PRIMARY RESONANCES OF AN INTERNALLY DAMPED ROTATING COMPOSITE SHAFT WITH NONLINEARITIES IN CURVATURE AND INERTIA

doi:10.6052/0459-1879-17-002

Abstract

Abstract:

The rotating shaft made of anisotropic composites is a class of typical rotor dynamic system which has a wide application in the structural design of advanced helicopter power transmission and automotive drive system. The nonlinear rotordynamic behavior study of these system has significance in theory and practice. However, at present, the research about nonlinear dynamic of rotordynamic system has restrainedly been the rotating isotropic shaft, and the effect of internal material damping is seldom considered. In this paper, the primary resonances of an internally damped rotating composite shaft are investigated. Nonlinearity comes from curvature and inertia induced by large deformation of in-extensionality composite shaft. Internal material damping comes from the dissipative properties of viscoelastic composite. The dynamical model incorporates rotary inertia and gyroscopic effect. The extended Hamilton principle is employed to derive the nonlinear equations of bending-bending vibration of rotating composite shaft. The Galerkin method is used to discretize these nonlinear equations, and the multiscale method is adopted to perturbtion analysis the ordinary differential equation, then the analytical expression of primary resonances are derived. The internal damping, external damping, ply angle, length-diameter ratio, stacking sequence, and eccentic distance are numerically analyzed, the effects of above parameters on stable forced vibration-response behaviors of rotating nonlinear composite shaft are discussed. The results show that the internal damping coefficient of angle-ply laminated shaft increases as the increase of ply angle. The primary resonance curves appeared at forward linear natural frequency are found to be of the hardening type. The developed model is capable of describing primary resonance behaviors of rotating composite shaft. This is an important generation of nonlinear dynamic model of in-extensional rotating isotropic shaft.

Key words:

primary resonances|rotating composite shaft|internal damping|in-extensional beam|multiple scales method

CLC Number:

TB33
TH113

Ren Yongsheng, Yao Donghui. PRIMARY RESONANCES OF AN INTERNALLY DAMPED ROTATING COMPOSITE SHAFT WITH NONLINEARITIES IN CURVATURE AND INERTIA[J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(4): 907-919.

