黏弹性传动结构非线性参数共振的分岔与混沌

Bifurcation and chaos in nonlinear parametric resonance of viscoelastic transporting structures

研究了非线性参数激励下,黏弹性径向传动结构横向振动的分岔和混沌.采用Kelvin本构关系描述连续体的黏弹性.给出了描述传动结构横向非线性振动的两类控制方程,即偏微分-积分方程和偏微分方程.基于微分求积方法,分别通过两组方程,仿真了径向传动结构横向非线性参数振动的非线性动力学行为.观察并比较了两组方程描述的、结构中点的位移、速度随平均速度以及黏性阻尼的分岔现象以及混沌运动特性.

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 differen- tial 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.