随机结构在随机激励下的二阶摄动随机势能泛函及其应用

利用小参数摄动法,建立了随机结构在随机激励下的二阶振动随机势能泛函。并由此推导了二阶摄动随机变原理,作为应用,建立了随机有限元的计算列式。     

一类非线性系统在随机激励下的分叉

本文研究一类阻尼为线性，弹性恢复力为非线性的振动系统在随机外部激励作用下的随机分叉。文中采用广义稳态势和方法，求解系统响应的稳态联合概率密度函数。在此基础上根据由不变测度定义的随机分叉，讨论了具有权式分叉的确定性非线性系统在随机扰动下分叉行为。     

地震作用下主-从结构的被动优化控制研究

提出了一种利用主－从结构间的相互作用来减少在地震作用下结构响应的控制方法。该方法通过优化设计主－从结构间的被动耗能单元,最大限度地耗散结构的相对振动能量能减小主、从结构的整体振动水平,或最大限度地吸收主结构的相对振动能量以减小主结构的振动。文章首先导出了在平稳白噪声激励下被动耗能单元优化刚度和阻尼的一般表达式,并分析了不同结构参数对控制效果的影响,比较了在不同的平稳过滤白噪声激励下主－从结构相对位     

全非平稳地震作用下地下空间结构随机反应及可靠度分析

为研究全非平稳地震作用下地下空间结构的随机地震反应特征及可靠度分析方法,本文基于非均匀调制演变随机过程,建立了一种同时考虑强度非平稳和频率非平稳的全非平稳随机地震动输入功率谱分析模型;利用频响函数和脉冲响应函数间的傅里叶变换关系,推导出了适用于地下空间结构随机反应分析的响应功率谱计算表达式,可结合有限元方法对全非平稳地震作用下地下空间结构进行随机反应分析．基于穿越过程为泊松过程假定,采用分部积分方法,进一步推导出了适用于首次超越破坏可靠度计算的互相关函数解析表达式．然后,本文以上海某两层三跨地铁车站为工程背景,建立土-地铁车站结构相互作用体系有限元模型,对全非平稳地震作用下地铁车站结构进行了随机反应分析和中柱可靠度分析．结果表明：在非均匀调制演变功率谱作用下,结构的响应功率谱也具有明显的演变特征;利用文中给出的互相关函数计算公式,可避开调制函数的数值微分,提高计算精度．     

非高斯随机激励下工程结构可靠性估计的一种方法

本文将工程结构考虑为振动系统,把随机载荷及在结构上的载荷效应作为随机过程,分析状态函数的高阶矩,进行最大熵概率分析,得到结构在随机载荷作用下失效的概率。此法为随机环境下工作的结构、构件或设备的安全设计、可靠性检验提供了一个可行的方法。     

多点输入下大跨空间网格结构的可靠度分析

在虚拟激励反应谱法的基础上进行了多点输入下大跨空间网格结构的可靠度分析,并且将之与一致输入下结构抗震可靠度的分析结果进行了对比,考查了两种输入方法下杆件内力可靠指标之间的变化,进而分析了危险杆件在结构分布、数量等方面的差异以及危险杆件随结构跨度、视波速的变化关系。通过工程实例可以看出本文的分析方法对于分析大跨度网架、网壳这样复杂结构在多点输入下的抗震性能非常合适,为理论研究向实际应用搭建了桥梁。     

随机激励下柔性智能梁结构振动的模糊自适应控制

对柔性智能梁结构提出了一种具有结构和参数学习能力的模糊神经网络控制方法,该法摒弃了常规的以BP算法来优化整个网络参数的作法,利用遗传算法对网络全局性参数进行离线优化,利用BP学习算法对网络局部性参数进行在线调节。以柔性智能悬臂梁为例,实现了对其在随机激励下的振动控制。仿真结果表明,模糊神经网络控制算法对智能结构的振动控制具有一定的鲁棒性和自适应性。     

Slow Effects of Fast Harmonic Excitation for Elastic Structures

High-frequency excitation may affect the slow behavior of a dynamical system. For example, equilibria may move, disappear, or gain or loose stability. We consider such slow effects of fast excitation for a simple mechanical system that incorporates features of many engineering structures. The study is intended to contribute to the general understanding of periodically excited linear and nonlinear systems, as well as to the current attempts to utilize high-frequency excitation for altering the low-frequency properties of structures.     