References

1 王震鸣, 杜善义, 张衡等. 复合材料及其结构的力学、设计、应用和评价 (第二册). 哈尔滨:哈尔滨工业大学出版社, 1998 (Wang Zhenming, Du Shanyi, Zhang Heng, et al. Mechanics, Design, Application and Evaluation of Composites and Structures(part Ⅱ). Harbin:Harbin Institute of Technology Press, 1998 (in Chinese))
2 Hetherington EL, Kraus RE, Darlow MS. Demonstration of a super critical composite helicopter power transmission shaft. Journal of American Helicopter Society, 1990, 35(1):23-28
3 Zinberg H, Symonds MF. The development of an advanced composite tail rotor driveshaft//26th Annual National Forum of the American Helicopter Society, Washington, DC, June. 1970:16-18
4 Singh SP, Gupta K. Composite shaft rotordynamic analysis using a layer wise theory. Journal of Sound and Vibration, 1996, 191(5):739-756
5 Kim CD, Bert CW. Critical speed analysis of laminated composite, hollow drive shafts. Composites Engineering, 1993, 3(7-8):633-643
6 Bert CW. The effect of bending-twisting coupling on the critical speed of a driveshaft//Japan-U. S. Conference on Composite Materials, 6th, Örlando, FL. 1992:29-36
7 Chang MY, Chen J, Chang C. A simple spinning laminated composite shaft model. International Journal of Solids & Structures, 2004, 41(41):637-662
8 Song Ö, Jeong NH, Librescu L. Implication of conservative and gyroscopic forces on vibration and stability of an elastically tailored rotating shaft modeled as a composite thin-walled beam. The Journal of the Acoustical Society of America, 2001, 109(3):972-981
9 Rehfield L W. Design analysis methodology for composite rotor blades//Proceedings of the seventh DoD/NASA conference on fibrous composites in structural design. 1985:17-20
10 Ren YS, Dai QY, Zhang XQ. Modeling and dynamic analysis of rotating composite shaft. Journal of Vibroengineering, 2013, 15(4):1790-1806
11 任勇生, 代其义, 张兴琦. 旋转复合材料薄壁轴的自由振动与稳定性. 振动工程学报, 2015, 28(1):59-66 (Ren Yongsheng, Dai Qiyi, Zhang Xingqi. Free vibration and stability of a rotating thin-walled composite shaft. Journal of Vibration Engineering, 2015, 28(1):59-
66 (in Chinese))
12 Berdichevsky V, Armanios E, Badir A. Theory of anisotropic thinwalled closed-cross-section beams. Composites Engineering, 1992, 2(5-7):411-432
13 Ishida Y. Nonlinear vibrations and chaos in rotordynamics. JSME International Journal, 1994, 37(2):237-245
14 Shaw J, Shaw SW. Non-linear resonance of an unbalanced rotating shaft with internal damping. Journal of Sound & Vibration, 1991, 147(3):435-451
15 Cveticanin L. Resonant vibrations of nonlinear rotors. Mechanism & Machine Theory, 1995, 30(4):581-588
16 Ishida Y, Nagasaka I, Inoue T, et al. Forced oscillations of a vertical continuous rotor with geometric nonlinearity. Nonlinear Dynamics, 1996, 11(2):107-120
17 Hosseini SAA, Khadem SE. Analytical solution for primary resonances of a rotating shaft with stretching non-linearity//Proceedings of the Institution of Mechanical Engineers, Part C. Journal of Mechanical Engineering Science, 2008, 222(9):1655-1664
18 Khadem SE. Two-mode combination resonances of an inextensional rotating shaft with large amplitude. Nonlinear Dynamics, 2011, 65(65):217-233
19 Shahgholi M, Khadem SE. Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity. Mechanism & Machine Theory, 2012, 51(5):131-144
20 Shad MR, Michon G, Berlioz A. Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending. Applied Mathematical Modelling, 2011, 35(5):2145-2159
21 Hosseini SAA, Zamanian M, Shams S, et al. Vibration analysis of geometrically nonlinear spinning beams. Mechanism & Machine Theory, 2014, 78(78):15-35
22 Ren YS, Zhang YH, Dai QY, et al. Primary resonance of a rotating composite shaft with geometrical nonlineary. Journal of Vibroengineering, 2015, 17(4):1694-1706
23 Saravanos DA, Varelis D. A shear beam finite element for the damping analysis of tubular laminated composite beams. Journal of Sound & Vibration, 2006, 291(3-5):802-823
24 Sino R, Baranger TN, Chatelet E, et al. Dynamic analysis of a rotating composite shaft. Composites Science & Technology, 2008, 68(2):337-345
25 Ren YS, Zhang XQ, Liu YH, et al. An analytical model for dynamic simulation of the composite rotor with internal damping. Journal of Vibroengineering, 2014, 16(8):4002-4016
26 Crespo da Silva MRM, Glynn CC. Nonlinear flexural-flexuraltorsional dynamics of inextensional beams. Ⅱ. Forced motions. Journal of Structural Mechanics, 1978, 6(4):449-461
27 Nayfeh AH, Pai PF. Linear and Nonlinear Structural Mechanics. New York:Wiley Interscience, 2004
28 Crespo da Silva MRM, Glynn CC. Nonlinear flexural-flexuraltorsional dynamics of inextensional beams. I. Equations of motions. Journal of Structural Mechanics, 1978, 6(4):437-448
29 Meirovitch L. Principles and Techniques of Vibrations. New Jersey:Prentice Hall, 1997
30 Meirovitch, Leonard. Analytical Methods in Vibrations. London:The Macmillan Co, 1967

