Investigation on the accuracy of the N2 method and the equivalent linearization procedure for different hysteretic models

In this paper, an extensive parametric study was carried out to evaluate the dynamic response of single degree of freedom (SDOF) systems with elasto-plastic and flag-shape hysteretic behaviour for three different dissipation capacities. Three sets of natural accelerograms were used, each one composed by at least 7 records which are on average spectrum-consistent in pseudo-acceleration, spectral displacement or both of them. All sets were also employed to draw the inelastic spectra for different ductility values. Such rigorous spectra were then compared with the approximated curves calculated using the N2 method and the Equivalent Linearization Procedure (ELP) based on the use of overdamped elastic spectra.The analyses demonstrate a general accuracy of the N2 method, which is mostly based on the ductility of the system, even for the hysteretic behaviour characterised by reduced energy dissipation. Larger discrepancies were found for systems with lower damping ratios and reduced fundamental periods. The ELP, which mainly depends upon the dissipated energy, led instead to overall slightly larger discrepancies than the N2 method, particularly for not dissipative and ductile systems, whereas the approximation is generally acceptable for elasto-plastic systems.     

非线性土木结构振动控制的逆系统方法

采用多变量非线性控制的逆系统理论,将多变量、非线性的复杂被控对象精确线性化成伪线性系统,对于该伪线性系统很容易基于线性系统理论设计综合最优控制器。克服了传统的非线性结构近似线性化控制方法不够精确的缺点,实现了非线性结构的动态精确线性化控制。给出了一个仿真实例,将其控制效果与一般的线性和近似线性化最优控制作了比较,达到同样控制效果时本方法所需控制力显著减小。     

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微种群遗传算法优化结构振动控制

本文将微种群遗传算法应用到结构振动控制中，用遗传算法优化控制器，以解决一类用经典线性反馈控制无法解决的半主动控制的优化问题，该方法提出将非线性控制问题线性化，导出了简化过程，然后利用遗传算法求解，它具有利用微种群遗传算法全局寻优，并且对目标函数的性态要求较少的特点，数值算例表明，本文方法是有效的。     

Studies on structural vibration control with MR dampers using μGA

A new approach to reducing the seismic response of spatial structures with magneto-rheological (MR) dampers is presented in this paper. The Genetic Algorithm with small populations (μGA) is used to optimize the control for the MR dampers to reduce structural vibration, which is difficult to achieve using classical optimal control. The advantages of μGA are the use of global properties and that fewer conditions are required to obtain the optimal function. Numerical results demonstrate the effectiveness of the proposed method in reducing the seismic response of structures.     

非线性二维转换模型的稳健总体最小二乘算法

针对应用线性最小二乘估计准则求解非线性平面转换模型参数时,通过定义间接参数将模型线性化的方法不能直接求解转换模型参数的问题,该文在非线性平面转换模型的基础上,建立线性模型,实现平面坐标的转换。为解决控制点已知坐标与观测坐标中均含有误差对转换参数求解的影响,对应用稳健总体最小二乘求解线性模型参数的算法进行讨论。最后,通过算例比较稳健总体最小二乘算法与最小二乘算法在抗差性方面的优势。结果表明,稳健总体最小二乘算法更适用于应用线性模型求解未知控制点的转换坐标。     

天津软弱土场地土层地震反应实例分析

对场地土层地震反应分析的主要方法进行介绍,在天津软弱土场地（Ⅳ类场地）上分别采用等效线性化和逐步积分的方法进行土层反应,并把土层反应得到的结果与天津地区Ⅳ类场地上的实际强震记录对比,发现等效线性化方法适用于天津软弱土场地土层地震反应。对软弱土场地土层地震反应结果进行分析,把该结果与GB50011—2010《建筑抗震设计规范》中相应的参数进行对比,分析两者之间的差别,为天津软弱土场地的抗震设防提供合理的建议。     

古河道对工程场地地震动参数的影响

以上海浦东机场二期航站楼软土场地为例,应用二维土体模型和一维土体模型分别计算了深覆盖土层的地震反应,讨论了古河道对场地地震动参数的影响。此外,在二维土层地震反应分析中,进一步对比了基岩面地震波行波输入和一致输入下,场地地震动参数的差异。     

Exact linearization of non-planar intermediary orbits in the satellite theory

In this paper we consider the reduction of the equations of motion for non-planar perturbed two body problems into linear form. It is seen that this can be easily accomplished for any element of the class of radial intermediaries to the satellite problem proposed by Deprit in 1981, since they have a functional dependence suitable for linearization. The transformation is worked out by using an adequate set of redundant variables. Four harmonic oscillators are obtained, of which two are coupled through gyroscopic terms. Their constant frequencies contain the secular contribution of the main problem of artificial satellite theory up to the order of the considered intermediary. Therefore, this result may well be interesting in relation to the study and prediction of accurate long-term solutions to satellite problems.     

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