用于检测同相轴的Duffing型系统恢复力项的讨论

在用于检测同相轴的Duffing型系统中,非线性恢复力项的选取至关重要.针对具有不同非线性恢复力项的混沌系统,本文首先就非线性恢复力项的来源进行了说明,通过对哈密顿系统和耗散系统的仿真实验分析,以及理论推导,确定了势能—哈密顿多项式方程中可用于混沌振子检测系统的各项幂次和各项系数组合关系,即非线性恢复力项的选取规则:幂次最高项为奇次,其系数大于零.     

微弱正弦信号检测模型混沌解的判定

运用Melnikov方法就混沌检测模型的混沌判据问题进行研究，证明并推导该数学模型为非线性混沌系统及系统出现混沌状的临界值。为正弦信号的混沌检测和混沌振子法用于准周期信号检测提供理论依据，也为从低信噪比地震勘探资料中提取有效信息建立理论基础。     

关于地震震级-频度关系式及其非线性项的讨论

研究了震级频度关系式中非线性项产生的原因,指出由于地震孕育过程是非线性的,很多地震现象都服从分形和混沌规律,因此传统的震级频度关系式中应含有非线性项,才能全面描述地震过程的非线性规律．得出了新的含有非线性项的震级频度关系式．讨论了该公式中非线性项的含义．     

含气溶胶、二氧化碳和云量参数的海冰-海温气候系统的数值模拟

在Saltzman模式的基础上引入了气溶胶参数和云反馈机制,从而建立了一个含气溶胶、CO2和云参数的海冰-海温高次非线性耦合气候模式。数值模拟表明,在各参数取当前值情况下,系统存在两个平衡态．系统将随参数值的变化而作有序─混沌或混沌─有序的非平衡相变．敏感性试验还揭示了系统发生了分岔（突变）时的临界参数值．     

跨孔地震CT中的逐次线性化方法

非线性问题的逐次线性化方法的每个线性化过程可通过最小二乘ＱＲ分解算法求解．为了精确地描述和控制逐次线性化迭代过程，引入迭代阻尼系数．首先根据模型拟合表最小的准则确定满足最佳一次线性化效果的最佳初始迭代阻尼系数；然后随遂次线性化迭代而减小迭代阻尼系数，并加入松弛因子对每次迭代输出的波速修正量进行控制；最后根据混沌理论，采用Ｌｙａｐｕｎｏｖ指数和模型拟合差的变化，描述第ｋ次迭代所处的状态，在解估计的方差急增之前及时停止迭代，获得可信度和分辨率最佳的解估计．模型计算与实例证明方法有效．     

强非线性杜芬系统随机振动的等效化研究

以相对穿阈率为评估指标，探讨了强非线性杜芬系统稳态随机振动的等效化问题。结果表明，在不同位移阈值条件下，随着系统振动非线性的增强，立方恢复力等效模型预测精度逐步提高。该等效模型对强非线性杜芬系统具有良好的适用性。     

隔震减震主次结构体系非线性随机地震反应分析

为研究隔震、减震装置非线性恢复力特性对2自由度主次结构体系均方根位移反应的影响规律,以隔震、减震装置微分型恢复力模式的滞回参数为变量,地震地面运动模拟成高斯白噪声过程,利用等效线性化方法得到主体结构和二次结构均方根位移反应的表达式.分析表明,主体结构隔震装置非线性恢复力特征对主、次结构的均方根位移反应的影响占主导地位;隔震、减震装置的恢复力特征产生适度非线性有利于减小主、次结构的均方根位移反应.     

