The study of the first order equivalent natural frequency for a cantilever beam with dry friction

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (10) : 46-49.

ZHAO Feng1,2,3，CAO Shu-qian1,2,3，FENG Wen-zhou1,2,3

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Abstract

The aim of this paper is to address the study of the natural frequency of a cantilever beam with dry friction using an equivalent method. The motion equation of the studied model and the equivalent model (a cantilever beam) is established using the Newton’s second law and the second kind of the Lagrange equation, respectively. Then the relationship between excitation force and frequency of the two models can be obtained, base on the idea of inputting same energy, thus the equivalent method can be carried out to obtain an analytical expression for the first order natural frequency of the studied model. The numerical method for the first order natural frequency is used to verify the effectiveness of this equivalent method. The results show that the first order natural frequencies obtained by numerical and analytical method are better unanimous under different dry friction, that is, the equivalent natural frequencies decrease as increasing dry friction. Furthermore, the analytical expression of the equivalent natural frequency can directly reflect a relationship between the frequency and dry friction.

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dry friction / cantilever beam / natural frequency / equivalent method

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ZHAO Feng1,2,3，CAO Shu-qian1,2,3，FENG Wen-zhou1,2,3. The study of the first order equivalent natural frequency for a cantilever beam with dry friction[J]. Journal of Vibration and Shock, 2015, 34(10): 46-49

References

[1] Den Hartog J P. Forced vibrations with combined viscous and coulomb damping[J]. Phil.Mag.S.7, 1930,59(9): 801-817.
[2] 赵峰,曹树谦,于跃斌,等. 干摩擦双层梁的工作模态实验方法[J]. 振动、测试与诊断, 2013, 33(6): 971 - 976.
ZHAO Feng, CAO Shu-qian, YU Yao-bin, et al. The experimental method study of operating modal analysis on a double beam model with dry friction[J]. Journal of Vibration, Measurement ＆ Diagnosis, 2013, 33(6): 971 - 976.
[3] 贾尚帅,丁千. 刹车系统的摩擦自激振动和控制[J]. 工程力学, 2012(3): 252 - 256.
JIA Shang-shuai, DING Qian. Friction-induced self-excited vibration and control of a brake system[J]. Engineering Mechanics, 2012(3): 252 - 256.
[4] 丁千,陈予恕. 转子碰摩运动的非稳态分析[J]. 航空动力学报, 2000(2): 191-195.
DING Qian, CHEN Yu-shu. Non-stationary analysis of rotor/casing rubbing [J]. Journal of Aerospace Power, 2000(2): 191-195.
[5] 陈予恕,吴志强. 非线性模态理论的研究进展[J]. 力学进展, 1997, 27(3): 289-299.
CHEN Yu-shu, WU Zhi-qiang. Advances in study on theories of nonlinear normal modes [J]. Advances in Mechanics, 1997, 27(3): 289-299.
[6] Vakakis A F, Bergman L A, McFarland D M, et al. Current efforts towards a non-linear system identification methodology of broad applicability[J]. Proceedings of the Institution of Mechanical Engineers[C]. Journal of Mechanical Engineering Science, 2011: 1-19.
[7] Whiteman W E, Ferri A A. Displacement-dependent dry friction damping of a beam-like structure[J]. Journal of Sound and Vibration, 1996, 198(3): 313-329.
[8] 严天宏,郑钢铁,黄文虎. 由摩擦阻尼铰实现桁架结构的被动减振研究[J]. 航空学报, 1999, 20(1): 17- 21.
YAN Tian-hong, ZHENG Gang-tie, HUANG Wen-hu. Research on passive vibration control of truss structures by displacement-dependent dry frictional joints[J]. Acta Aeronauticaet Astronautica Sinica, 1999, 20(1): 17-21.
[9] Ren Y S, Qin H Z, Zhao Z L. Nonlinear vibration analysis of a beam with dry friction at the supports[J]. Mechanics Research Communications, 1999, 26(1): 83-89.
[10] Ferri A A, Dowell E H. Frequency domain solutions to multi-degree-of-freedom, dry friction damped systems[J]. Journal of Sound and Vibration, 1988, 124(2): 207-224.
[11] Dowell E H, Schwartz H B. Forced response of a cantilever beam with a dry friction damper attached, part 1: theory[J]. Journal of Sound and Vibration, 1983, 91(2): 255-267.
[12] Young J G, Kim Y H, Chang H G. An analysis of the behavior of a simply supported beam with a dry friction damper attached[J]. Applied Acoustics, 1998, 55(1): 31-41.
[13] 郝淑英,陈予恕,张琪昌. 连接结构松动对系统非线性动力学特性的影响[J]. 天津大学学报, 2001, 34(4): 452-454.
HAO Shu-ying, CHEN Yu-shu, ZHANG Qi-chang. Effects of connect loosing and sliding on dynamic characteristics[J]. Journal of Tianjin University, 2001, 34(4): 452-454.
[14] Ferri A A, Whiteman W E. Free response of a system with negative viscous damping and displacement-dependent dry friction damping[J]. Journal of Sound and Vibration, 2007, 306: 400-418.
[15] Ostachowicz W M. A discrete linear beam model to investigate the nonliear effects of slip friction[J]. Computer and Structures, 1990, 36(4): 721-728.
[16] Poudou O J. Modeling and analysis of the dynamics of dry-friction-damped structural systems[D]. USA:University of Michigan, 2007.
[17] Dowell E H. The behavior of a linear, damped modal system with a non-linear spring-mass-dry friction damper system attached[J]. Journal of Sound and Vibration, 1983, 89(1): 65 - 84.
[18] Dowell E H. Damping in beams and plates due to slipping at the support boundaries[J]. Journal of Sound and Vibration, 1986, 105(2): 243-253.
[19] Kerschen G, Worden K, Vakakis A F, et al. Past, present and future of nonlinear system identification in structural dynamics[J]. Mechanical Systems and Signal Processing, 2006, 20(3): 505-592.
[20] 丁虎, 张国策, 陈立群. 超临界轴向运动梁横向非线性振动频域分析[J]. 固体力学学报, 2011, 32(4): 360-363.
DING Hu, ZHANG Guo-ce, CHEN Li-qun. Frequency domain analysis of supercritical nonlinear vibration of axially moving beams[J]. Chinese Journal of Solid Mechanics, 2011, 32(4): 360-363.
[21] 佟德纯. 设备故障诊断技术讲座,第四讲:机械设备振动特征分析[J]. 振动与冲击, 1993, 12(2): 70-78.
DONG De-chun. Lectures of diagnostic techniques of Equipment failures, the fourth section: vibration characteristics analysis of mechanical equipments [J]. Journal of Vibration and Shock, 1993, 12(2): 70-78.