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Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 971-984页

作者： Qiaoyun YAN Hu DING Liqun CHEN Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Department of Mechanics Shanghai University

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

关键词： axially accelerating Timoshenko beam viscoelasticity nonlinear dynamics,parametric excitation external excitation

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