Chaotic behaviors of a bilinear hysteretic oscillator

In the present research, concentration is focused on dynamic response of a bilinear hysteretic oscillator with clearance, and equivalent damping and stiffness are then determined by means of asymptotic and numerical method. A variety of dynamic responses of the nonlinear system are analyzed, and some new phenomena are discussed.     

Linear state representations for identification of bilinear discrete-time models by interaction matrices

Bilinear systems can be viewed as a bridge between linear and nonlinear systems, providing a promising approach to handle various nonlinear identification and control problems. This paper provides a formal justification for the extension of interaction matrices to bilinear systems and uses them to express the bilinear state as a linear function of input–output data. Multiple representations of this kind are derived, making it possible to develop an intersection subspace algorithm for the identification of discrete-time bilinear models. The technique first recovers the bilinear state by intersecting two vector spaces that are defined solely in terms of input–output data. The new input–output-to-state relationships are also used to extend the equivalent linear model method for bilinear system identification. Among the benefits of the proposed approach, it does not require data from multiple experiments, and it does not impose specific restrictions on the form of input excitation.     

Parametric resonance of a single-degree-of-freedom system with double bilinear hysteresis

A simple pendulum with a hinge of double bilinear hysteretic restraining moment-rotation characteristic under parametric excitation is studied. In contrast with a linear system with viscous damping, a double bilinear hysteretic system leads, in general, to finite response under parametric resonance. The response curves and the conditions under which unbounded response results are given. Further, it is shown that unlike the bilinear hysteretic system, a double bilinear hysteretic system may be shock excited into parametric resonance even when the exciting frequency is outside the parametrically resonant frequency range.     

指数模量成层土非线性地震反应的半解析算法

运用文献[1]所建议的动态应力应变关系及其推广的Masing加卸载准则,考虑土体在地震等产生的不规则加载条件下的非线性滞回特征,将增量法与相应场地地震线性反应解析解[2]相结合,提出了该动力非线性方程的半解析时域算法,基于改进的一维剪切梁模型,对剪切模量是其深度的某一指数函数的成层非均质土层,建立了求解土体地震反应的非线性分析技术。针对文献[2]中的土层剖面,做了计算、分析和讨论。     

Analysis of spatially extended excitable Izhikevich neuron model near instability

The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed.

     

Secondary System Analysis for Space Pay-Load

The paper deals with the response of a secondary system carried on by a space vehicle during its orbital flight, i.e. when subjected to gravitational and fluid dynamical actions. The vibrations of the inner load are passively controlled using an adequate base isolation device whose behaviour can be represented by a nonlinear endochronic hysteretic model.The possibility of an efficient analysis of the globally nonlinear space-vehicle/pay-load system is investigated. In particular, the possibility of substituting a coupled structural dynamic analysis with an analysis which decouples the responses of the primary (vehicle) and secondary (pay-load) systems is investigated. The accuracy of the latter approach is studied for increasing values of the secondary mass.     

非高斯随机激励下滞迟系统响应与首次穿越失效

针对由有界噪声、泊松白噪声和高斯白噪声共同构成的非高斯随机激励,通过Monte Carlo数值模拟方法研究了此激励作用下双线性滞迟系统和Bouc-Wen滞迟系统这两类经典滞迟系统的稳态响应与首次穿越失效时间。一方面,分析了有界噪声和泊松白噪声这两种分别具有连续样本函数和非连续样本函数的非高斯随机激励,在不同激励参数条件下对双线性滞迟系统和Bouc-Wen滞迟系统的稳态响应概率密度、首次穿越失效时间概率密度及其均值的不同影响;另一方面,揭示了在这类非高斯随机激励荷载作用下,双线性滞迟系统的首次穿越失效时间概率密度将出现与Bouc-Wen滞迟系统的单峰首次穿越失效时间概率密度截然不同的双峰形式。     

Drift response of a bilinear hysteretic system to periodic excitation under sustained load effects

