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1.
针对平稳激励下线性结构随机地震动响应方差和谱矩时频域法无解析解或时域法解析解复杂的问题,提出了结构响应功率谱的二次正交化法,并成功获得线性结构基于李鸿晶随机地震谱的系列响应(结构层位移和层间位移)的 0~2 阶谱矩和方差的简明封闭解。综合虚拟激励法和复模态方法,提出了线性结构频率响应特征值函数的二次正交法,即将频率响应特征值函数表示为振动复特征值和频域变量二次方和的线性组合;以李鸿晶随机地震动谱为例,基于留数定律获得该谱的二次正交式,进而获得结构地震动系列响应功率谱的二次正交式;获得了建筑结构随机地震动系列响应方差及 0~2 阶谱矩的统一简明封闭解。利用本文方法对一单自由度结构和一多自由度TMD 耗能结构地震动响应进行分析,并与虚拟激励法进行了对比研究,结果表明本文所提方法为封闭解且可用于验证虚拟激励法谱矩分析时的精度。此外,本文方法可适用于各种线性结构基于各类平稳随机地震谱的随机响应封闭解的分析。  相似文献   

2.
非线性流滞阻尼器耗能结构随机地震响应和首超时间分析   总被引:3,自引:0,他引:3  
对非线性流滞阻尼器耗能结构在Kanai-Tajimi谱地震激励下的随机响应及其随机失效时间和动力可靠性进行了系统研究。首先建立了结构的非线性运动方程;然后,基于随机平均法,将结构响应幅值近似为一维markov扩散过程,获得了扩散过程漂移系数和扩散系数的解析表达式;其次,利用扩散过程与FPK方程的对应关系,获得了幅值平稳概率密度函数和幅值任意阶矩的解析表达式;再次,利用幅值与结构位移和速度的相互转化关系,获得了结构位移与速度的平稳联合概率密度函数和位移、速度方差以及位移期望穿越率的解析表达式;最后,利用扩散过程的后向Kolmogrov方程,基于首超失效模型,建立了结构动力可靠性函数方程和结构随机失效时间统计矩方程,并利用一维扩散过程的边界分类性质,将统计矩方程的奇异定性边界条件转化为等价的定量边界条件,进而获得了失效时间任意阶统计矩的解析解,并利用此矩,对结构动力可靠性和失效时间概率分布函数进行了近似分析,给出了算例,从而建立了结构非线性随机地震响应及其随机失效时间和动力可靠性的分析方法。  相似文献   

3.
本文研究了一类重组细胞恒化培养的连续时间Markov链模型.首先利用累积母函数表示出数字特征所满足的矩方程,然后通过对数正态分布近似的矩封闭技术得到了封闭后的矩方程,最后运用Euler-Maruyama方法构建了时间和状态都是连续的It随机微分方程.为了验证矩封闭的合理性,利用数值模拟给出了确定模型、随机模型和矩封闭后的方程的比较,并分析了重组细胞的变化趋势,结果表明其随机游走趋势与相应确定性模型是一致的.  相似文献   

4.
提出了一种新的计算弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法,它是一种时域复模态分析方法。利用此方法获得了弹性-粘弹性复合结构在白噪声、滤过白噪声等典型平稳随机激励下随机响应的各阶谱矩的解析表达式,分析了粘弹性对各阶谱矩的影响。此计算方法简便、易用,无论单自由度或多自由度系统均适用,为进一步研究弹性-粘弹性复合结构在随机激励下的可靠性打下良好基础。  相似文献   

5.
研究了受非高斯色噪声参激的Van der Pol-Duffing振子在平凡解邻域内的随机稳定性.首先利用物理学中已有的经典结果,经过近似处理,将非高斯色噪声简化为Ornstein-Uhlenbeck过程,然后通过尺度变换和线性随机变换得到了与系统响应的矩Lyapunov指数相关的特征方程,通过摄动法求得了矩Lyapunov指数、稳定指标、最大Lyapunov指数的二阶近似解,给出了系统响应p阶矩渐进稳定和几乎肯定渐进稳定的条件.最后通过对数值结果的分析,讨论了噪声参数及系统参数对系统响应矩稳定性的影响.  相似文献   

6.
由于随机微分方程(SDE)的解析解求解困难,所以推导SDE解的不等式估计式是十分必要的.在随机系统的稳定性分析和控制设计中,李亚普诺夫函数常常采用二次型函数.本文把SDE解的传统的欧几里德范数形式估计式推广到SDE解的二次型估计式,包括解的矩估计和几乎必然估计.我们分别在加权线性增长条件和加权单边增长条件下给出了二次型矩估计式以及样本李亚普诺夫指数的上界表达式.  相似文献   

