标题：Nonlinear bending vibration of an unbalanced rotating composite thin-walled shaft
作者：Ren, Yong-Sheng ;Zhang, Xing-Qi ;Dai, Qi-Yi
作者机构：[Ren, Yong-Sheng ;Zhang, Xing-Qi ;Dai, Qi-Yi ] College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingda 更多
来源：Zhendong yu Chongji/Journal of Vibration and Shock
摘要：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.
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