旋转复合材料薄壁轴的不平衡非线性弯曲振动

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

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。

The dynamic behavior of rotating composite thin-walled shafts with geometrical non-linearity was studied here.The nonlinear tensional-bending-torsional vibration equations for a rotating composite thin-walled shaft were derived using Hamilton＇s energy principle and variational-asymptotical method （VAM）.On the basis of von Karman＇s assumption, the geometrical nonlinearity was included in the relationship of strain and displacement of the shaft. In order to emphatically study the shaft＇s nonlinear bending vibration,the tensional and torsional deformations were ignored.Thus, the nonlinear bending vibration equations for the rotating composite thin-walled shaft were obtained considering the external and internal viscous dampings.Galerkin＇s method was used to discretize the governing equations and the ordinary differential equations of the rotating shaft hending vibration were obtained.By using the fourth-order Runge-Kutta method, the differential equations were integrated numerically in time domain,the displacement-time responses,phase plane curves and power spectra of the shaft were obtained.The effects of external damping,internal damping,mass eccentricity and rotating speed on the nonlinear bending vibration responses of the shaft were studied.The numerical simulation results showed that the shaft may exhibit a chaotic motion.