弹塑性随机振动系统中恢复力学数学模型的若干形式

本文基于弹塑性机振动系统恢复力数学模型的统一形式，提出了能考虑刚度下降段和系统在滞变过程中强度退化的四种恢复力数学模型为，为适应系统在多镒强随机干扰下的反应分析需要，并建立了相应的数学表达式，最后针对钢筋砼框架结构在主余震作用下的弹塑性地震反应分析给出了具体算例。     

非对称非线性随机系统的等价线性化方法及其应用

本文提出了非对称非线性系统在随机干扰下的等价线性化方法以及系统随机反应统计矩的迭代求解方法；在此基础上，利用文献（３）中建立的有损伤结构非对称滞变恢复力模型，研究了结构在主余震作用下的随机反应，最后通过算例比较，验证了本文所提方法的合理性。     

基于Liapunov理论的结构非线性振动的混合控制

研究了地震激励下高层建筑进入塑性阶段后，结构非线性振动的混合控制问题。高层建筑简化为剪力墙形式，具有非线性滞变恢复力。采用被动基础隔振和主动控制力相结合的策略，对结构的非线性振动进行混合控制。基于Liapunov第二法，从系统的能量角度出发进行稳定性分析，找到控制系统的Liapunov函数，本着工程抗震设计中安全与经济的原则，应用允许结构反应进入非线性或塑性阶段的理论，判定所提出的混合控制方法具有Liapunov意义下的稳定。     

建筑结构爆破地震反应弹塑性精细时程分析

针对爆破地震作用下建筑结构的安全评估问题,提出利用时程分析方法全面评估爆破地震波的安全度;建立了基于精细积分算法的结构弹塑性动力分析架构模式,编制了建筑结构爆破地震反应弹塑性精细时程分析程序;通过算例验证了该算法的准确性与高效性,弹性时程分析与不同恢复力模型弹塑性时程分析的结果曲线具有类似特征和数值差异;建议选择合理的恢复力模型,使用弹塑性时程分析方法模拟爆破地震作用下结构的动力响应,全面评估爆破地震波的安全性。     

钢筋混凝土结构在主余震作用下的概率累积损伤分析

本文利用我们在文献［１］中建立的主震与余震地面运动随机过程模型，以及在文献［２］中给出的带有负刚度段的三线性模型解析表达式，提出了钢筋砼结构在主震作用后，余震１作用下以及余震１作用后、余震２作用下的恢复力模型及其解析表达式；通过弹塑性随机地震反应分析，提出了结构在主震、余震１和余震２作用下的累积损伤模型及期望波损度与可靠性分析方法，最后给出了一两层钢筋砼框的算例。     

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。     

非均质材料弹塑性破裂过程的数值模拟研究

阐述了岩土类材料的非均质特性，根据这种特性提出了对材料参数进行随机赋值的方法。为了对非匀质类材料的弹塑性破裂过程进行数值模拟研究，必须在有限元计算中实现材料的参数随机赋值。还给出了实例－－平面应力状态下试样的弹塑性破裂过程的数值模拟分析。     

抗震加固用消能减震结构的弹塑性时程分析研究

对用于抗震加固的消能减震结构进行了弹塑性时程分析研究,主要解决以下几个问题:确定结构的振动模型;质量矩阵和阻尼矩阵的处理;确定结构或构件在反复荷载下的力-位移关系,或恢复力特性;附加阻尼矩阵及附加刚度矩阵;阻尼器的优化布置等.提出了简化优化设计法,针对加固工程,确定控制函数.最后给出了四层混凝土框架加固工程实例分析.     

空间钢构件考虑损伤累积效应的恢复力模型及试验验证

本文从损伤对钢材性能的影响出发,根据弹塑性损伤铰概念,提出了一种考虑损伤累积效应的空间钢构件非线性恢复力模型,并在这一模型的基础上建立了空间钢构件考虑损伤累积效应的弹塑性刚度矩阵。最后,把试验测得的试件位移曲线和利用模型计算的试件位移曲线进行对比。对比结果表明,试验位移曲线和计算和位移曲线吻合得较好,这说明本文瓣考虑损伤累积效应的空间钢构件非线性恢复力模型的正解性。     

含模糊参数的随机振动

本文在抗震结构模糊随机振动的研究基础上,进一步研究含模糊参数的随机振动分析方法,为了较好地描述具有模糊性的随机干扰,首先在Zadeh定义的模糊变量的基础上,定义了含模糊参数的随机变量和含模糊参数的随机过程,并讨论了它们的概率分布和数字特征;然后将模糊随机干扰模拟为含模糊参数的随机过程,提出了在这种模糊随机干扰下振动体系的模糊随机反应分析的基本方法和数值方法;最后对于抗震结构的模糊随机振动给出了具体的分析和算例     

