. The governing equation and simple support boundary condition are derived with the extended Hamilton's principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscosity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.

关键词: extended Hamilton's principle, transverse vibration, eigen-frequencies, Ritz method, parametric resonance, axially moving Rayleigh beam, differential quadrature method (DQM)

Abstract:

Key words: axially moving Rayleigh beam, transverse vibration, eigen-frequencies, Ritz method, parametric resonance, extended Hamilton's principle, differential quadrature method (DQM)

中图分类号:

Bo WANG. Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 717-732.

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Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

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