周期和随机联合激励作用下滞回系统非平稳随机响应的一种近似方法

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摘要提出了一种用于求解非平稳随机和确定性谐波联合作用下，单自由度滞回系统非平稳响应的统计线性化方法。首先，在系统响应表示为确定性和零均值非平稳随机分量之和的基础上，将原滞回运动方程等效地化为两组耦合的、分别以确定性和随机动力响应为未知量的非线性微分方程。随后，利用统计线性化方法处理非平稳激励下的随机运动微分方程，导出关于随机响应分量二阶矩的Lyapunov微分方程。联立Lyapunov微分方程与确定性运动微分方程，并利用标准数值算法求解响应。最后，数值算例验证该方法的适用性和精度。
关键词：Bouc-Wen滞回模型；统计线性化；非平稳；周期和随机联合激励

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	孔凡1
	沈子恒1
	何卫2
	李书进1

关键词 ： Bouc-Wen滞回模型, 统计线性化, 非平稳, 周期和随机联合激励

Abstract：A statistical linearization method is proposed for determining the non-stationary response of a single-degree-of-freedom Bouc-Wen system subjected to a combined stochastic and periodic excitation. Specifically, first, representing the system response into a combination of a deterministic and of a zero-mean random component, the equation of motion is decomposed into a set of two non-linear differential equations, governing deterministic response and stochastic response, respectively. Next, the statistical linearization method is utilized to treat the non-linear stochastic differential equation, deriving the related Lyapunov differential equation in terms of response variance. The system response can be obtained by solving the Lyapunov differential equation and the deterministic equation of motion, simultaneously using standard numerical methods. Finally, pertinent numerical examples demonstrate the applicability and accuracy of the proposed method.
Key words: Bouc-Wen hysteresis model； statistical linearization；nonstationary； combined excitation

Key words： Bouc-Wen hysteresis model statistical linearization nonstationary combined excitation

收稿日期: 2021-04-08 出版日期: 2022-08-28

引用本文:

孔凡1，沈子恒1，何卫2，李书进1. 周期和随机联合激励作用下滞回系统非平稳随机响应的一种近似方法[J]. 振动与冲击, 2022, 41(16): 108-116.
KONG Fan1，SHEN Ziheng1，HE Wei2，LI Shujin1. An approximate approach for non-stationary stochastic response of a hysteretic system subjected to combined periodic and stochastic excitation. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(16): 108-116.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I16/108