This paper presents an investigation of response characteristics for hysteretic systems idealized as a bilinear hysteretic model subjected to period excitations composed of a harmonic function and a sustained load. It is shown that the displacement solution can exhibit a drift sequence persistently repeated at a frequency identical to the excitation frequency in the case of zero post-yielding stiffness. The periodic-like drift sequence is further classified into three major types according to their different hysteretic looping behaviors. An approximate solution approach based on the method of weighted residuals is proposed to analyze the drift amplitude per response cycle. The assumed response shape is composed of two concatenated harmonic functions each with a frequency slightly detuned from the excitation frequency. The method is accompanied with a subsequent first-order analysis to obtain a closed-form approximation for the drift response. Good response predictions of the proposed solution method are demonstrated through both undamped and damped drift-frequency analyses.     

Finite Element Model Calibration for Ares I-X Flight Vehicle

Ares I-X is a flight test vehicle developed by NASA to demonstrate a new class of crew launch vehicle. For this first flight test, the first stage was a four segment solid rocket booster with mass simulators used to represent the other sections of the Ares I vehicle. Although this vehicle is significantly simpler than the Ares I, model calibration was required for the finite element model used in loads analysis and flight control evaluations before its maiden flight. The process of calibrating models involves updating parameters and reconciling predictions with test data. This work presents a probabilistic approach to the calibration process. The approach uses Analysis of Variance (ANOVA) for parameter sensitivity, nonlinear optimization to minimize the error between test and analysis, and multiple FEM models to bound the system response and to assess the probability of finding a reconciling solution. To reduce the computational burden associated with ANOVA, response surface models are used in lieu of computationally intensive finite element solutions. Uncertainty in the parameters and their effect on the frequency response function is studied in terms of Principal Values of the frequency response functions. Uncertainty bounds of the principal values are established across multiple models to allow one to determine the probability of finding a solution that reconciles analysis with test results. Results from applying this model calibration process to the Ares I-X project are described. Findings presented in the paper confirmed that the baseline model used for pre-flight assessments was within the acceptable range established for guidance and control.     

Evaluation of cyclic plasticity models in ratcheting simulation of straight pipes under cyclic bending and steady internal pressure

This paper evaluates seven cyclic plasticity models for structural ratcheting response simulations. The models evaluated are bilinear (Prager), multilinear (Besseling), Chaboche, Ohno–Wang, Abdel Karim–Ohno, modified Chaboche (Bari and Hassan) and modified Ohno–Wang (Chen and Jiao). The first three models are already available in the ANSYS finite element package, whereas the last four were implemented into ANSYS for this study. Experimental responses of straight steel pipes under cyclic bending with symmetric end rotation history and steady internal pressure were recorded for the model evaluation study. It is demonstrated that when the model parameters are determined from the material response data, none of the models evaluated perform satisfactorily in simulating the straight pipe diameter change and circumferential strain ratcheting responses. A detailed parameter sensitivity study with the modified Chaboche model was conducted to identify the parameters that influence the ratcheting simulations and to determine the ranges of the parameter values over which a genetic algorithm can search for refinement of these values. The refined parameter values improved the simulations of straight pipe ratcheting responses, but the simulations still are not acceptable. Further, improvement in cyclic plasticity modeling and incorporation of structural features, like residual stresses and anisotropy of materials in the analysis will be essential for advancement of low-cycle fatigue response simulations of structures.     

Tailoring of pinched hysteresis for nonlinear vibration absorption via asymptotic analysis

The method of multiple scales is adopted to investigate the dynamic response of a nonlinear Vibration Absorber (VA) whose constitutive behavior is governed by hysteresis with pinching. The asymptotic analysis is first devoted to study the response of the absorber to harmonic excitations and to evaluate its sensitivity to the main constitutive parameters. The frequency response obtained in closed form allows to carry out the stability analysis together with a parametric study leading to behavior charts characterizing multi-valued softening/hardening responses or single-valued, quasi-linear responses. A two-degree-of-freedom model of a primary nonlinear structure endowed with the hysteretic vibration absorber is investigated to explore transfers of energy from the structure to the absorber resulting into optimal vibration amplitude reduction. The asymptotic solution is proved to be in good agreement with the numerical solution obtained via continuation. The asymptotic approach is embedded into a differential evolutionary algorithm to obtain a multi-parameter optimization procedure by which the optimal hysteresis parameters are found.     

