地震作用的相关性对结构瞬态响应的影响
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摘要
地震作用一般分解为水平运动分量和竖向运动分量,在这两个运动分量的作用下,结构发生大变形时,可能会经历由地震运动分量演变的外部激励和参数激励过程。由于运动分量间的相关性,推导出实际上这两个激励过程也是相关的,而且是完全相关的,但在过去的研究中,为了简化分析,常常假设这两个激励过程是完全独立的。该文以高斯白噪声和过滤高斯白噪声过程模拟地震动过程,以某一单层框架结构为研究对象,采用累积矩截断法,分析高斯白噪声和过滤高斯白噪声这两种地震动激励下单层框架结构的非平稳地震响应。同时考虑地震动分量间的相关性,得到更为精细化的结构随机地震响应,并分析这种相关性对结构响应的影响。结果表明:将地震动作用模拟为更接近实际的过滤高斯白噪声过程时,地震作用相关性对结构响应的影响更为明显,更为不可忽略。
Seismic action is generally decomposed into horizontal motion components and vertical motion components. Under the action of these two motion components, external excitation and parametric excitation processes may be experienced when the structure undergoes large deformation. Although these two incentive processes are completely related, it is often assumed that the two incentive processes are completely independent in the past research in order to simplify the analysis. A single-layer frame structure is studied. The correlation between external excitation and parameter excitation is considered, and a more accurate structural random seismic response is obtained. The influence of this correlation on the structural response is analyzed. Starting from the vibration equation of the structure, the cumulative moment truncation method is used to solve the non-stationary seismic response of a single-layer frame structure under the excitation of Gaussian white noise and filtered white noise. The results show that when the simulated ground motion is closer to the actual Gaussian white noise process, the influence of seismic correlation on the structural response is more obvious.
Seismic action is generally decomposed into horizontal motion components and vertical motion components. Under the action of these two motion components, external excitation and parametric excitation processes may be experienced when the structure undergoes large deformation. Although these two incentive processes are completely related, it is often assumed that the two incentive processes are completely independent in the past research in order to simplify the analysis. A single-layer frame structure is studied. The correlation between external excitation and parameter excitation is considered, and a more accurate structural random seismic response is obtained. The influence of this correlation on the structural response is analyzed. Starting from the vibration equation of the structure, the cumulative moment truncation method is used to solve the non-stationary seismic response of a single-layer frame structure under the excitation of Gaussian white noise and filtered white noise. The results show that when the simulated ground motion is closer to the actual Gaussian white noise process, the influence of seismic correlation on the structural response is more obvious.
引文
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[2]Kanai K.Semi-empirical formula for the seismic characteristics of the ground[J].Earthquake Research Institute,the University of Tokyo,1957,35(2):309―325.
[3]Ruiz P,Penzien J.Probabilistic study of the behavior of structures during earthquakes[R].Earthquake Engineering Research Center,UCB,CA,Report No.EERC 69―03,1969.
[4]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,1991,11(3):45―54.Ou Jinping,Niu Ditao,Du Xiuli.Random earthquake ground motion model and its parameter determination used in asismic design[J].Earthquake Engineering and Engineering Vibration,1991,11(3):45―54.(in Chinese)
[5]杜修力,陈厚群.地震动随机模型及其参数确定方法[J].地震工程与工程振动,1994,14(4):1―5.Du Xiuli,Chen Houxiong.Random simulation and its parameter determination method of earthquake ground motion[J].Earthquake Engineering and Engineering Vibration,1994,14(4):1―5.(in Chinese)
[6]赖明,叶天义,李英民.地震动的双重过滤白噪声模型[J].土木工程学报,1995,28(6):60―66.Lai Ming,Ye Tianyi,Li Yingmin.Multi-filtered white noise model for ground motion[J].Chinese Journal of Civil Engineering,1995,28(6):60―66.(in Chinese)
[7]Deng Weihua.Numerical algorithm for the time fractional Fokker-Planck equation[J].Journal of Computational Physics,2007,227(2):1510―1522.
