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1.
一种不对称滞回受迫振动系统及其分析 总被引:7,自引:0,他引:7
许多系统或结构在动载荷作用下会表现出非线性滞回行为。通常情况下,人们往往认为滞回环是对称的。但是,在工程实际中还存在一些特殊的、不对称的滞回现象。例如,在对物料进行振动压实的过程中,由于压实机构的压下和回程中物料弹塑性变形规律不同,该振动压实系统存在不对称的滞回恢复力。本文提出用一种不对称模型描述这种不对称滞回性质,该不对称滞回模型由分段曲线组成。文章对这类系统在简谐激励下的响应特征进行了分析,得到一次近似解析解以及特有的直流分量和二次谐波等成分。然后又通过实验和数值模拟分别验证了模型的合理性。 相似文献
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一种不对称滞回受迫振动系统及其应用 总被引:2,自引:0,他引:2
许多系统或结构在动载荷作用下会表现出非线性滞回行为。通过情况下,人们往往认为滞回环是对称的。但是,在工程实际中还存在一些特殊的、不对称的滞回现象。例如,在对物料进行振动压实的过程中,由于压实机构的压下和回程中物料弹塑性变形不同。该振动产系统存在不对称的滞回恢复力。本文提出用一种不对称模型描述这种不对称滞回性质,该不对称滞回模型由分段曲线组成。文章对这类系统在简谐激励下的响应特征进行了分析,得到一次 相似文献
3.
IHB法在多自由度Bouc-Wen滞回非线性系统响应特性研究中的应用 总被引:1,自引:0,他引:1
工程中常用Bouc-Wen模型来描述具有滞回特性的振动系统,此类系统是一种多值性的非解析系统,其动力学理论分析比较困难。由于Bouc-Wen滞回模型的微分形式,一般采用数值方法进行积分求解,但对于多自由度系统来说求解速度非常慢,且难以求得不稳定解。故提出将滞回力引入为一个增加的自由度,重新建立振动系统的微分方程,将增量谐波平衡(IHB)法推广至求解该类含Bouc-Wen模型的多自由度滞回非线性系统,并引入弧长法解决由迟滞非线性引起的跳跃和多映射现象。利用该法分析了一些滞回系统的响应特性,通过与数值方法进行精度和效率对比,体现了该方法的优越性。 相似文献
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提出一种用于求解确定性周期与非平稳随机激励联合作用下,单自由度非线性系统非平稳响应的统计线性化方法。将系统响应分解为确定性周期和零均值随机分量之和,则原非线性运动方程可等效地化为一组耦合的、分别以确定性和随机动力响应为未知量的非线性微分方程。利用统计线性化方法将非平稳随机激励作用下的非线性随机动力方程化为等效线性方程,得到关于线性随机响应二阶矩的李雅普诺夫方程。联立李雅普诺夫方程与谐波激励作用下的确定性微分方程,并利用数值算法对其进行求解。以蒙特卡洛模拟验证了此方法的适用性和精度。 相似文献
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《工程数学学报》2021,38(2)
经济周期演化具有非常复杂的非线性和随机性特征,对其演化响应研究可以更好地掌握经济周期演化规律.本文首先建立了具有前两个时期收入差的一次方项与三次方项的非线性经济周期动力模型,用于模拟收入对投资的非线性影响,并采用两个互相独立的高斯白噪声随机函数分别模拟不确定因素干扰与收入随机干扰.然后运用基于短时高斯转移概率密度和Gauss-Legendre积分的路径积分法,求解收入与收入变化率的概率密度函数.最后研究了收入随机干扰和补充储蓄率对非线性经济周期演化的影响.研究表明:随机干扰下的收入早期变化波动显著,后期趋于稳定.收入随机干扰增强显著加大了收入的随机性,使得收入更加难于预测与控制.此外,提高补充储蓄率会降低获得高收入的概率. 相似文献
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不确定结构非线性动力分析的增量随机有限元法 总被引:1,自引:0,他引:1
针对不确定性结构能力分析中采用线弹性假设的不足。本文提出了预测具有随机参数的非线性结构动力响应的一种数值方法-增量随机有限元方法,可以同时考虑结构参数的随机性和材料非线民生,算例表明,增量随机有限元法可以较地预测随机结构的非线性动力行为。 相似文献
9.