Stochastic Response of Offshore Structures via Statistical Cubicization

This paper deals with the stochastic response of single-degree-of-freedom structures with polynomial restoring force excited by random Morisons forces with mean current. The problem is recast by expressing the excitation by means of a cubic polynomial of the wave elevation, which in turn is assumed as a stationary zero-mean Gaussian process, whose spectral density is given by the output of a cascade of two second order linear filters having a Gaussian white noise as primary excitation. Thus, Itôs stochastic differential calculus becomes applicable, and the solution is pursued with a moment equation approach by using a suitable closure scheme. The results of the applications compare well with digital simulation.     

随机桁架结构的非平稳随机动力响应分析

本文研究了随机桁架结构在非平稳随机激励下的动力响应问题。在利用随机因子法分析随机结构动力特性的基础上，给出了一种分析随机结构非平稳随机响应的新方法。从结构非平稳随机响应的表达式出发，同时考虑桁架结构的物理参数、几何尺寸的随机性，利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法，导出了随机桁架结构在非平稳随机激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。通过算例，分析了结构物理参数和几何尺寸的随机性对结构位移响应均方值和应力响应均方值随机变量随机性的影响。本文方法具有对随机结构进行一次动力分析便可求得动力响应的数字特征，且可以考察结构任一参数的随机性对结构非平稳随机响应分析结果的影响之优点。     

Energy Based Stochastic Estimation of Nonlinear Oscillators with Parametric Random Excitation

A new energy-based system identification method is developed, applicable in situations where the dynamic response of a structure is measurable but the excitation is unmeasurable and describable only in terms of a stochastic process. It is shown that, in the case of a non-linear single degree of freedom system subjected to purely parametric, non-white random excitation, the power spectrum of the excitation can be identified through an estimation of the diffusion coefficient relating to the energy envelope of the response process. Through an estimation of the drift coefficient an identification of the system damping is also possible. The method is validated through application to simulated data relating to a Duffing oscillator with non-linear damping.     

含随机参数的非线性黏弹性有限元计算

进行了粗粒土与结构接触面单调和循环加载试验，基于宏细观测量结果, 扩展了 损伤概念以 描述该类接触面在受载过程中的物态演化, 及由于物态演化导致的力学特性从初始状态到最终 稳定状态的连续变化过程. 揭示了接触面损伤的细观物理基础主要是接触面内土的颗粒破碎 和剪切压密这两种物态演化；指出接触面的剪胀体应变可以划分为可逆性和不可逆性剪胀体 应变两部分，其中不可逆性剪胀体应变可作为接触面损伤发展的宏观量度，因此其归一化 形式可作为一种损伤因子的定义；提出了建立粗粒土与结构接触面一种损伤本构关系的基本思路.     

线性随机桁架结构的平稳随机响应分析

研究了随机桁架结构的平稳随机响应问题。同时考虑结构的物理参数、几何尺寸的随机性，从结构平稳随机响应在频域上的表达式出发，利用求解随机变量函数矩的方法，导出了随机桁架结构在平稳随机激励下位移响应均方值的均值、均方差和变异系数的计算表达式。通过算例考察了随机荷载激励下结构物理参数、几何尺寸的随机性对结构随机响应的影响。     

随机激励对软弹簧杜芬振子动力学的分散作用

讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔至混沌运动的影响。利用蒙特卡罗方法,通过对系统受侵蚀安全盆的变化状况进行了观察,并由此对后继动力学分析的初始点进行了选取。系统的相图、倍周期分岔图以及庞加莱映射图等方面的数值结果表明,外加随机激励的作用往往掩盖原确定性系统内在的规则运动,对原确定性系统的运动具有较典型的分散作用,可延缓系统的倍周期分岔,也可使得系统内在随机行为提前发生,即可使得系统更容易出现混沌运动。     