[1] BOOTON R C. The analysis of nonlinear control systems with random inputs[C]//Proceedings of the Symposium on Nonlinear Circuit Analysis.New York:SNCA,1953.
[2] CAUGHEY T K. Equivalent linearization techniques[J]. Journal of the Acoustical Society of America, 1962, 35(11): 1706-1711.
[3] SPANOS P D. Stochastic linearization in structural dynamics[J]. Applied Mechanics Reviews, 1981, 34(1): 1-8.
[4] MILES R N. An approximate solution for the spectral response of Duffing's oscillator with random input[J]. Journal of Sound and Vibration, 1989, 132(1): 43-49.
[5] SOBIECHOWSKI C, SOCHA L. Statistical linearization of the Duffing oscillator under non-Gaussian external excitation[J]. Journal of Sound and Vibration, 2000, 231(1): 19-35.
[6] CAUGHEY T K. Response of Van Der Pol's oscillator to random excitation[J]. Journal of Applied Mechanics, 1959, 26(3):345-348.
[7] ASANO K, IWAN W D. An alternative approach to the random response of bilinear hysteretic systems[J]. Earthquake Engineering and Structural Dynamics, 1984, 12(2): 229-236.
[8] KONG F, SPANOS P D. Stochastic response of hysteresis system under combined periodic and stochastic excitation via the statistical linearization method[J]. Journal of Applied Mechanics, 2021, 88(5): 051008.
[9] KANAI K. Semi-empirical formula for the seismic characteristics of the ground motion[J]. Bulletin of the Earthquake Research Institute, University of Tokyo, 1957, 35(2): 308-325.
[10] CLOUGH R W，PENZIEN J．Dynamics of structure[M]．2nd ed．New York: McGraw Hill，1993．
[11] 欧进萍,牛荻涛,杜修力.设计用随机地震动的模型及其参数确定[J].地震工程与工程振动,1991(3):45-54.
OU Jinping, NIU Ditao, DU Xiuli. Random earthquake ground motion model and its parameter determination used in aseismic design[J]. Earthquake Engineering and Engineering Vibration, 1991(3):45-54.
[12] 彭凌云. 地震动随机模型及结构响应控制[D]. 北京:北京工业大学,2008.
[13] PRIESTLEY M B. Power spectral analysis of non-stationary random processes[J]. Journal of Sound and Vibration, 1967, 6(1): 86-97.
[14] WIRSCHING P H, YAO J T P. Monte Carlo study of seismic structural safety[J]. Journal of the Structural Division, 1971, 97(5): 1497-1519.
[15] HOWELL L J, LIN Y K. Response of flight vehicles to nonstationary atmospheric turbulence[J]. AIAA Journal, 1971, 9(11): 2201-2207.
[16] YANG J N. Nonstationary envelope process and first excursion probability[J]. Journal of Structural Mechanics, 1972, 1(2): 231-248.
[17] FUJIMORI Y, LIN Y K. Analysis of airplane response to nonstationary turbulence including wing bending flexibility[J]. AIAA Journal, 1973, 11(3): 334-339.
[18] ZHANG Z C, LIN J H, ZHANG Y H, et al. Non-stationary random vibration analysis for train–bridge systems subjected to horizontal earthquakes[J]. Engineering Structures, 2010, 32(11): 3571-3582.
[19] ABBAS A M, MANOHAR C S. Reliability-based vector nonstationary random critical earthquake excitations for parametrically excited systems[J]. Structural Safety, 2007, 29(1): 32-48.
[20] IWATSUBO T, KAWAHARA I, NAKAGAWA N, et al. Reliability design of rotating machine against earthquake excitation[J]. Bulletin of JSME, 1979, 22(173): 1632-1639.
[21] SONI A H, SRINIVASAN V. Seismic analysis of rotating mechanical systems[D]. Stillwater ：Oklahoma State University, 1984.
[22] LY B L. Seismic response of a gyroscopic system by the response spectrum method[C]//Transactions of the 8th International Conference on Structural Mechanics in Reactor Technology. Brussels：SMRT, 1985.
[23] MEGERLE B, STEPHEN RICE T, MCBEAN I, et al. Numerical and experimental investigation of the aerodynamic excitation of a model low-pressure steam turbine stage operating under low volume flow[J]. Journal of Engineering for Gas Turbines and Power, 2013, 135(1):012602.
[24] 江辉, 朱晞.脉冲型地震动模拟与隔震桥墩性能的能量分析[J]. 北方交通大学学报, 2004,28(4):6-11.
    JIANG Hui, ZHU Xi. Simulation of pulse-type earthquake excitation and energy performance of isolated bridge piers[J]. Journal of Northern Jiaotong University, 2004,28(4):6-11.
[25] 龚微, 熊世树.线性阻尼隔震与非线性隔震系统近断层地震反应分析[J]. 振动与冲击, 2016,35(24):108-114.
    GONG Wei, XIONG Shishu. Seismic response analysis of linear damping and nonlinear base-isolated systems under near-fault ground motion[J]. Jounal of Virbation and Shock, 2016,35(24):108-114.
[26]王亚楠, 李慧, 杜永峰. TMD-基础隔震混合控制体系在近场地震作用下的能量响应与减震效果分析[J]. 振动与冲击, 2014,33(4):204-209.
    WANG Yanan, LI Hui, DU Yongfeng. Energy response and anti-vibration effect analysis for a base-isolated structure with TMD under near-field earthquake base-isolated structure with TMD under near-field earthquake[J]. Jounal of Virbation and Shock, 2014,33(4):204-209.
[27] 孔凡, 韩仁杰, 张远进, 等.色噪声与确定性谐波联合激励下Bouc-Wen动力系统响应的统计线性化方法[J]. 振动工程学报，2022, 35(1)：82-92.
    KONG Fan, HAN Renjie, ZHANG Yuanjin, et al. Stochastic response of a hysteresis system subjected to combined periodic and colored noise excitation via the statistical linearization method[J]. Journal of Vibration Engineering，2022, 35(1)：82-92.
[28] ？？孔凡, 韩仁杰, 张远进.确定性周期与随机激励联合作用下非线性系统非平稳响应的统计线性化方法[J]. 振动工程学报:1-10[2021-07-23]. http://kns.cnki.net/kc
ms/detail/32.1349.TB.20210621.1715.002.html.
    KONG Fan, HAN Renjie, ZHANG Yuanjin. Non-stationary response of non-linear systems subjected to combined periodic and non-stationary stochastic excitation via the statistical linearization method[J]. Journal of Vibration Engineering:1-11[2021-07-23]. http://kns.cnki.
net/kcms/detail/32.1349.TB.20210621.1715.002.html