旋转复合材料薄壁轴的不平衡非线性弯曲振动

研究几何非线性复合材料薄壁轴在偏心激励作用下的非线性振动特性。在轴的应变位移关系中引入Von Kármán几何非线性,基于Hamilton原理和变分渐进法(VAM)导出复合材料传动轴的拉-弯-扭耦合非线性振动偏微分方程组。为了着重研究轴的横向弯曲非线性振动特性,在上述模型中忽略轴向变形和扭转变形,得到轴的横向弯曲非线性振动偏微分方程,其中考虑了黏滞外阻和内阻的影响。采用Galerkin法,将偏微分方程转离散化为常微分方程,在此基础上利用四阶Runge-Kutta法对常微分方程组进行数值模拟,获得位移时间响应图、相平面图和功率谱图,研究了外阻、内组、偏心距和转速对非线性振动响应的影响,发现旋转复合材料薄壁轴存在混沌运动。

Nonlinear bending vibration of an unbalanced rotating composite thin-walled shaft

The dynamic behavior of the rotating composite thin-walled shafts with geometrical nonlineary is studied in the paper. The nonlinear extensional-bending-torsional equations of motion for the rotating composite thin-walled shaft are derived using Hamilton’s energy principle and variational-asymptotical method (VAM). On the basis of von Karman’s assumption, the geometrical nonlineary is included in the relationship of strain and displacement of the shaft. In order to emphatically study nonlinear transverse bending vibration, the effects of extensional and torsional deformations are ignored.Thus, the nonlinear transverse bending equations of motion for the rotating composite thin-walled shaft are obtained, in which external and internal viscous dampings are also considered. Galerkin’s method is used to discretize the governing equations and the ordinary differential equations of the rotating shaft are obtained. By using fourth-order Runge-Kutta method the time respone waveforms, phase plane curves and power spectrums are obtained. The study shows the effect of the external damping, internal damping, eccentricity and rotating speed on nonlinear dynamic behavior of the shaft. Specifically, the numerical simulation results shows that the shaft may exhibit chaotic motion.