Vibration and stability of an axially moving viscoelastic beam with hybrid supports |
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Authors: | Li-Qun Chen Xiao-Dong Yang |
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Affiliation: | aDepartment of Mechanics, Shanghai University, Shanghai 200444, China;bShanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China;cDepartment of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang 110034, China |
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Abstract: | Vibration and stability are investigated for an axially moving beam constrained by simple supports with torsion springs. A scheme is proposed to derive natural frequencies and modal functions from given boundary conditions of an elastic beam moving at a constant speed. For a beam constituted by the Kelvin model, effects of viscoelasticity on the free vibration are analyzed via the method of multiple scales and demonstrated via numerical simulations. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams in parametric resonance. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity. |
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Keywords: | Axially moving beam Vibration frequency Dynamic stability Method of multiple scales Viscoelasticity |
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