轴向运动粘弹性弦线的横向非线性动力学行为

采用Poincaré映射和分岔图分析轴向运动黏弹性弦线横向振动的非线性动力学行为。考虑由积分型本构关系描述的黏弹性弦线,并计及微小但有限的变形导致的几何非线性,建立了系统的控制方程。应用Galerkin方法将系统控制方程截断,并通过引入辅助变量将截断后的方程转化为便于数值积分的形式。计算了弦线中点Poincaré映射对轴向张力涨落幅值、轴向运动速度、黏弹性系数和黏弹性指数的分岔图。

TRANSVERSE NONLINEAR DYNAMICAL BEHAVIOR OF AXIALLY MOVING VISCOELASTIC STRINGS

Nonlinear dynamical behaviors for transverse vibation of axially moving viscoelastic strings are investingated based on the Poincaré map and bifurcation diagram. The governing equation is derived for the viscoelastic string using the integral constitutive relation. The geometrical nonlinearity due to small but finite deformation is taken into account in the derivation. The Galerkin method is used to control the truncation error of the governing equation. Auxiliary variables are introduced to transform the truncated system into the form which is convenient to integrate numerically. The bifurcation diagrams of the Poincaré maps of the string center are calculated versus the amplitude of tension fluctuation, the axial traveling speed, the viscoelastic coefficient and exponent of the string material.