具有内阻的旋转复合材料轴的非线性自由振动与稳定性

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (1) : 117-127.

论文

任勇生，时玉艳，张玉环

作者信息 +

Nonlinear free vibration and stability of a rotating composite shaft with internal damping

Ren Yongsheng, Shi Yuyan, Zhang Yuhuan

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文章历史 +

摘要

研究具有内阻的旋转复合材料轴的非线性自由振动和稳定性。采用大振幅不可伸缩旋转梁的假定，对复合材料轴进行非线性建模, 模型引入非线性曲率和惯性的影响。根据复合材料的粘弹性耗散特性描述材料内阻。从复合材料本构关系、应变-位移关系基本方程出发，在导出动能、势能和内阻耗散能的基础上，基于扩展的Hamilton原理，建立旋转复合材料轴的弯-弯耦合非线性振动偏微分方程组。采用 Galerkin法将偏微分方程离散化为常微分方程。为了预测旋转复合材料轴的稳定边界，对线性化方程进行特征值分析，给出了临界速度和失稳阈的表达式。采用四阶Runge-Kutta法对常微分方程组进行数值积分，获得位移时间响应图、相平面图和功率谱图，研究了铺层角、长径比和铺层方式对非线性振动响应和稳定性的影响。

Abstract

The nonlinear free vibration and stability of an internally damped rotating composite shaft were investigated. The shaft was assumed as an inextensional rotating beam with nonlinear curvature and inertia. The internal damping was described by the dissipative behavior of composite. Based on the constitutive relations and the strain-displacement relations of composite, the strain energy, virtual dissipative work and kinetic energy of the shaft were obtained. The equations of motion governing the nonlinear bending-bending vibration of the rotating composite shaft were derived using the extended Hamilton principle. The partial differential equations of motion were reduced into ordinary differential equations by the Galerkin’s method. In order to find the boundaries of stability, the corresponding linearized model of the composite shaft was used in eigenvalue analysis. The critical rotating speeds and instability thresholds of composite shaft were provided. The fourth-order Runge-Kutta method was used to integrate numerically the differential equations of motion. The displacement-time responses, phase plane curves and power spectra of the shaft were presented. The effects of the ply angle, ratio of length to outer radius and stacking sequence on the nonlinear bending vibration responses of the composite shaft were evaluated.

导出引用

任勇生，时玉艳，张玉环. 具有内阻的旋转复合材料轴的非线性自由振动与稳定性[J]. 振动与冲击, 2018, 37(1): 117-127

Ren Yongsheng, Shi Yuyan, Zhang Yuhuan. Nonlinear free vibration and stability of a rotating composite shaft with internal damping[J]. Journal of Vibration and Shock, 2018, 37(1): 117-127

参考文献

[1]Ishida Y, Ikeda T,Yamamoto T. Nonlinear forced oscillations caused by quartic nonlinearity in a rotating shaft system[J].ASME J. Vib.Acoust., 1990,112:288-297.
[2]Ishida Y, Ikeda T,Yamamoto T, Akita T. Internal resonance in a rotating shaft systems: the coincidence of two critical speeds for subharmonic oscillations of the order 1/2 and synchronous backward precession[J].Bull, JSME, 1986, 29:1564-1571.
[3]Ishida Y, Ikeda T, Yamamoto T, Murakami S. Nonstationary vibration of a rotating shaft with nonlinear spring characteristics during acceleration through a critical speed[J]. JSME Int.J.C, 1992, 35:360-368.
[4]L Cveticanin. Large in-plane motion of a rotor[J]. Journal of Vibration and Acoustics, 1998,120 (1): 267-271.
[5]Hosseini S A A, Khadem S E. Free vibrations analysis of a rotating shaft with nonlinearities in curvature and inertia[J]. Mechanism and Machine Theory, 2009,44:272-288.
[6]Rizwan Shad M R, Michon G, Berlioz A. Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending[J].Applied Mathematical Modelling, 2011, 35:2145-2159.
[7]Shahgholi M, Khadem S E. Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity[J]. Mechanism and Machine Theory, 2012,51:131-144.
[8]Khadem S E, Shahgholi M, Hosseini S A A. Two-mode combination resonances of an in-extensional rotating shaft with large amplitude[J]. Nonlinear Dyn, 2011,65:217-233.
[9]Saravanos D A, Varelis D, Plagianakos T S, et al. A shear beam finite element for the damping analysis of tubular laminated composite beams[J]. Journal of Sound and Vibration, 2006, 291:802-823.
[10]Sino R, Baranger T N, Chatelet E, Jacque T G. Dynamic analysis of a rotating composite shaft[J].Composites Science and Technology, 2008, 68:337-345.
[11]Yongsheng Ren, Xingqi Zhang, Yanghang Liu, Xiulong Chen. An analytical model for dynamic simulation of the composite rotor with internal damping[J]. Journal of Vibroengineering, 2014, 16(8):4002-4016.
[12]Shaw J and Shaw S W. Instabilities and bifurcations in a rotating shaft [J]. Journal of Sound and Vibration,1989,132(2):227-244.
[13]Luczko J. A geometrically non-linear model of rotating shafts with resonance and self-excited vibration [J]. Journal of Sound and Vibration,2002, 255(3):433-456.
[14]Shaw J and Shaw S W. Non-linear resonance of an unbalanced rotating shaft with internal damping [J]. Journal of Sound and Vibration,1991,147(3):435-451.
[15]陈予恕,丁千.非线性转子动力学的稳定性和分岔[J].非线性动力学报,1996,3(1):13-22.
CHEN Yushu, DING Qian.A study on stability and bifurcation of nonlinear rotor dynamics[J].Journal of Nonlinear Dynamics in Science and Technology,1996,3(1):13-22.
[16]曹树谦. 高维复杂转子系统非线性动力学的若干现代问题研究[D].天津:天津大学,2003.
Chao Shuqian. Studies on some modern problems of nonlinear dynamics in high–dimensional complex rotor systems[D].Tian Jin: Tian Jin University, 2003.
[17]Ishida Y, Yamamoto T. Forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping (1/2order subharmonic oscillations and entrainment)[J].Nonlinear Dyn.,1993, 4:413-431.
[18]Hosseini S A A. Dynamic stability and bifurcation of a nonlinear in-extensional rotating shaft with internal damping[J].Nonlinear Dyn., 2013,74:345-358.
[19]任勇生，张兴琦，代其义. 旋转复合材料薄壁轴的不平衡非线性弯曲振动[J].振动与冲击，2015，34(3):150-155.
[20]RenYongsheng, Zhang Yuhuan,Dai Qiyi and Zhang Xingqi. Primary resonance of a rotating composite shaft with geometrical nonlineary[J].Journal of Vibroengineering,2015,17(4):1694-1706.
[21]Crespo da silva M R M , Glynn C C. Nonlinear flexural-flexural-torsional dynamics of inextensional beams. II. Forced motions[J]Journal of Structural Mechanics,1978, 6:449-461.
[22]Nayfeh A H, Pai P F. Linear and Nonlinear Structural Mechanics[M]. Wiley Interscience, New York, 2004.