含迟滞力约束悬臂梁的非线性振动研究

doi:10.7527/S1000-6893.2013.0184

Abstract

Abstract:

To study the effects of microslip of mechnical joints on the structural dynamic behaviors of a structure with mechanical joints, the primary resonance of a base excitated cantilever beam with a hysteresis force constraining at the free end is analyzed in this paper. The hysteresis constraint is constructed by an Iwan model, and the method of multiple scales is applied to determine the steady-state response for the primary resonance of the governing equation of the beam with this nonlinear boundary condition. The nonlinear amplitude-frequency relationship of the steady-state response is derived from the solvability condition, and the stability of the steady-state response is analyzed by the Lyapunov-linearized stability theory. The results of the examples show that all the resonance peaks are left-bended as expected, exhibiting a softening effect. When the parameters of the equation are within a certain range, an unstable branch arises in each of the amplitude-frequency curves and the relationship curves of response amplitude vs excitation amplitude. It is found that the scope of the unstable branch of the amplitude-frequency curve is influenced by the parameters of excitation amplitude, viscous damping and constraint stiffness.

Key words: hysteresis, beam, multiple scales, primary resonance, stability

CLC Number:

ZHANG Xiangmeng, WANG Benli, LIU Yuan. Nonlinear Vibration of a Cantilever Beam Constrained by a Hysteresis Force[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(11): 2539-2549.

References

[1] Chen C Y,Song H W,Wang D Y,et al.Preliminary research on natural frequency shift in satellite vibration test.Journal of Vibration and Shock,2003,22(4): 23-26.(in Chinese) 陈昌亚,宋汉文,王德禹,等.卫星振动试验中固有频率"漂移"现象初步研究.振动与冲击,2003,22(4): 23-26.

[2] He R,Luo W B,Wang B L,et al.Natural frequency decrease analysis of aluminum honeycomb sandwich board based on Lyapunov exponent.Journal of Astronautics,2009,30(2): 463-468.(in Chinese) 何蕊,罗文波,王本利,等.基于Lypunov指数的铝蜂窝板频率漂移机理分析.宇航学报,2009,30(2): 463-468.

[3] Wei H T,Kong X R,Wang B L,et al.Effects of nonlinearities of sleeve joint on the frequency shift of a beam.Journal of Vibration Engineering,2012,25(4): 373-379.(in Chinese) 卫洪涛,孔宪仁,王本利,等.套筒连接结构非线性对梁频漂的影响.振动工程学报,2012,25(4): 373-379.

[4] Wei H T,Kong X R.Non-linear vibration of a beam with a type of clamped-jointed boundary condition with a gap.Spacecraft Environment Engineering,2010,27(6): 742-746.(in Chinese) 卫洪涛,孔宪仁.一个带间隙连接结构对梁基频漂移影响研究.航天器环境工程,2010,27(6): 742-746.

[5] Ibrahim R,Pettit C.Uncertainties and dynamic problems of bolted joints and other fasteners.Journal of Sound and Vibration,2005,279(3-5): 857-936.

[6] Ma X,Bergman L,Vakakis A.Identification of bolted joints through laser vibrometry.Journal of Sound and Vibration,2001,246(3): 441-460.

[7] Hartwigsen C J,Song Y,McFarland D M,et al.Experimental study of non-linear effects in a typical shear lap joint configuration.Journal of Sound and Vibration,2004,277(1-2): 327-351.

[8] Heller L,Foltete E,Piranda J.Experimental identification of nonlinear dynamic properties of built-up structures.Journal of Sound and Vibration,2009,327(1-2): 183- 196.

[9] Bai S J,Wei F,Zheng G T.Modeling of a marman clampband joint and its nonlinear dynamic analysis.Journal of Vibration and Shock,2010,29(5): 6-10.(in Chinese) 白绍竣,尉飞,郑钢铁.包带连接建模与非线性动力学特性分析.振动与冲击,2010,29(5): 6-10.

[10] Ouyang H,Oldfield M J,Mottershead J E.Experimental and theoretical studies of a bolted joint excited by a torsional dynamic load.International Journal of Mechanical Sciences,2006,48(12): 1447-1455.

[11] Song Y,Hartwigsen C J,McFarland D M,et al.Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements.Journal of Sound and Vibration,2004,273(1-2): 249-276.

[12] Ahmadian H,Jalali H,Pourahmadian F.Nonlinear model identification of a frictional contact support.Mechanical Systems and Signal Processing,2010,24(8): 2844-2854.