多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象, 其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要. 静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法, 在多体系统碰撞动力学中存在诸多共性与差异. 本文分别从上述两类接触模型的发展历程入手, 详细介绍了两类模型的区别与联系. 首先, 根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型, 讨论了能量指数与Hertz接触刚度之间的关系, 阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题. 其次, 着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段), 分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点. 同时, 以恢复系数为桥梁和借助线性化的弹塑性接触刚度, 避免了Hertz刚度对弹塑性接触刚度的计算误差, 根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子. 探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系, 数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性. 另外, 为了避免阻尼项分母中初始碰撞速度在计算颗粒物质动态性能时导致的数值奇异问题, 通过求解等效的线性单自由度欠阻尼非受迫振动方程获得了阻尼项分母中不含初始碰撞速度的连续接触力模型, 并以一维球链为例, 证明了该模型相比EDEM软件使用的连续接触力模型具有更高的精度. 最后, 本文分析了当前多体系统碰撞动力学的研究现状, 并简要展望了多体系统碰撞动力学中接触力模型的发展趋势与面临的挑战.      

非线性滞迟系统的随机振动分析

本文采用非线性滞后函数模型，对于粘弹性系统的随机振动问题，应用等效线性化和方差分析的方法进行了分析研究，给出了白噪声激励下的响应计算解。     

Formulation of a Hysteretic Restoring Force Model. Application to Vibration Isolation

This article focuses on the formulation of a hysteretic model used as anisolator restoring force model. The proposed model is based on operatorgoverning input and output functions that depend on the deflection andthe restoring force of the isolator. First, the mathematical formulationis demonstrated, then the hysteretic model proposed is applied toisolators having different types of behavior. The model parameters aresought using the experimental force-deflection loop of each of theisolators studied. Next, the transient response of a flexible structuremounted on an all-metal isolator is predicted by coupling the firstorder differential equation of the restoring force and the second orderdifferential equations of the structure's motion. The experimentalinvestigation validates the proposed hysteretic model applied to theall-metal mount.     

Periodic and Non-Periodic Oscillations of a Class of Hysteretic Two Degree of Freedom Systems

The equations governing the response of hysteretic systems to sinusoidal forces, which are memory dependent in the classical phase space, can be given as a vector field over a suitable phase space with increased dimension. Hence, the stationary response can be studied with the aids of classical tools of nonlinear dynamics, as for example the Poincaré map. The particular system studied in the paper, based on hysteretic Masing rules, allows the reduction of the dimension of the phase space and the implementation of efficient algorithms. The paper summarises results on one degree of freedom systems and concentrates on a two degree of freedom system as the prototype of many degree of freedom systems. This system has been chosen to be in 1:3 internal resonance situation. Depending on the energy dissipation of the elements restoring force, the response may be more or less complex. The periodic response, described by frequency response curves for various levels of excitation intensity, is highly complex. The coupling produces a strong modification of the response around the first mode resonance, whereas it is negligible around the second mode. Quasi-periodic motion starts bifurcating for sufficiently high values of the excitation intensity; windows of periodic motions are embedded in the dominion of the quasi-periodic motion, as consequence of a locking frequency phenomenon.     

Asymptotic response of a two DOF elastoplastic system under harmonic excitation. Internal resonance case

The study of a two DOF elastoplastic system is formulated in a suitable phase space, velocity and force, in which an originally multi-valued restoring force is represented by a proper function. The asymptotic response can thus be studied using the Poincaré map concept and avoiding approximate analytical techniques. On account of the peculiarity of this hysteretic system, which has a well-defined yielding point, its dynamics is studied in a reduced dimension phase space using an efficient numerical algorithm. It is shown that the asymptotic response is always periodic with the period of the driven frequency and is always stable. Thus the response of the oscillator is described by its frequency response curves at various intensities of the excitation. The results presented refer to a system with two linear frequencies in a ratio of 1 : 3. The response is highly complex with numerous peaks corresponding to higher harmonics. The effect of coupling in conditions of internal resonance is a strong modification of the frequency response curves and of the oscillation shape of the structure.     

