Abstract
Based on nonlinear parametric resonance,this paper investigates the bifurcation and chaos in transverse vibration of a longitudinal accelerating viscoelastic structure.The kelvin model is used to describe the viscoelastic property of the continuum material.The transverse nonlinear vibration of the longitudinal transporting structures is governed by a nonlinear integro-partial-differential equation and a nonlinear partial-differential equation respectively.The differential quadrature scheme is developed to numerically solve the two nonlinear governing equations.Based on the numerical solutions of the two nonlinear equations,the chaotic motions and the bifurcation diagrams of the transverse displacement and the transverse velocity respectively via the mean axial speed and the viscosity coefficient are presented and compared for the two nonlinear governing equations.
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