[1]	Li Zheng, Yang Qingsheng, Shang Junjun, Liu Xia. PIEZORESISTIVE SENSING MECHANISM AND PIEZORESISTIVE PERFORMANCE OF IN-PLANE RANDOM STACKED GRAPHENE COMPOSITES ¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1700-1708.
[2]	Yang Zhengmao,Liu Hui,Yang Junjie. DAMAGE CONSTITUTIVE MODEL FOR THERMAL SHOCKED-CERAMIC MATRIX COMPOSITE¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1797-1809.
[3]	Zhang Jiehao, Duan Yuechen, Hou Yuliang, Tie Ying, Li Cheng. MULTI-SCALE METHOD OF PLAIN WOVEN COMPOSITES SUBJECTED TO LOW VELOCITY IMPACT BASED ON ASYMPTOTIC HOMOGENIZATION¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1411-1423.
[4]	Ye Tiangui, Jin Guoyong, Liu Zhigang. A SPECTRAL-DIFFERENTIAL QUADRATURE METHOD FOR 3-D VIBRATION ANALYSIS OF MULTILAYERED SHELLS [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 847-852.
[5]	Tan Bingdong, Xu Jinsheng, Sun Chaoxiang, Jia Yunfei, Fan Xinggui. A TRANSVERSELY ISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(3): 677-684.
[6]	Tan Bingdong, Xu Jinsheng, Jia Yunfei, Yu Jiaquan. HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM INHIBITOR FILM [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(2): 317-323.
[7]	Hua Jun, Hou Yan, Duan Zhirong, He Yu. STUDY ON IRRADIATION DAMAGE AND MECHANICAL PROPERTY OF GRAPHENE [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(5): 1080-1087.
[8]	Hua Jun, Wu Xiaxia, Duan Zhirong. NUMERICAL STUDY ON NANOINDENTATION OF DEFECTIVE BILAYER GRAPHENE [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(4): 917-925.
[9]	Guo Hongbao, Wang Bo, Jia Purong, Yang Chengpeng. MESOSCOPIC DAMAGE BEHAVIORS OF PLAINWOVEN CERAMIC COMPOSITE UNDER IN-PLANE SHEAR LOADING [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(2): 361-368.
[10]	Huang Xiaoshuang, Peng Xiongqi, Zhang Bichao. AN ANISOTROPIC VISCO-HYPERELASTIC CONSTITUTIVE MODEL FOR CORD-RUBBER COMPOSITES [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(1): 140-145.
[11]	Li Nian, Chen Puhui. CONTINUUM DAMAGE MECHANICS MODEL FOR LOW-VELOCITY IMPACT DAMAGE ANALYSIS OF COMPOSITE LAMINATES [J]. , 2015, 47(3): 458-470.
[12]	Guo Hongbao, Jia Purong, Wang Bo, Jiao Guiqiong, Zeng Zeng. STUDY ON CONSTITUENT PROPERTIES OF A 2D-SiC/SiC COMPOSITE BY HYSTERESIS MEASURMENTS [J]. , 2015, 47(2): 260-269.
[13]	Zhao Yuping, Yuan Hong, Han Jun. ANALYSIS OF THE MACROSCOPIC INTERFACIAL BEHAVIOUR OF THE FIBRE PULLOUT USING ELASTIC-PLASTIC COHESIVE MODEL [J]. , 2015, 47(1): 127-134.
[14]	Zhang Zhenguo, Chen Yongqiang, Huang Zhuping. EFFECTIVE SPECIFIC HEATS OF SPHERICAL PARTICULATE COMPOSITES WITH INHOMOGENEOUS INTERPHASES [J]. Chinese Journal of Theoretical and Applied Mechani, 2014, 46(6): 896-904.
[15]	Li Longbiao. INVESTIGATION ON FATIGUE HYSTERESIS LOOPS MODELS OF FIBRE-REINFORCED CERAMIC-MATRIX COMPOSITES [J]. Chinese Journal of Theoretical and Applied Mechani, 2014, 46(5): 710-729.