基于数字散斑相关实验测量的材料构型力的计算方法

材料构型力学主要研究材料中的缺陷(夹杂、空穴、位错、裂纹、塑性区等)的构型(形状、尺寸和位置)改变时,所引起的系统自由能的变化。本研究将基于数字散斑相关技术,实验测量材料试件的位移场分布,随后通过材料构型力的定义式,计算求得弹塑性材料中缺陷构型力的分布。其方法概括如下:位移场通过数字图像相关技术测得;应变及位移梯度场利用三次样条拟合获得;线弹性材料应力通过简单线弹性本构方程获取,而塑性材料的表面应力场通过Ramberg-Osgood本构方程计算求得;弹塑性应变能密度分布则由应力-应变曲线数值积分获得。该方法对普通弹性材料或者弹塑性材料均适用,可以用于各种不同的缺陷及缺陷群的材料构型力测量。     

Dynamical responses of airfoil models with harmonic excitation under uncertain disturbance

In this paper, we investigate nonlinear dynamical responses of two-degree-of-freedom airfoil (TDOFA) models driven by harmonic excitation under uncertain disturbance. Firstly, based on the deterministic airfoil models under the harmonic excitation, we introduce stochastic TDOFA models with the uncertain disturbance as Gaussian white noise. Subsequently, we consider the amplitude–frequency characteristic of deterministic airfoil models by the averaging method, and also the stochastic averaging method is applied to obtain the mean-square response of given stochastic TDOFA systems analytically. Then, we carry out numerical simulations to verify the effectiveness of the obtained analytic solution and the influence of harmonic force on the system response is studied. Finally, stochastic jump and bifurcation can be found through the random responses of system, and probability density function and time history diagrams can be obtained via Monte Carlo simulations directly to observe the stochastic jump and bifurcation. The results show that noise can induce the occurrence of stochastic jump and bifurcation, which will have a significant impact on the safety of aircraft.     

First passage of stochastic fractional derivative systems with power-form restoring force

In this paper, the first-passage failure of stochastic dynamical systems with fractional derivative and power-form restoring force subjected to Gaussian white-noise excitation is investigated. With application of the stochastic averaging method of quasi-Hamiltonian system, the system energy process will converge weakly to an Itô differential equation. After that, Backward Kolmogorov (BK) equation associated with conditional reliability function and Generalized Pontryagin (GP) equation associated with statistical moments of first-passage time are constructed and solved. Particularly, the influence on reliability caused by the order of fractional derivative and the power of restoring force are also examined, respectively. Numerical results show that reliability function is decreased with respect to the time. Lower power of restoring force may lead the system to more unstable evolution and lead first passage easy to happen. Besides, more viscous material described by fractional derivative may have higher reliability. Moreover, the analytical results are all in good agreement with Monte-Carlo data.     

Optimization of hysteretic characteristics of damping devices based on pseudoelastic shape memory alloys

In order to develop a fundamental understanding and the feasibility of SMA devices for passive vibration control, an undamped SDOF system with a pseudoelastic SMA restoring force is investigated to find the basic relationship between the shape of the hysteresis loop of SMA elements and their performance as a damping device. The dynamic characteristics of the device are evaluated by the steady-state response at the resonance point in order to focus on the damping effect. Dynamic analysis utilizing the equivalent linearization approach results in two major findings that, to the best of the authors’ knowledge, have not yet been reported in the literature. These results which characterize the unique behavior of the SMA hysteresis include: (a) for a given excitation amplitude, the “scale” of the hysteresis loop, which is a measure of displacement and restoring force, needs to be adjusted so that the response sweeps the maximum loop but does not exceed it; (b) the ratio of the area confined within the hysteresis loop to the area of a corresponding envelope of triangular shape should be as large as possible. The results of this study would be quite useful not only as a guideline for the design of actual SMA devices, but also as a basis for the development of new autoadaptive materials in future.     

An intelligent parameter varying (IPV) approach for non-linear system identification of base excited structures

Health monitoring and damage detection strategies for base-excited structures typically rely on accurate models of the system dynamics. Restoring forces in these structures can exhibit highly non-linear characteristics, thus accurate non-linear system identification is critical. Parametric system identification approaches are commonly used, but require a priori knowledge of restoring force characteristics. Non-parametric approaches do not require this a priori information, but they typically lack direct associations between the model and the system dynamics, providing limited utility for health monitoring and damage detection. In this paper a novel system identification approach, the intelligent parameter varying (IPV) method, is used to identify constitutive non-linearities in structures subject to seismic excitations. IPV overcomes the limitations of traditional parametric and non-parametric approaches, while preserving the unique benefits of each. It uses embedded radial basis function networks to estimate the constitutive characteristics of inelastic and hysteretic restoring forces in a multi-degree-of-freedom structure. Simulation results are compared to those of a traditional parametric approach, the prediction error method. These results demonstrate the effectiveness of IPV in identifying highly non-linear restoring forces, without a priori information, while preserving a direct association with the structural dynamics.