Dynamic Modeling and Parametric Instability Analysis of Rotating Composite Shafts Under Periodic Axial Loads

doi:10.3901/JME.2025.07.396

Abstract

Abstract: The dynamic model of rotating composite shafts with internal damping is established and its parametric instability under periodic loads is studied. Based on Bernoulli-Euler beam theory and Kelvin-Voigt viscoelastic model, the governing equations of rotating composite shafts in inertial frame are derived. The partial differential equations are transformed into Mathieu-Hill ordinary differential equations with periodic coefficients using Galerkin method. Based on Floquet exponent method, which is widely used in parametric systems, the parametric stability behaviors of rotating composite shafts under axial periodic excitation are analyzed. The correctness of the model and the stability method is verified by comparing with other literatures and numerical integration results. On this basis, the effects of ply angle, internal damping and static load factor on the size and location of instability region of composite shafts are studied. The results show that due to the influence of rotation effect, only the combination instability region exists, and the internal damping has a significant influence on the parametric instability characteristics. Increasing the ply angle and decreasing the static load factor will improve the stability.

Key words: rotating composite shaft, axial loads, parametric instability, internal damping, Floquet exponent method

CLC Number:

TH113

DAI Qiyi, HAN Qinkai, QIN Zhaoye, CHU Fulei. Dynamic Modeling and Parametric Instability Analysis of Rotating Composite Shafts Under Periodic Axial Loads[J]. Journal of Mechanical Engineering, 2025, 61(7): 396-405.

References

[1] 王帅，梁福东，鲁雄. 复合材料在直升机传动系统的应用与发展趋势[J]. 航空动力，2019(5)：22-24. WANG Shuai，LIANG Fudong，LU Xiong. Application and development trend of composite caterials in helicopter drive system [J]. Aerospace Power，2019(5)：22-24.
[2] 张运东，杨丹，陶骏. 碳纤维复合材料传动轴的开发与实践[J]. 汽车工艺与材料，2022(4)：20-24. ZHANG Yundong，YANG Dan，TAO Jun. Development and practice of carbon fiber reinforced polymer transmission shaft[J]. Automobile Technology & Material，2022(4)：20-24.
[3] 尹志垚，谢旻，景伟，等. 船用复合材料轴系的设计研究[J]. 纤维复合材料，2022，39(4)：93-101. YIN Zhiyao，XIE Min，JING Wei，et al. Research on design technology of carbon fiber composite shaft[J]. Fiber Composites，2022，39(4)：93-101
[4] 任勇生，张玉环，时玉艳. 考虑不可伸长和材料内阻的旋转复合材料轴的非线性自由振动分析[J]. 振动工程学报，2018，31(3)：468-482. REN Yongsheng，ZHANG Yuhuan，SHI Yuyan. Nonlinear free vibration analysis of an inextensional rotating composite shaft with material internal damping[J]. Journal of Vibration Engineering，2018，31(3)：468-482.
[5] KIM C D，BERT C W. Critical speed analysis of laminated composite，hollow drive shafts[J]. Composites Engineering，1993，3(7-8)：633-643.
[6] BERT C W，KIM C D. Whirling of composite-material driveshafts including bending-Twisting coupling and transverse shear deformation[J]. Journal of Vibration and Acoustics，1995，117(1)：17-21.
[7] CHANG M Y，CHEN J K，CHANG C Y. A simple spinning laminated composite shaft model[J]. International Journal of Solids and Structures，2004，41：637-662.
[8] ARAB S B，JOSÉ DIAS R，BOUAZIZ S，et al. A finite element based on equivalent single layer theory for rotating composite shafts dynamic analysis[J]. Composite Structures，2017，178：135-144.
[9] SINO R，BARANGER T N，CHATELET E，et al. Dynamic analysis of a rotating composite shaft[J]. Composites Science and Technology，2008，68：337-345.
[10] ROGER D P M W，DE MEDEIROS E C，REZENDE P A L，et al. The dynamic analysis of rotors mounted on composite shafts with internal damping[J]. Composite Structures，2017，167：50-62.
[11] ARAB S B，JOSÉ DIAS R，BOUAZIZ S，et al. Stability analysis of internally damped rotating composite shafts using a finite element formulation[J]. Comptes Rendus Mecanique，2018，346(4)：291-307.
[12] RI K，HAN P，KIM I，et al. Stability analysis of composite shafts considering internal damping and coupling effect[J]. International Journal of Structural Stability and Dynamics，2020，2050118.
[13] BARBOSA P C P F，VERGILIO T S，SOUSA M S，et al. Experimental analysis of the SHBT approach for the dynamic modeling of a composite hollow shaft[J]. Composite Structures，2020，236：111892.
[14] 任勇生，时玉艳，张玉环. 材料内阻对旋转复合材料轴动力学稳定性的影响研究[J]. 振动与冲击，2017，36(23)：181-186. REN Yongsheng，SHI Yuyan，ZHANG Yuhuan. Effects of internal damping on dynamic stability of a rotating composite shaft[J]. Journal of Vibration and Shock，2017，36(23)：181-186.
[15] CHEN L W，PENG W K. Dynamic stability of rotating composite shafts under periodic axial compressive loads[J]. Journal of Sound and Vibration，1998，212(2)：215-230.
[16] 辛健强，王建军. 时变转速下裂纹圆柱壳的参数振动稳定性分析[J]. 航空动力学报，2011，26(10)：2227-2236. XIN Jianqiang，WANG Jianjun. Stability analysis of parametric resonance of a crack cylindrical shell with time-varying rotating speed[J]. Journal of Aerospace Power，2011，26(10)：2227-2236.
[17] PEI Y C. Stability boundaries of a spinning rotor with parametrically excited gyroscopic system[J]. European Journal of Mechanics-A/Solids，2009，28(4)：891-896.
[18] BARTYLLA D. Stability investigation of rotors with periodic axial force[J]. Mechanism and Machine Theory，2012，58：13-19.
[19] SONG Z，CHEN Z，LI W，et al. Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method[J]. Meccanica，2016，52(4)：1-15.
[20] HAN Q，QIN Z，LU W，et al. Dynamic stability analysis of periodic axial loaded cylindrical shell with time-dependent rotating speeds[J]. Nonlinear Dynamics，2015，81(4)：1-16.
[21] TURHAN O，BULUT G. Dynamic stability of rotating blades (beams) eccentrically clamped to a shaft with fluctuating speed[J]. Journal of Sound and Vibration，2005，280：945-964.
[22] DAI Q，LIU Y. Dynamic stability analysis of periodic loaded rotating conical shells using Floquet exponent method[J]. Mechanics Based Design of Structures and Machines，2024，52(3)：1399-1413.