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Journal of Shanghai University >

2018 , Vol. 24 >Issue 5: 713 - 720

DOI: https://doi.org/10.12066/j.issn.1007-2861.1870

Research Articles

Bifurcation and chaos of axially moving viscoelastic beam constituted by standard linear solid model

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  • 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
    2. College of Sciences, Shanghai University, Shanghai 200444, China

Received date: 2016-11-14

  Online published: 2018-10-26

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Abstract

The nonlinear dynamic behavior of an axially moving viscoelastic beam under parametric excitation is investigated. A standard linear solid model is used in the constitutive relation. Newton's second law is applied to derive a nonlinear integral-partial-differential governing equation of the beam. The fourth-order Galerkin truncation method is applied to truncate the governing equation into a set of ordinary differential equations solved with the fourth-order Runge-Kutta method. Based on the diagrams of time history, phase, Poincaré map and frequency analysis, the dynamical behavior is identified. The investigation is focused on the effects of the standard linear solid model's viscoelasticity on the nonlinear dynamic behavior. Numerical simulations show that vibration of an axially accelerating viscoelastic beam is sensitive to all parameters of the standard linear solid model.

Key words： axially moving beam; standard linear solid model; Galerkin truncation; bifurcation; chaos

Cite this article

LI Yi, YAN Qiaoyun, DING Hu, CHEN Liqun . Bifurcation and chaos of axially moving viscoelastic beam constituted by standard linear solid model[J]. Journal of Shanghai University, 2018 , 24(5) : 713 -720 . DOI: 10.12066/j.issn.1007-2861.1870

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