Stochastic Dynamic Response of Multiply Supported Tuned Subsystems to Nonstationary Seismic Excitation

ABSTRACT

Stochastic dynamic response of multiple degree of freedom (MDOF) subsystems that are attached at multiple points to an MDOF supporting structure that is subjected to seismic excitation is obtained by using a modal time domain random vibration approach. An earthquake is modeled as a nonstationary, nonwhite, vector random process that has a realistic spectral shape and finite ground displacement, velocity, and acceleration. Analyses of secondary systems are decoupled from the primary system without loss of accuracy when the cascading assumption is appropriate. This makes the design process of subsystems convenient and efficient. When tuning occurs, cascading assumptions are no longer appropriate. Previously obtained results for the modal properties of combined systems in terms of modal properties of the primary system and subsystems are then utilized. Results account for tuning spatial coupling in terms of stiffness and inertia. Exact analytical expressions are obtained for the elements of the state transition matrix and the evolutionary covariance matrix of various responses. The solution is exact, within the limitations of modal analysis, since all the cross terms between modal coordinates are considered. Finally the capabilities of this approach are illustrated through analysis of an example.     

Identification and Damage Detection in Structures Subjected to Base Excitation

This paper presents an experimental study of different algorithms for the health monitoring of frame structures subjected to base excitation (e.g. earthquake ground motion). These algorithms use only the acceleration time histories of the input and of the response output and are tested for the identification of the dynamic characteristics of the structure (natural frequencies and damping ratios) and for detecting and quantifying any possible structural damage that occurs in the frame. Three algorithms were considered: (1) a frequency domain decomposition algorithm, (2) a time domain Eigensystem Realization Algorithm together with Observer Kalman Identification algorithm, and (3) a subsequent physical parameter identification algorithm (MLK). Through extensive experimental testing of a four-story steel frame model on a uniaxial shake table, the performance of the various methods as well as the inherent complications of physical instrumentation and testing are explored.     

Kinematic Approach to Reliability Estimate of Stochastically Loaded Plastic Structures

ABSTRACT

A method to evaluate the reliability and to predict the lifetime of rigid-plastic structures is developed when the dynamic loading is a stochastic function of time alone. The method uses the mode approximation assumption relative to the deformed shape of the structure and supposes high reliability of the structure against plastic collapse under static loading. Failure of the structure is understood to be the first crossing of the level of admissible displacements. The random displacement field is determined by numerical simulation limited to the generation of a two-dimensional random variable.

The method is illustrated by means of an example of a simply supported plate uniformly subjected to a stochastically varying pressure. The influence of the statistical parameters of stochastic loading on the reliability and on the lifetime of the structure is discussed.     

塑性节点法的研究及其在薄壳结构中的应用

本文采用变分原理及离散塑性流动定律假设研究了弹塑性有限元的新方法—塑性节点法及其所表示的物理意义。结果表明:该方法的物理实质是所述的塑性流动定理的离散。在一般意义下,本文对其进行了修正,典型板壳例题和复杂壳体结构的弹塑性有限元分析显示,计算结果与文献资料和实验数据符合较好。证明用文中方法进行壳体结构的弹塑性分析是行之有效的和可靠的。     

考虑材料强化的塑性安定性分析

采用较真实的材料本构模型，在Ｐｏｎｔｅｒ和Ｋａｒａｄｅｎｉｚ提出的扩展的安定性理论以及彭得到的考虑混合强化的安定性定量的基础上，发展了计及应变强化和循环强化的结构塑性安定区的分析方法。通过将循环强化和应变强化分别引入子区域ＶＦ和ＶＳ，利用材料安定性假设，得到了较为合理的塑性安定边界，克服了以前的工作中对处于ＶＦ和ＶＳ区中材料分别采用完全各向同性强化（或假设热应力史是弹性应力史）和完全塑性的理想材料