A conserved quantity and the stability of axially moving nonlinear beams |
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| Authors: | Li-Qun Chen Wei-Jia Zhao |
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| Institution: | a Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China
b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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| Abstract: | Free nonlinear transverse vibration is investigated for an axially moving beam modeled by an integro-partial-differential equation. Based on the equation, a conserved quantity is defined and confirmed for axially moving beams with pinned or clamped ends. The conserved quantity is applied to demonstrate the Lyapunov stability of the straight equilibrium configuration in transverse nonlinear of beam with a low axial speed. |
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