基于Hertz接触的单自由度碰振系统的随机响应近似闭合解

摘要
图/表
参考文献(23)
相关文章 (10)

全文: PDF (2395 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要碰振系统普遍存在于工程领域中，因此开展碰撞振动的研究具有重要的实际意义。本文应用随机振动研究的最新成果——迭代加权残值法，求解了高斯白噪声激励下基于Hertz接触的单自由度碰振系统的随机响应近似闭合解。首先，结合概率环流和概率势流的概念，构造系统FPK方程稳态解的近似表达式；然后，运用加权残值法获得近似表达式中的待定系数；最后，应用迭代技术在指定均方误差下获得特定精度的概率密度估计。为了说明本文方法的有效性，分别考察了Duffing碰振系统和干摩擦碰振系统，再将蒙特卡罗模拟结果与理论解析解进行对比验证。研究表明，理论解析解与模拟结果吻合的非常好。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章

关键词 ：碰撞振动, Hertz接触理论模型, 迭代加权残值法, 高斯激励

Abstract：Vibro-impact systems exist widely in engineering fields, and studying collision-vibration is of great practical significance.Here, the latest achievement in studying random vibration, i.e., the iterative weighted residual method, was employed to obtain the approximate closed-form solution to random response of a SDOF vibro-impact system based on Hertz contact theory under Gaussian white noise excitation.Firstly, the approximate expression of the steady-state solution to Fokker-Planck-Kolmogorov (FPK) equation was constructed using concepts of the probabilistic circulation and probabilistic potential flow.Then, undetermined coefficients in the approximate expression were obtained using the weighted residual method.Finally, the iterative technique was used to gain the probability density estimation of specific accuracy under specified mean square error.To demonstrate the effectiveness of the proposed method, a Duffing vibro-impact system and a dry friction vibro-impact one were investigated, respectively.The theoretical analytical solutions were compared with the simulation results of Monte Carlo method.It was shown that the theoretical analytical solutions agree well with Monte Carlo simulation results.

Key words： vibro-impact Hertz contact theory model iterative method of weighted residual Gaussian excitation

收稿日期: 2019-03-07 出版日期: 2019-10-28

引用本文:

祝海生1 陈林聪1 孙建桥2，3 赵珧冰1. 基于Hertz接触的单自由度碰振系统的随机响应近似闭合解[J]. 振动与冲击, 2019, 38(21): 6-14.
ZHU Haisheng1, CHEN Lincong1, SUN Jianqiao2,3,ZHAO Yaobing1. Approximate closed-form solution to random response of a SDOF vibro-impact system based on Hertz contact theory. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(21): 6-14.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2019/V38/I21/6

