用虚拟激励法求解非比例阻尼线性体系的非平稳随机地震响应
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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非平稳随机激励,应用虚拟激励法原理,推导得到了广义复振子动力坐标计算的一般公式,进而得到了非比例阻尼线性体系非平稳随机地震响应计算的一般解答。由于可以选择少量共轭复振型的影响进行计算,对于大型复杂非比例阻尼结构,其随机地震响应计算工作量可以大幅度减小。算例证实了这种方法的可靠性及可行性。
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 non-stationary random excitation, the higher accuracy numerical algorithm of these complex oscillators were developed in virtue of the principle of pseudo-excitation method. A delicate general solution of non-proportional damped MDOF systems subjected to an earthquake ground motion, completely in real value form, was presented. Numerical examples are 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 non-stationary random excitation, the higher accuracy numerical algorithm of these complex oscillators were developed in virtue of the principle of pseudo-excitation method. A delicate general solution of non-proportional damped MDOF systems subjected to an earthquake ground motion, completely in real value form, was presented. Numerical examples are given to demonstrate the validity and efficiency of the algorithm.
引文
[1] Zhou Xiyuan. Complex mode superposition algorithm for seismic responses of non-classically damped linear MDOF system[J]. Journal of Earthquake Engineering, 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．
[3] Lin J H. A fast CQC algorithm of PSD matrices for seismic responses[J]. Computers and Structures 1992, 44(3) :683 - 687.
[4] Lin J H, Zhao Y, Zhang Y H. Accurate and highly efficient algorithms for structural stationary/non-stationary random responses[J]. Computer Methods 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．
[6] Mengfu Wang, Au F T K. Assessment and improvement of precise time step integration method[J]. Computers and Structures, 2006, 84(12):779-786.
[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．
[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．
[3] Lin J H. A fast CQC algorithm of PSD matrices for seismic responses[J]. Computers and Structures 1992, 44(3) :683 - 687.
[4] Lin J H, Zhao Y, Zhang Y H. Accurate and highly efficient algorithms for structural stationary/non-stationary random responses[J]. Computer Methods 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．
[6] Mengfu Wang, Au F T K. Assessment and improvement of precise time step integration method[J]. Computers and Structures, 2006, 84(12):779-786.
[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．