7.
在基础隔震层设置侧向黏弹性阻尼器组成混合基础隔震体系,可有效降低基础隔震结构过大的侧移,然而此类结构基于Clough-Penzien谱(C-P谱)的随机地震动响应解法较为复杂,提出了一种简明解析法。首先利用滤波方程,将混合基础隔震耗能结构基于C-P谱的地震动精确的转化为基于白噪声激励的地震动;其次运用复模态法获得耗能结构随机地震动系列响应(相对于地面位移及速度、层间位移及其变化率)协方差的统一简明表达式;然后基于随机振动理论,获得耗能结构地震动系列响应的方差及0-2阶谱矩的简明解析解;最后研究了基于首超破坏准的混合基础隔震结构的动力可靠度。将该方法应用于一算例,并与虚拟激励法进行对比分析,研究表明:该方法计算响应方差和谱矩为解析解,而虚拟激励法是数值解;同时也验证了混合基础隔震耗能结构能有效降低结构侧移及提高结构体系的可靠度。  相似文献   

8.
基于随机振动理论,建立了梁结构在随机地震动作用下的振动方程。将地震地面运动考虑为随机过程,利用地震响应谱方法,推导了结构在随机地震动作用下最大位移响应的计算过程。以某简支梁和悬臂梁为例,推导了其位移功率谱密度函数、峰值位移功率谱密度函数及最大位移反应的功率谱密度函数。  相似文献   

9.
频域法在计算线性系统随机响应时应用较广泛,但其显著缺点为:计算多自由度动力系统随机响应功率谱无显示封闭解;获得结构响应的方差和谱矩需要数值积分,分析精度和效率受积分步长和积分区间影响较大。基于以上问题,研究了六参数黏弹性耗能多自由度结构基于Kanai-Tajimi谱地震作用下平稳响应的解析解法。运用该方法对一榀5层建筑结构进行分析,获得了线性多自由度耗能结构地震动系列响应方差及0~2阶谱矩的简明封闭解,并将其与虚拟激励法进行对比分析。研究表明,简明封闭解法是一种非常有效的计算线性多自由度系统随机稳态响应的简明解法。  相似文献   

10.
针对设置广义Maxwell阻尼器多自由度耗能结构在欧进萍谱激励下响应分析较复杂的问题,提出了一种求解系统响应简洁的解析解法。将广义Maxwell阻尼器本构方程、原结构运动方程与欧进萍谱滤波方程联立,重构结构运动方程;采用复模态法将其解耦,得到结构位移及结构速度、层间位移及层间速度、阻尼器受力及其变化率等响应基于白噪声激励的统一杜哈梅积分表达式;根据功率谱密度函数与其协方差函数的Wiener-Khinchin关系,获得了耗能结构及阻尼器响应谱矩的简明解析解。算例通过与虚拟激励法进行对比,表明了该方法的正确性,同时也具有更高计算效率的优点。  相似文献   

11.
分析研究球对称压电壳在边界随机激励下的最优控制问题。给出压电壳的机电动力学方程、应力和电位移表达式,建立其随机最优控制问题方程;通过电势积分转化为机械振动控制方程。通过位移变换和Galerkin法,导出关于模态位移的多自由度振动最优控制方程。根据随机动态规划原理,建立HJB方程,得到压电壳的最优控制电势;并给出受控壳系统的频响函数、响应谱密度和相关函数等表达式,以计算其随机响应。最后给出数值结果,显示压电壳的随机最优控制效果。  相似文献   

12.
An Adomian decomposition based mathematical framework to derive the mean square responses of nonlinear structural systems subjected to stochastic excitation is presented. The exact mean square response estimation of certain class of nonlinear stochastic systems is achieved using Fokker–Planck–Kolmogorov (FPK) equations resulting in analytical expressions or using Monte Carlo simulations. However, for most of the nonlinear systems, the response estimation using Monte Carlo simulations is computationally expensive, and, also, obtaining solution of FPK equation is mathematically exhaustive owing to the requirement to solve a stochastic partial differential equation. In this context, the present work proposes an Adomian decomposition based formalism to derive semi-analytical expressions for the second order response statistics. Further, a derivative matching based moment approximation technique is employed to reduce the higher order moments in nonlinear systems into functions of lower order moments without resorting to any sort of linearization. Three case studies consisting of Duffing oscillator with negative stiffness, Rayleigh Van-der Pol oscillator and a Pendulum tuned mass damper inerter system with linear auxiliary spring–damper arrangement subjected to white noise excitation are undertaken. The accuracy of the closed form expressions derived using the proposed framework is established by comparing the mean square responses of the systems with the exact solutions. The results demonstrate the robustness of the proposed framework for accurate statistical analysis of nonlinear systems under stochastic excitation.  相似文献   

