非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法
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摘要
应用复振型分解方法,将非比例阻尼线性体系在地震作用下的动力方程求解问题转化为若干个广义复振子的求解与叠加问题。通过假定地震地面运动为一零均值的平稳随机激励,应用虚拟激励法原理,推导得到了广义复振子动力坐标的解析计算公式,进而得到了以复振型为基础的非比例阻尼线性体系随机地震响应计算的一般实数解析解答。算例证实了这种方法的可靠性及高效率。
In terms of the complex mode superposition method,the motion equations of general multiple degrees of freedom(MDOF) discrete system can be transferred into the combination of many complex oscillators.Assuming that the earthquake ground motion is a zero-mean-valued stationary random excitation,the analytic solutions of these complex oscillators are derived in virtue of the principle of pseudo-excitation method;then a delicate general solution of non-proportionally damped MDOF systems subjected to earthquake ground motion,complete in real value form,is presented in this paper.Comparing with the traditional pesudo-excitation method,to ensure the accuracy in the dynamic response analysis of non-proportionally damped MDOF systems,the less modes in complex conjugate pairs is required in using the proposed pseudo-excitation method in this paper,so that the computing efficiency is mproved greatly.A numerical example is given to demonstrate the validity and efficiency of the algorithm.
In terms of the complex mode superposition method,the motion equations of general multiple degrees of freedom(MDOF) discrete system can be transferred into the combination of many complex oscillators.Assuming that the earthquake ground motion is a zero-mean-valued stationary random excitation,the analytic solutions of these complex oscillators are derived in virtue of the principle of pseudo-excitation method;then a delicate general solution of non-proportionally damped MDOF systems subjected to earthquake ground motion,complete in real value form,is presented in this paper.Comparing with the traditional pesudo-excitation method,to ensure the accuracy in the dynamic response analysis of non-proportionally damped MDOF systems,the less modes in complex conjugate pairs is required in using the proposed pseudo-excitation method in this paper,so that the computing efficiency is mproved greatly.A numerical example is given to demonstrate the validity and efficiency of the algorithm.
引文
[1]ZHOU Xi-yuan.Complex mode superposition algo-rithm for seismic responses of non-classically dampedlinear MDOF system[J].Journal of Earthquake En-gineering,2004,8(4):597-641.
[2]林家浩.随机地震响应的确定性算法[J].地震工程与工程振动,1985,5(1):89-94.(LIN Jia-hao.A deter-ministic method for the computation of stochasticearthquake response[J].Earthquake Engineeringand Engineering Vibration,1985,5(1):89-94.(inChinese))
[3]LIN J H.A fast CQC algorithm of PSD matrices forseismic responses[J].Computers and Structures,1992,44(3):683-687.
[4]LIN J H,ZHAO Y,ZHANG Y H.Accurate andhighly efficient algorithms for structural stationary/non-stationary random responses[J].Computer Meth-ods in Applied Mechanics and Engineering,2001,191(1-2):103-11.
[5]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(4):131-136.(ZHONG Wan-xie.On precise time-integration method for structural dy-narnics[J].Joumal of Dalian University of Tech-nology,1994,34(2):131-136.(in Chinese))
[6]汪梦甫,区达光.精细积分方法的评估与改进[J].计算力学学报,2004,21(6):728-733.(WANG Meng-fu,OU Da-guang.Assessment and improvement ofprecise time step integration method[J].Journal ofComputational Mechanics,2004,21(6):728-733.(inChinese))
[7]汪梦甫.高层建筑结构动力分析的Lanczos向量叠加法及其应用[J].计算力学学报,1999,16(1):115-119.(WANG Meng-fu.Improvement of Lanczos vec-tor superposition method and its application to dy-namic analysis of tall building[J].Journal of Compu-tational Mechanics,1999,16(1):115-119.(in Chi-nese))
[8]汪梦甫.Ritz向量叠加法的改进及其应用[J].湖南大学学报,1996,23(3):110-118.(WANG Meng-fu.Im-provement of Ritz vector superposition method and itsapplication[J].Journal of Hunan University,1996,23(3):110-118.(in Chinese))
[2]林家浩.随机地震响应的确定性算法[J].地震工程与工程振动,1985,5(1):89-94.(LIN Jia-hao.A deter-ministic method for the computation of stochasticearthquake response[J].Earthquake Engineeringand Engineering Vibration,1985,5(1):89-94.(inChinese))
[3]LIN J H.A fast CQC algorithm of PSD matrices forseismic responses[J].Computers and Structures,1992,44(3):683-687.
[4]LIN J H,ZHAO Y,ZHANG Y H.Accurate andhighly efficient algorithms for structural stationary/non-stationary random responses[J].Computer Meth-ods in Applied Mechanics and Engineering,2001,191(1-2):103-11.
[5]钟万勰.结构动力方程的精细时程积分[J].大连理工大学学报,1994,34(4):131-136.(ZHONG Wan-xie.On precise time-integration method for structural dy-narnics[J].Joumal of Dalian University of Tech-nology,1994,34(2):131-136.(in Chinese))
[6]汪梦甫,区达光.精细积分方法的评估与改进[J].计算力学学报,2004,21(6):728-733.(WANG Meng-fu,OU Da-guang.Assessment and improvement ofprecise time step integration method[J].Journal ofComputational Mechanics,2004,21(6):728-733.(inChinese))
[7]汪梦甫.高层建筑结构动力分析的Lanczos向量叠加法及其应用[J].计算力学学报,1999,16(1):115-119.(WANG Meng-fu.Improvement of Lanczos vec-tor superposition method and its application to dy-namic analysis of tall building[J].Journal of Compu-tational Mechanics,1999,16(1):115-119.(in Chi-nese))
[8]汪梦甫.Ritz向量叠加法的改进及其应用[J].湖南大学学报,1996,23(3):110-118.(WANG Meng-fu.Im-provement of Ritz vector superposition method and itsapplication[J].Journal of Hunan University,1996,23(3):110-118.(in Chinese))
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