考虑参数不确定的系统固有频率统计分析
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- 英文论文题名：Statistical Analysis of Natural Frequency of the System with Parameter Uncertainties
- 论文作者：高超 ; 李亚轩 ; 肖斌 ; 邱瑞 ; 张艾萍
- 英文论文作者：GAO Chao ; LI Ya-xuan ; XIAO Bin ; QIU Rui ; ZHANG Ai-ping ; School of Energy and Power Engineering ; Northeast Dianli University ; China Power Engineering Consulting Group Northeast Electric Power Design Institute Co. ; Ltd
- 年：2016
- 作者机构：东北电力大学能源与动力工程学院;中国电力工程顾问集团东北电力设计院有限公司;
- 论文关键词：固有频率 ; 参数不确定性 ; 随机本征值 ; 正交多项式展开 ; Monte-Carlo模拟
- 英文论文关键词：natural frequency ; parameter uncertainty ; random eigenvalue ; orthogonal polynomial expansion ; Monte Carlo simulation
- 会议召开时间：2016-07-28
- 会议录名称：第二十七届全国振动与噪声应用学术会议论文集
- 语种：中文
- 分类号：TB12
- 学会代码：ZDZD
- 会议名称：第二十七届全国振动与噪声应用学术会议
- 会议地点：中国黑龙江哈尔滨
- 主办单位：中国振动工程学会振动与噪声控制专业委员会
- 学会名称：中国振动工程学会振动与噪声控制专业委员会
- 页数：6
- 文件大小：1724k
- 原文格式：D
- 会议级别：全国
摘要
在实际结构动力系统中,固有频率作为结构动力特征参数,是系统设计、结构分析和稳定性、敏感度分析中一个关键参数,而考虑系统不确定性时其具有随机性特征。为此,针对随机系统固有频率,在系统质量、刚度均服从Gauss分布条件下,利用Fourier-Hermite多项式展开,以及通过广义模型降维、多重Gauss-Hermite数值积分的方法确定展开系数,以获得其显式正交多项式函数形式,并通过嵌入局部Monte Carlo模拟分析系统固有频率统计特征。数值仿真结果表明:与Monte Carlo模拟结果相比,提出的方法能够获得较一致统计分析结果;将其应用于具有参数不确定的动力系统中,能够实现其固有频率的统计特征。
In the practical structural dynamic system,as one of the structural dynamic characteristic parameters,natural frequency is a key parameter of system design,structure analysis and stability,sensitivity analysis.And when considering the uncertainties of the system,it has the characteristics of randomness.Therefore,under the condition of that mass and stiffness of the system obey Gauss distribution,statistical characteristics of the natural frequency of stochastic systems are analyzed by embedding the local Monte Carlo simulation,which emply the Fourier-Hermite polynomial expansion,generalized ROM and multi-dimensional Gauss-Hermite quadrature to determine expansion coefficients and to obtain the explicit orthogonal polynomial function of them.Numerical simulation results show that the proposed method can obtain a more consistent statistical analysis compared with the Monte Carlo simulation results;It can be applied to the dynamic system with uncertain parameters,and the statistical characteristics of the natural frequency can be realized.
In the practical structural dynamic system,as one of the structural dynamic characteristic parameters,natural frequency is a key parameter of system design,structure analysis and stability,sensitivity analysis.And when considering the uncertainties of the system,it has the characteristics of randomness.Therefore,under the condition of that mass and stiffness of the system obey Gauss distribution,statistical characteristics of the natural frequency of stochastic systems are analyzed by embedding the local Monte Carlo simulation,which emply the Fourier-Hermite polynomial expansion,generalized ROM and multi-dimensional Gauss-Hermite quadrature to determine expansion coefficients and to obtain the explicit orthogonal polynomial function of them.Numerical simulation results show that the proposed method can obtain a more consistent statistical analysis compared with the Monte Carlo simulation results;It can be applied to the dynamic system with uncertain parameters,and the statistical characteristics of the natural frequency can be realized.
引文
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[11]陈杰春,张恒,赵丽萍.基于蒙特卡罗方法的边界检测不确定度估计[J].东北电力大学学报,2012,32(3):75-78.
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[16]李庆扬,王能超,易大义.数值分析[M].第5版.北京:清华大学出版社,2008.
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[2]张义民,刘巧伶,闻邦椿.多自由度非线性随机参数振动系统响应分析的概率摄动有限元法[J].计算力学学报,2003(01):8-11.
[3]车星儒,白国华,李国庆,等.计及不确定因素影响的交直流系统可用输电能力评估[J].东北电力大学学报,2014,34(1):52-58.
[4]Choi K-M,Cho S-W,Ko M-G,et al.Higher order eigensensitivity analysis of damped systems with repeated eigenvalues[J].Computers&structures,2004,82(1):63-69.
[5]黄超,吕祥照,安荣涛.基于偏微分方程数值方法与边界条件的电机转子振动固有频率计算与试验测量[J].东北电力大学学报,2013,33(3):52-54.
[6]Adhikari S,Friswell M.Random matrix eigenvalue problems in structural dynamics[J].International Journal for Numerical Methods in Engineering,2007,69(3):562-591.
[7]Mehta ML.Random matrices[M].Access Online via Elsevier,2004.
[8]Kapur JN,Kesavan HK.Entropy optimization principles with applications[M].Academic Pr,1992.
[9]Pascual B,Adhikari S.Hybrid perturbation-Polynomial Chaos approaches to the random algebraic eigenvalue problem[J].Computer Methods in Applied Mechanics and Engineering,2012,217:153-167
[10]Ghosh D,Ghanem R.Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions[J].International journal for numerical methods in engineering,2008,73(2):162-184.
[11]陈杰春,张恒,赵丽萍.基于蒙特卡罗方法的边界检测不确定度估计[J].东北电力大学学报,2012,32(3):75-78.
[12]Wright M,Weaver R.New Directions in Linear Acoustics and Vibration:Quantum Chaos,Random Matrix Theory,and Complexity[M].Cambridge University Press,2006.
[13]Rabitz H,Ali??.F.General foundations of high-dimensional model representations[J].Journal of Mathematical Chemistry,1999,25(2-3):197-233.
[14]Rahman S.A polynomial dimensional decomposition for stochastic computing[J].International Journal for Numerical Methods in Engineering,2008,76(13):2091-2116.
[15]Xu H,Rahman S.A generalized dimension-reduction method for multidimensional integration in stochastic mechanics[J].International Journal for Numerical Methods in Engineering,2004,61(12):1992-2019.
[16]李庆扬,王能超,易大义.数值分析[M].第5版.北京:清华大学出版社,2008.
[17]Adhikari S,Friswell M I.Random eigenvalue problems in structural dynamics[C]//Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics&Materials Conference,Palm Springs,California.[Links].2004.