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS 1)

包含立方刚度和Bouc-Wen 型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg-Marquardt 迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc-Wen 型滞回和立方刚度的综合影响下,隔振系统呈现渐软–渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。     

Response analysis of randomly excited nonlinear systems with symmetric weighting Preisach hysteresis

An approximate method for analyzing the response of nonlinear systems with the Preisach hysteresis of the non-local memory under a stationary Gaussian excitation is presented based on the covariance and switching probability analysis. The covariance matrix equation of the Preisach hysteretic system response is derived. The cross correlation function of the Preisach hysteretic force and response in the covariance equation is evaluated by the switching probability analysis and the Gaussian approximation to the response process. Then an explicit expression of the correlation function is given for the case of symmetric Preisach weighting functions. The numerical result obtained is in good agreement with that from the digital simulation. The project supported by the National Natural Science Foundation of China (19972059) and Zhejiang Provincial Natural Science Foundation (101046)     

基于等效阻尼理论的金属橡胶弹性迟滞力学模型及实验研究

针对弹性多孔金属橡胶非线性迟滞特性力学行为,将迟滞恢复力-位移曲线分解为非线性单值曲线和椭圆,并将等效阻尼理论用于动态力学性能参数识别,从而建立了一种新型的适用于黏弹性阻尼材料的宏观唯象力学模型。采用不同相对密度的环形金属橡胶进行动态实验测试,以验证理论模型的准确性,结果表明该模型可将具有非线性特性的金属橡胶系统进行降阶处理,提高金属橡胶力学模型的预测效率,并能很好地描述金属橡胶的迟滞力学行为。另外,研究了在不同激励频率条件下金属橡胶的阻尼耗能特性。实验结果表明:在高频加载的条件下,黏性阻尼系数对动态加载频率不敏感,阻尼耗能与加载幅值之间呈线性正相关。基于等效阻尼理论的弹性迟滞力学模型具有一定的普适性,可进一步推广应用于类似弹性多孔材料的力学性能表征,为其工程应用提供理论基础。     

Continuous-time bilinear system identification using single experiment with multiple pulses

A novel method is presented for the identification of a continuous-time bilinear system from the input?Coutput data generated by a single experiment with multiple pulses. In contrast to the conventional approach utilizing multiple experiments, the current work documents the advantage of using a single experiment and sets up a procedure to obtain bilinear system models. The special pulse inputs employed by earlier research can be avoided and accurate identification of the continuous-time system model is possible by performing a single experiment incorporating a class of control input sequences combining pulses with free-decay response. The algorithm presented herein is more attractive in practice for the identification of bilinear systems. Numerical examples presented demonstrate the methodology developed in the paper.     

Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty

Parametric uncertainties play a critical role in the response predictions of a gear system. However, accurately determining the effects of the uncertainty propagation in nonlinear time-varying models of gear systems is awkward and difficult. This paper improves the interval harmonic balance method (IHBM) to solve the dynamic problems of gear systems with backlash nonlinearity and time-varying mesh stiffness under uncertainties. To deal with the nonlinear problem including the fold points and uncertainties, the IHBM is improved by introducing the pseudo-arc length method in combination with the Chebyshev inclusion function. The proposed approach is demonstrated using a single-mesh gear system model, including the parametrically varying mesh stiffness and the gear backlash nonlinearity, excited by the transmission error. The results of the improved IHBM are compared with those obtained from the scanning method. Effects of parameter uncertainties on its dynamic behavior are also discussed in detail. From various numerical examples, it is shown that the results are consistent meanwhile the computational cost is significantly reduced. Furthermore, the proposed approach could be effectively applied for sensitivity analysis of the system response to parameter variations.     