[8]戚鲁媛,徐伟,高维廷.色噪声激励Rayleigh-Duffing振子瞬态响应及最优有界控制[J].工程力学,2013,30(12):24―30.Qi Luyuan,Xu Wei,Gao Weiting.Transient response and optimal bounded control of colored noise excited Rayleigh-Duffing oscillator[J].Engineering Mechanics,2013,30(12):24―30.(in Chinese)
[9]杨杰,马萌璠,王旭.随机结构动力可靠度计算的条件概率方法[J].工程力学,2018,A01(增刊1):17―21.Yang Jie,Ma Mengfan,Wang Xu.Conditional probability method for dynamic reliability calculation of random structures[J].Engineering Mechanics,2018,A01(Suppl 1):17―21.(in Chinese)
[10]Xie W C.Moment Lyapunov exponents of a two-dimensional system under combined harmonic and real noise excitations[J].Journal of Sound&Vibration,2007,303(1):109―134.
[11]Xie W C.Moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation[J].Journal of Sound&Vibration,2002,239(1):139―155.
[12]Loh C H,Ma M J.Reliability assessment of structure subjected to horizontal-vertical random earthquake excitations[J].Structural Safety,1997,19(1):153―168.
[13]Bobryk R V,Chrzeszczyk A.Stability regions for Mathieu equation with imperfect periodicity[J].Physics Letters A,2009,373(39):3532―3535.
[14]Paola M D,Floris C.Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes[J].Computers&Structures,2008,86(11/12):1285―1296.
[15]Su Z,Falzarano J M.Gaussian and non-Gaussian cumulant neglect application to large amplitude rolling in random waves[J].International Shipbuilding Progress,2011,58(2):97―113.
[16]Floris C.Mean square stability of a second-order parametric linear system excited by a colored Gaussian noise[J].Journal of Sound&Vibration,2015,336(1):82―95.
[17]刘章军,王磊,黄帅.非平稳随机地震作用的结构整体可靠度分析[J].工程力学,2015(12):225―232.Liu Zhangjun,Wang Lei,Huang Shuai.Structural reliability analysis of non-stationary random earthquakes[J].Engineering Mechanics,2015(12):225―232.(in Chinese)
[18]Lin Y K,Shih T Y.Column response to horizontal-vertical earthquakes[J].Journal of the Engineering Mechanics Division,1980,106(6):1099―1109.
[19]李创第,李暾.结构在水平与竖向随机地震同时作用下的相关函数和谱密度[J].工程力学,2008,25(8):156―163.Li Chuangdi,Li Tun.Correlation function and spectral density of structures under horizontal and vertical random earthquakes[J].Engineering Mechanics,2008,25(8):156―163.(in Chinese)
[20]Dimentberg M,Bucher C.Combinational parametric resonance under imperfectly periodic excitation[J].Journal of Sound&Vibration,2012,331(19):4373―4378.
[21]Guo S S.Probabilistic solutions of stochastic oscillators excited by correlated external and parametric white noises[J].Journal of Vibration&Acoustics,2014,136(3):031003.
[22]Guo S S,Er G K,Chi C L.Probabilistic solutions of nonlinear oscillators excited by correlated external and velocity-parametric Gaussian white noises[J].Nonlinear Dynamics,2014,77(3):597―604.
[23]李创第,邹万杰,黄天立,等.结构在水平与竖向地震同时作用的非平稳响应[J].土木工程学报,2005,38(6):25―34.Li Chuangdi,Zou Wanjie,Huang Tianli.The nonstationary response of structure to horizontal and vertical earthquakes[J].China Civil Engineering Journal,2005,38(6):25―34.(in Chinese)
[24]Joseph Emans,Marian Wiercigroch.Cumulative effect of structural nonlinearities:chaotic dynamics of cantilever beam system with impacts[J].Chaos,Solitons and Fractals,2005(23):1661―1670.
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