地震活动的随机标度和非线性标度律

把地震作为一个复杂系统，研究了地震活动的随机性质．当不考虑震级范围时，全球地震活动、人震的余震和区域震群均有以幂次律为特征的长尾现象．地震的强度由震级确定，具有一特定震级的地震可形成一个地震活动系列，很多这样的地震活动系列就形成具有各种震级的地震的集合．不同地震系列间的统计特征由随机标度来表征，随机标度表明了由地震震级分类的不同地震系列间统计时刻的标度关系．为了统一地方、区域和全球地震活动性的统计特性，引入了非线性标度率．     

晨昏起伏电场对中性片离子的随机加热

本文从哈密顿原理出发,讨论磁尾中性片中粒子受晨昏起伏电场的影响问题,并把它归结于讨论标准映射的性质.中性片本身是非线性系统,外加起伏场会导致其进入混沌状态.本文计算了进入该状态的临界电场E_c以及不同E下的粒子轨迹.计算表明,观测到的晨昏电场可以使离子进入混沌状态,但远小于电子的临界场值.这样离子运动是随机的,电子运动是规则的.仅对离子的随机加热可能是导致中性片中离子温度高于电子温度的原因.     

极低屈服点软钢阻尼器恢复力模型的研究

本文通过试验和理论分析探讨极低屈服点软钢阻尼器的恢复力特性。随着塑性变形的发展将恢复力模型中的骨架曲线进行平移,其卸载曲线用Ramberg—Osgood函数来描述,由此得到的恢复力模型定义为骨架平移模型,将其应用于描述极低屈服点软钢阻尼器的恢复力特性、为了验证该馍型的有效性并确定合理的参数,对安装极低屈服点软钢阻尼器的3层钢框架结构进行了拟动力试验．同时用该骨架平移模型模拟极低屈服点软钢阻尼器的恢复力特性进行了大量的弹塑性地震反应分析,通过取用不同平移系数时的数值计算结果与拟动力试验结果的比较,发现平移系数为0．6左右时,该模型具有较高的精度。     

研究地震和岩石破裂现象的非线性科学方法

本文以地震孕育和岩石破裂过程的阶段(包括裂纹系形成、变形局部化和断层形成、断层活动和松弛)为线索,阐述了非线性科学方法(包括分形几何学,自组织临界现象和混沌动力学)的应用,提出了地震孕育过程和岩石破裂各阶段的普适性特征、机理和要着重研究的课题.     

Selection of time step for pseudodynamic testing

Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples.     

Nonlinear dynamics of level variations in the Caspian Sea

Caspian Sea level variations, which have several equilibrium states, are studied by the methods of the theory of nonlinear dynamic systems. Normal monthly values of sea level according to data collected at Makhachkala gauge from 1900 to 2000 are considered. The diagnostic characteristics of dynamic chaos are used to show that sea level variations have some properties of series with chaotic behavior. A model of level variations in the Caspian Sea, comprising a system of water balance equations for the sea basin, the dynamics of river runoff, and water balance of the sea itself, is proposed. Equation of a nonlinear oscillator is derived and shown to have solutions with chaotic regimes at some combinations of parameters.     

基于Duffing振子混沌系统的地震速度分析方法

强随机噪声干扰是导致地震勘探资料低信噪比的主要原因,如何在强随机噪声干扰下获取有效的信息是值得关注的问题.Duffing振子混沌系统是一个非线性的动力学系统,其对强随机噪声具有免疫能力,而对特定的周期性信号具有敏感性.本文提出一种基于Duffing振子混沌系统的速度分析方法.对CMP道集按照时距曲线关系进行移动窗口截取,将所截取的信号构建为待测信号加入Duffing振子混沌系统,通过相图网格分割方法(GPM)判断系统状态的改变,从而在强随机噪声背景下获得高分辨率的速度谱.理论模型和实际资料的处理结果表明,与传统的水平叠加速度分析方法相比,本方法能够在强随机噪声背景下获得更准确的速度分析结果.     