A robust online parametric identification method for non-deteriorating and deteriorating distributed element models with viscous damping

The online parametric identification of deteriorating and non-deteriorating distributed element models (DEMs) with viscous damping is studied using a generalization of Masing model to provide the proper framework for identification. The approach renders the hysteretic response of the DEM into a time-independent single-valued mapping from equivalent displacement values into equivalent force values, while considering the effect of damping as a parallel element. This approach allows for parametric identification of this non-linear rate-dependent hysteretic behavior to be performed using non-linear optimization techniques. A changing objective function, defined as a norm of force estimation error over a shifting window of recent data, is employed so that classic non-linear optimization techniques can be used for the online identification problem. A variation of the steepest descent method is used with significant modifications. Special measures are taken to guarantee robustness of the results in presence of noise. The results show that the proposed identification method exhibits a very good performance in identifying the correct values of the parameters in real time, and is robust in dealing with noise. The proposed method can be applied to many other types of hysteretic behavior as well.     

滞后细观模型在岩石力学中的应用

对以砂岩为代表的所谓``NME材料'的力学行为研究方面的一些新的概念和模型进行了评介.首先介绍了一种基于所谓``滞后单元'的描述滞后现象的物理模型------Preisach-Mayergoyz(P-M)模型,然后详细阐述了P-M模型应用于模拟岩石的非线性滞后应力应变关系的过程和结果.这种唯象模型很好地描述了宏观上的滞后表现和``离散记忆'效应.接着本文对应变能耗散的力学机制进行了简单分析. 最后,介绍了一种描述弹性波在``NME材料'中传播规律的数学方法, 该方法从一般的弹性波传播规律出发,分析了``NME材料'特殊的力学性质给弹性波传播带来的影响,揭示了产生特殊的弹性波传播规律的原因.      

一类加权全局迭代参数卡尔曼滤波算法

结合参数卡尔曼滤波算法和全局迭代推广卡尔曼滤波算法本文提出了加权全局迭代参数卡尔曼滤波算法。参数卡尔曼滤波算法可避免系统参数和状态变量之间的非线性耦合 ,同时通过带有目标函数的全局迭代算法保证能够获取到稳定、收敛的识别结果。分别针对线性结构模型和随动强化双线性结构模型进行了仿真参数识别。结果显示 ,不加权的全局迭代参数卡尔曼滤波算法对线性系统是有效的 ,而对非线性系统必须使用加权的全局迭代参数卡尔曼滤波算法。当信噪比较大 ,迭代无法得到收敛的结果时 ,目标函数保证了较好识别结果的获得     

Force-displacement characteristics of simply supported beam laminated with shape memory alloys

As a preliminary step in the nonlinear design of shape memory alloy(SMA) composite structures,the force-displacement characteristics of the SMA layer are studied.The bilinear hysteretic model is adopted to describe the constitutive relationship of SMA material.Under the assumption that there is no point of SMA layer finishing martensitic phase transformation during the loading and unloading process,the generalized restoring force generated by SMA layer is deduced for the case that the simply supported beam vibrates in its first mode.The generalized force is expressed as piecewise-nonlinear hysteretic function of the beam transverse displacement.Furthermore the energy dissipated by SMA layer during one period is obtained by integration,then its dependencies are discussed on the vibration amplitude and the SMA’s strain(Ms-Strain) value at the beginning of martensitic phase transformation.It is shown that SMA’s energy dissipating capacity is proportional to the stiffness difference of bilinear model and nonlinearly dependent on Ms-Strain.The increasing rate of the dissipating capacity gradually reduces with the amplitude increasing.The condition corresponding to the maximum dissipating capacity is deduced for given value of the vibration amplitude.The obtained results are helpful for designing beams laminated with shape memory alloys.