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Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 971–984 | Cite as

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

  • Qiaoyun Yan
  • Hu Ding
  • Liqun ChenEmail author
Article

Abstract

This investigation focuses on the nonlinear dynamic behaviors in the transverse vibration of an axially 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 relationship between the dual-frequency excitations.

Keywords

axially accelerating Timoshenko beam viscoelasticity nonlinear dynamics parametric excitation external excitation 

Chinese Library Classification

O242 

2010 Mathematics Subject Classification

74S05 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina
  2. 2.Department of MechanicsShanghai UniversityShanghaiChina

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