Parametric Vibration and Numerical Validation of Axially Moving Viscoelastic Beams with Internal Resonance, Time and Spatial Dependent Tension and Tension Dependent Speed

[+] Author and Article Information
You-Qi Tang

100 Hai Quan Road, Feng Xian District Shanghai, Shanghai 201418 China tangyouqi2000@163.com

Zhao-Guang Ma

School of Mechanical Engineering, Shanghai Institute of Technology Shanghai, Shanghai 201418 China 1336463823@qq.com

Shuang Liu

100 Haiquan Road Shanghai, Shanghai 201418 China lsbbsh@126.com

Lan-Yi Zhang

100 Hai Quan Road, Feng Xian District Shanghai, Shanghai 201418 China 2830360524@qq.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received September 4, 2018; final manuscript received July 25, 2019; published online xx xx, xxxx. Assoc. Editor: Mohammed Daqaq.

ASME doi:10.1115/1.4044449 History: Received September 04, 2018; Accepted July 26, 2019


In this paper, the idea of an axially moving time dependent beam model is briefly introduced. The nonlinear response of an axially moving beam is investigated. The effects of a time and spatial dependent tension depending on the external forces at the boundary and a tension dependent speed are highlighted, which gives a new model to study the parametric vibration of axially moving structures. This paper focuses on simultaneous resonant cases that are principal parametric resonance of first mode and internal resonance of the first two modes. In general, the method of multiple scales can study nonlinear vibration of axially moving structures with homogeneous boundary conditions. Taking Kelvin viscoelastic constitutive relation into account, the inhomogeneous boundary conditions makes the solvability conditions fail, which is also one of the highlights of this paper. In order to resolve this problem, the technique of the modified solvability conditions is employed. The influence of some parameters, such as material's viscoelastic coefficients, viscous damping coefficients, and the axial tension fluctuation amplitudes, on the steady-state vibration responses are demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method (DQM).

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