[13] Jalali H,Ahmadian H,Pourahmadian F.Identification of micro-vibro-impacts at boundary condition of a nonlinear beam.Mechanical Systems and Signal Processing,2011,25(3): 1073-1085.

[14] Turner J A.Non-linear vibrations of a beam with cantilever－Hertzian contact boundary conditions.Journal of Sound and Vibration,2004,275(1-2): 177-191.

[15] Hu Q Q,Lim C W,Chen L Q.Nonlinear vibration of a cantilever with a Derjaguin-MÜller-Toprov contact end.International Journal of Structural Stability and Dynamics,2008,8(1): 25-40.

[16] Chen L Q,Lim C W,Hu Q Q,et al.Asymptotic analysis of a vibrating cantilever with a nonlinear boundary.Science in China Series G: Physics,Mechanics and Astronomy,2009,52(9): 1414-1422.

[17] Chen W,Deng X.Structural damping caused by micro-slip along frictional interfaces.International Journal of Mechanical Sciences,2005,47(8): 1191-1211.

[18] Segalman D J.Modelling joint friction in structural dynamics.Structural Control & Health Monitoring,2006,13(1): 430-453.

Nonlinear Vibration of a Cantilever Beam Constrained by a Hysteresis Force

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Da MO, Yuzhen LIN, Xiao HAN, Hongyu MA, Yixiong LIU. Research progress and future prospect of hydrogen micromix combustion technology [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(7): 28994-028994.
[2]	Zhe ZHU, Jiangtao HUANG, Sheng ZHANG, Fei LI, Xin DU, Enguang SHAN, Jigang TANG, Chunyang WANG. Modeling and control for actively stabilized aerial refueling drogue with momentum rings [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(7): 128882-128882.
[3]	Jidong SU, Weilin XU, Shenghua ZHAI, Wei WANG, Yating HE. Practice and prospect of space AD hoc network technology [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(5): 529912-529912.
[4]	Xueliang LI, Chuangchuang LI, Wei SU, Jie WU. Experiment of influence of distributed roughness elements on hypersonic boundary layer instability [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(2): 128627-128627.
[5]	Dawei ZHANG, Guoping LIU. A high⁃order fully actuated predictive control approach of spacecraft flying⁃around under time⁃variant communication constraints [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 628633-628633.
[6]	Guangren DUAN. Fully actuated system approach for stabilization control of sub-strict feedback systems [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 629552-629552.
[7]	Kailing ZHANG, Siyi LI, Yi DUAN, Chao YAN. Uncertainty quantification of parameters in SST turbulence model for inlet simulation [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729429-729429.
[8]	Hongjian ZHANG, Yanxin ZHANG, Jianjun XIONG, Zhao ZHAO, Lin RAN, Xian YI. Numerical simulation of phased array ultrasonic beam propagation characteristics in ice layer [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729289-729289.
[9]	Runchang HU, Zian WANG, Yongliang CHEN, Dapeng ZHOU, Dapeng YANG, Zheng GONG. Stability augmentation control of thrust-vectored V/STOL aircraft based on L1 adaptive control [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727642-727642.
[10]	Siyuan CHANG, Yao XIAO, Guangli LI, Zhongwei TIAN, Kaikai ZHANG, Kai CUI. Effect of wing dihedral and anhedral angles on hypersonic aerodynamic characteristics of high-pressure capturing wing configuration [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(8): 127349-127349.
[11]	Fangjian WANG, Ke XIE, Jin LIU, Yuhui SONG, Han QIN, Lan CHEN. Unsteady flow and wing rock characteristics of low aspect ratio flying-wing [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 126449-126449.
[12]	Bian LI, Lili QU, Yuping GAO. Methods for J0613-0200 steering a cesium clock [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(3): 526500-526500.
[13]	Jing ZHANG, Kai GUO, Hongwei GUO, Rongqiang LIU, Ziming KOU. Structural design and stiffness analysis of deployable tensegrity mast [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(24): 228584-228584.
[14]	Yutian WANG, Jianxin LIU, Xiaokun WANG, Xiaoming LI. Effects of porous wall on secondary instability of optimal growth streaks in high speed boundary layers [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(22): 128519-128519.
[15]	Sihua LIU, Zhanying WANG, Lijian LI, Mindi ZHANG. Influence of nose shapes on high-speed water entry stability of projectile [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(21): 528437-528437.