13.
提出基于固定界面子结构模态的结构随机响应精确综合方法。首先用固定界面子结构的中阶模态与精确剩余约束模态表达子结构频域位移;再利用界面力与位移的协调关系进一步消去界面自由度,建立双协调的精确缩聚变换;然后根据里兹法,得到结构精确综合的广义频响函数;并由此独立地计算各子结构的功率谱密度,进一步得到其均方值等响应统计;最后通过数值结果验证该方法的综合能力与准确性。  相似文献   

14.
不均匀随机参数桁架结构的随机反应分析   总被引:1,自引:1,他引:0  
以随机荷载作用下的不均匀随机参数桁架结构为研究对象,提出了求解结构反应数字特征的矩法。从结构有限元方程出发,推导出结构刚度矩阵对各单元的弹性模量、横截面积以及各节点坐标的导数,进一步导得结构位移反应对各随机参数的敏度。利用随机变量函数的矩法,导出了结构位移反应的均值和方差,依据单元位移应力的转换表达式,分析了应力反应的均值和方差。算例表明,结构反应的方差取决于各随机参数的分散性和参数间的相关性。  相似文献   

15.
A method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.  相似文献   

16.
This paper presents a new, univariate dimension-reduction method for calculating statistical moments of response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of a multi-dimensional response function into multiple one-dimensional functions, an approximation of response moments by moments of single random variables, and a moment-based quadrature rule for numerical integration. The resultant moment equations entail evaluating N number of one-dimensional integrals, which is substantially simpler and more efficient than performing one N-dimensional integration. The proposed method neither requires the calculation of partial derivatives of response, nor the inversion of random matrices, as compared with commonly used Taylor expansion/perturbation methods and Neumann expansion methods, respectively. Nine numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the proposed method. Results indicate that the univariate dimension-reduction method provides more accurate estimates of statistical moments or multidimensional integration than first- and second-order Taylor expansion methods, the second-order polynomial chaos expansion method, the second-order Neumann expansion method, statistically equivalent solutions, the quasi-Monte Carlo simulation, and the point estimate method. While the accuracy of the univariate dimension-reduction method is comparable to that of the fourth-order Neumann expansion, a comparison of CPU time suggests that the former is computationally far more efficient than the latter.  相似文献   

17.
This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

18.
采用概率密度函数和数值模拟的方法研究随机横浪中船舶的混沌运动特性和发生混沌运动的临界参数条件。综合考虑非线性阻尼、非线性恢复力矩以及白噪声横浪激励,建立了船舶的横摇非线性随机微分方程。用随机Melnikov均方准则确定混沌运动的系统参数域后,应用路径积分法求解随机微分方程得到了响应的概率密度函数。研究发现:当噪声强度大于混沌临界值时,船舶出现随机混沌运动;对于高的白噪声激励强度,系统响应有两种较大可能的状态并在这两个状态间随机跳跃,这时船舶的运动不稳定并可能发生倾覆。  相似文献   

19.
Using non-orthogonal polynomial expansions, a recursive approach is proposed for the random response analysis of structures under static loads involving random properties of materials, external loads, and structural geometries. In the present formulation, non-orthogonal polynomial expansions are utilized to express the unknown responses of random structural systems. Combining the high-order perturbation techniques and finite element method, a series of deterministic recursive equations is set up. The solutions of the recursive equations can be explicitly expressed through the adoption of special mathematical operators. Furthermore, the Galerkin method is utilized to modify the obtained coefficients for enhancing the convergence rate of computational outputs. In the post-processing of results, the first- and second-order statistical moments can be quickly obtained using the relationship matrix between the orthogonal and the non-orthogonal polynomials. Two linear static problems and a geometrical nonlinear problem are investigated as numerical examples in order to illustrate the performance of the proposed method. Computational results show that the proposed method speeds up the convergence rate and has the same accuracy as the spectral finite element method at a much lower computational cost, also, a comparison with the stochastic reduced basis method shows that the new method is effective for dealing with complex random problems.  相似文献   

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