[1] Dimentberg M F, Iourtchenko D V. Towards incorporating impact losses into random vibration analyses: a model problem [J]. Probabilistic Engineering Mechanics, 1999, 14(4): 323-328.
[2] Iourtchenko D V, Dimentberg M F. Energy balance for random vibrations of piecewise-conservative systems [J]. Journal of Sound and Vibration, 2001, 248(5): 913-923.
[3] 王亮,徐伟,李颖.随机激励下二自由度碰撞振动系统的响应分析[J]. 物理学报, 2008, 57(10):6169-6173.
WANG Liang, XU Wei, LI Ying. Response analysis of two-degree-of-freedom impact oscillator to random excitation [J]. Acta Phys. Sin., 2008, 57(10): 6169-6173.
[4] 田海勇, 刘卫华, 赵日旭. 随机干扰下碰撞振动系统的动力学分析[J]. 振动与冲击, 2009, 28(9):163-167.
TIAN Haiyong, LIU Weihua, ZHAO Rixu. Analysis of the Dynamics of vibro-impact system with random disturbance [J]. Journal of Vibration and Shock, 2009, 28(9): 163-167.
[5] 伍新, 徐慧东, 文桂林, 魏克湘. 三自由度碰撞振动系统Poincare映射叉式分岔的反控制[J]. 振动与冲击, 2016, 35 (20):24-29.
WU Xin, XU Huidong, WEN Guilin, WEI Kexiang. Anti-controlling Pitchfork bifurcation on Poincaré map of a three-degree-of-freedom vibro-impact system [J]. Journal of Vibration and Shock, 2016, 35(20): 24-29.
[6] GU X D, ZHU W Q. A stochastic averaging method for analyzing vibro-impact systems under Gaussian white noise excitations [J]. Journal of Sound and Vibration, 2014, 333(9):2632-2642.
[7] LIU D, LI M, LI J L. Probabilistic response and analysis for a vibro-impact system driven by real noise [J]. Nonlinear Dynamics, 2017, 91(2–4):1-13.
[8] LI C, XU W, FENG J Q, WANG L. Response probability density functions of Duffing-Van der Pol vibro-impact system under correlated Gaussian white noise excitations [J]. Physic a-Statistical Mechanics and Its Applications, 2013, 392(6): 1269-1279.
[9] 徐伟, 杨贵东, 岳晓乐. 随机参激下Duffing-Rayleigh碰撞振动系统的P-分岔分析[J]. 物理学报,2016, 65(21):61-66.
XU Wei, YANG Guidong, YUE Xiaole. P-bifurcations of a Duffing-Rayleigh vibro-impact system under stochastic parametric excitation [J]. Acta Physica2 Sinica, 2016, 65(21):210501.
[10] ZHU H T. Stochastic response of vibro-impact Duffing oscillators under external and parametric Gaussian white noises [J]. Journal of Sound and Vibration, 2014, 333(3): 954-961.
[11] ZHU H T. Stochastic response of a vibro-impact Duffing system under external Poisson impulses [J]. Nonlinear Dynamics, 2015, 82(1-2):1001-1013.
[12] CHEN L C, QIAN J M, ZHU H S, SUN J Q. The closed-form stationary probability distribution of the stochastically excited vibro-impact oscillators [J]. Journal of Sound and Vibration, 2019, 439:260-270.
[13] JING H S, SHEU K C. Exact stationary solutions of the random response of a single-degree-of-freedom vibro-impact system [J]. Journal of Sound and Vibration, 1990, Vol. 141(3): 363-373.
[14] JING H S, YOUNG M H. Random response of a single-degree-of-freedom vibro-impact system with clearance [J]. Earthquake Engineering & Structural Dynamics, 1990, Vol. 19(6): 789-798.
[15] HUANG Z L, LIU Z H, ZHU W Q. Stationary response of multi-degree-of-freedom vibro-impact systems under white noise excitations [J]. Journal of Sound and Vibration, 2004, 275(1): 223-240.
[16] XU M, WANG Y, JIN X L, HUANG Z L, YU T X. Incorporating Dissipated impact into random vibration analyses through the modified Hertzian contact model [J]. Journal of Engineering Mechanics, 2013, 139(12): 1736-1743.
[17] XU M, WANG Y, JIN X L, HUANG Z L. Random vibration with inelastic impact: equivalent nonlinearization technique [J]. Journal of Sound and Vibration, 2014, 333(1): 189-199.
[18] 徐明, 金华斌. 非弹性碰撞振动系统的首次穿越分析[J]. 振动与冲击, 2016, 35(17):197-212.
XU Ming, JIN Huabin. First-passage failure of the non-elastic vibro-impact system [J]. Journal of Vibration and Shock, 2016, 35(17): 197-200.
[19] YONG Y, LIN Y K. Exact stationary-response solution for second order nonlinear systems under parametric and external white-noise excitations [J]. Journal of Applied Mechanics, 1987, 54(2) : 414–418.
[20] LIN Y K, CAI G Q. Exact stationary response solution for second order nonlinear systems under parametric and External White Noise Excitations: Part II [J]. Journal of Applied Mechanics, 1988, 55(3): 702–705.
[21] CHEN L C, LIU J, SUN J Q. Stationary response probability distribution of SDOF nonlinear stochastic systems [J]. Journal of Applied Mechanics, 2017, 84(5): 051006–051006 –8.
[22] CHEN L C, SUN J Q. The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems [J]. Communications in Nonlinear Science & Numerical Simulation, 2016, 41(12):1-10.
[23] CHEN L C, SUN J Q. The closed-form steady-state probability density function of van der pol oscillator under random excitations [J]. Journal of Applied Nonlinear Dynamics, 2016, 5(4):495-502.