轴压粘弹性圆柱壳在横向扰动下的混沌行为

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (6) : 172-175.

论文

轴压粘弹性圆柱壳在横向扰动下的混沌行为

王建军;韩志军;路国运;张善元

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Chaotic Behavior of Viscoelastic Cylindrical Shell under Axial Pressure and Transverse Periodic Excitation

WANG Jian-Jun ; HAN Zhi-Jun ; LU Guo-Yun ; ZHANG Shan-Yuan

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摘要

基于大挠度薄壳的Donnell-Kármán理论和Kelvin–Voigt粘弹性本构关系，对轴压粘弹性圆柱壳在横向扰动下的混沌行为进行了研究。导出了关于挠度和应力函数的控制方程，借助Galerkin原理将粘弹性圆柱壳的控制方程转化为二阶三次非线性微分动力系统，用Melnikov函数给出了系统发生Smale马蹄型混沌的临界条件。数值计算分析了轴压载荷和粘性阻尼系数对混沌运动的影响。通过分岔图、位移时程曲线、相平面图和Poincaré映射描述了系统的运动行为。研究表明：当轴压载荷与圆柱壳的材料参数满足一定关系时，系统才有可能发生Smale马蹄型混沌；随着轴压载荷的增大，混沌运动区域逐渐减小；随着粘性系数与外阻尼系数比值的增大，混沌运动区域逐渐减小；轴压粘弹性圆柱壳在横向扰动下既会发生定常运动也会发生混沌运动

Abstract

Chaotic behavior of viscoelastic cylindrical shell under axial pressure and transverse periodic excitation was investigated on the basis of Donnell-Kármán theory of thin shell with large deflection and Kelvin–Voigt constitutive relation.The governing equations for the deflection and stress function are derived,and the governing equations of viscoelastic cylindrical shell are changed into the square-order and cubic nonlinear differential dynamic system by Galerkin method.The critical conditions of horseshoe-type chaos are obtained by using Melnikov function.The influences of axial pressures and viscous damper coefficients on chaotic motion of system are analysed by numerical calculation.The motion behaviors of system are described through the bifurcation diagrams, the time-history curve, phase portrait and Poincaré map.The results are given as follows.When the relation between axial pressure and material parameters of cylindrical shell is given,the system can occur horseshoe-type chaos.The chaotic motive region will decrease with increase of axial pressure and the ratio of viscous damper coefficients to external damper coefficients.The system of viscoelastic cylindrical shell under axial pressure and transverse periodic excitation may occur steady motion and chaotic motion

导出引用

王建军;韩志军;路国运;张善元. 轴压粘弹性圆柱壳在横向扰动下的混沌行为 [J]. 振动与冲击, 2011, 30(6): 172-175

WANG Jian-Jun;HAN Zhi-Jun;LU Guo-Yun;ZHANG Shan-Yuan. Chaotic Behavior of Viscoelastic Cylindrical Shell under Axial Pressure and Transverse Periodic Excitation[J]. Journal of Vibration and Shock, 2011, 30(6): 172-175