Performance‐based seismic assessment of conventional and base‐isolated steel buildings including environmental impact and resilience

Sustainability and resilience are issues that are recognized worldwide, and increased attention should be placed on strategies to design and maintain infrastructure systems that are hazard resilient, damage tolerant, and sustainable. In this paper, a methodology to evaluate the seismic sustainability and resilience of both conventional and base‐isolated steel buildings is presented. Furthermore, the proposed approach is used to explore the difference between the performance associated with these buildings by considering the three pillars of sustainability: economic, social, and environmental. Sustainability and resilience are both considered to cover a comprehensive performance‐based assessment content. The uncertainties associated with performance and consequence evaluation of structural and non‐structural components are incorporated within the assessment process. The proposed performance‐based assessment approach is illustrated on conventional and base‐isolated steel buildings under given seismic scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic resilience of retrofitted RC buildings

Existing buildings can be at a greater seismic risk due to non-conformance to current design codes and may require structural retrofitting to improve building performance. The performance of buildings is measured in terms of immediate consequences due to direct damage, but the continuing impacts related to recovery are not considered in seismic retrofit assessment. This paper introduces a framework of retrofit selection based on the seismic resilience of deficient buildings retrofitted with the conventional mitigation approaches. The assembly-based methodology is considered for the seismic resilience assessment by compiling a nonlinear numerical model and a building performance model. The collapse fragility is developed from the capacity curve, and the resulting social, economic, and environmental consequences are determined. The seismic resilience of a building is assessed by developing a downtime assessment methodology incorporating sequence of repairs, impeding factors, and utility availability. Five functionality states are developed for the building functionality given investigated time interval, and a functionality curve for each retrofit is determined. It is concluded that seismic resilience can be used as a performance indicator to assess the continuing impacts of a hazard for the retrofit selection.     

Rayleigh 阻尼作用下斜拉桥扭转振动

在侧向风力或侧向水平地源力作用下,斜拉桥容易发生扭转振动。本文采用非线性Rayleigh阴尼,它能反映在低速振动时有激发而加速振动,至一定高速后又衰减的完整振动过程。对非线性的统辖方程及定解条件,先使之无量纲化,再按非线性项的系数这个小参数展开未知函数,得到线性化的各级近似方程。把待求函数展成梁轴坐标的Fourier级数,其系数为待定的时间函数,应用Fourier级数的正交性,得到求解未知时间函数的二阶常微分方程,完全类似单自由度质点在线性粘滞性阻尼作用下的统辖方程,其解为已知。     

标致性景观设计抗震避灾韧性评估模型分析

现有的抗震避灾韧性评估模型存在着评估精准性差、模型灵活性差的缺陷,为了解决上述问题,提出标致性景观设计抗震避灾韧性评估模型分析与研究。通过对现有模型的分析,对构建的抗震避灾韧性评估模型整体架构进行提出,以此为基础构建整体结构数值分析模型,并采用回归分析方法对非线性动力时程进行分析,得到标致性景观抗震避灾韧性评估指标-损伤指数,采用pushover分析方法对损伤分布系数进行计算,以得到的损伤分布系数为依据建立标致性景观性易损性曲面,由其推导出抗震避灾韧性指数公式,从而实现标致性景观设计抗震避灾韧性的评估。通过实验得到,与现有的抗震避灾韧性评估模型相比较,构建的抗震避灾韧性评估模型极大的提升了评估的精准性与模型的灵活性,充分说明构建的标致性景观设计抗震避灾韧性评估模型具备更好的评估性能。     

非线性地震道的混沌反演——Ⅱ.关于Lyapunov指数和吸引子

在本文上篇《非线性地震道的混沌反演--1.理论和数值试验》中讨论了非线性反问题逐次线性化方法及迭代过程的系统特性、递推法和广义线性反演法输出波阻抗序列的特征。本篇参照混沌理论中关于Lyapunov指数、相空间和吸引子的概念,深入研究逐次线性化迭代的状态变化的阶段性及其定量描述.当引用相空间描述系统的演化时,对于随迭代变化的阻尼因子可以发现几种吸引子.最后,总结了非线性地震混沌反演的要点,指出非线性反演迭代的复杂阶段性要川混沌理论来描述,而Lyapunov指数等才是控制迭代过程的实质性参数.