强迫Duffing振动系统的主共振鞍结分岔控制 总被引:4,自引:0,他引:4
设计了非线性参数控制器来改变非线性系统的稳态响应,减小了系统的响应幅值并消除了共振时的鞍结分岔。首先由多尺度法得到系统的近似频响方程,再由奇异性理论来分析分岔特性,从而实现非线性控制的目标。最后对强迫Duffing系统的主共振形式进行了分析,由数值模拟来确定分岔控制是可行的和有效的。 相似文献
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研究了单自由度非线性单边约束碰撞系统在窄带随机噪声参数激励下的响应问题,窄带噪声采用有界随机噪声模型。用Zhurav lev变换将碰撞系统转化为连续的非碰撞系统,然后用随机平均法得到了关于慢变量的随机微分方程。在没有随机扰动情形,给出了系统响应幅值满足的代数方程;在有随机扰动情形,结合线性化方法和矩方法给出了系统响应幅值二阶矩近似解的解析表达式。讨论了系统阻尼项、非线性项、窄带随机噪声的带宽、中心频率和振幅以及碰撞恢复系数等参数对于系统响应的影响。理论计算和数值模拟表明,系统响应将随激励频率和振幅的增大而增大,而随系统阻尼和非线性强度的增大而减少。并发现了随机跳跃现象,即当随机激励的振幅超过某个阈值时,系统的稳态响应将从零解跳跃为一个较大的非零解;而当随机扰动的强度超过某个阈值时,系统的稳态响应将从一个较大的非零解跳跃为零解。 相似文献
11.
迟滞的磁流变阻尼器的随机最优控制力 总被引:1,自引:1,他引:1
用Bouc-Wen迟滞模型描述磁流变阻尼器的动力学特性,分离阻尼器控制力的半主动部分和被动部分,被动部分结合到受控系统.先将该系统变换成等价的非迟滞的非线性随机控制系统,再运用随机平均法导出关于能量的It随机微分方程.根据随机动态规划原理,建立控制总能量的动态规划方程,并由此确定非clip的最优控制力.最后通过数值结果表明该控制力的有效性. 相似文献
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The nonlinear stochastic optimal control of Preisach hysteretic systems is studied, and the control procedure is illustrated with an example of the single-degree-of-freedom Preisach system. The Preisach hysteretic system subjected to a stochastic excitation is first replaced by an equivalent non-hysteretic nonlinear stochastic system with displacement-amplitude-dependent damping and stiffness, by using the generalized harmonic balance technique. Then, the relationship between the displacement amplitude and total system energy is established, and the equivalent damping and stiffness coefficients are expressed as functions of the system energy. The averaged Itô stochastic differential equation for the system energy as one-dimensional controlled diffusion process, is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is obtained based on the stochastic dynamical programming principle, and is solved to yield the optimal control force. Finally, the Fokker–Planck–Kolmogorov equation associated with the averaged Itô equation is established, and the stationary probability density of the system energy is obtained, from which the variances of the controlled system response and the optimal control force are predicted and the control efficacy is evaluated. Numerical results show that the proposed control strategy for Preisach hysteretic systems is very effective and efficient. 相似文献
13.
An analytical method for determining stochastic response and survival probability of nonlinear oscillators endowed with fractional element and subjected to evolutionary excitation is developed in this paper. This is achieved by the variational formulation of the recently developed analytical Wiener path integral (WPI) technique. Specifically, the stochastic average/linearization treatment of the fractional-order non-linear equation of motion yields an equivalent linear time-varying substitute with integer-order derivative. Next, relying on the path integral technique, a closed-form analytical approximation of the response joint transition probability density function (PDF) for small intervals is obtained. Further, a combination of the derived joint transition PDF and the discrete version of Chapman–Kolmogorov (C–K) equation, leads to analytical solution of the non-stationary response and survival probability of non-linear oscillator under the evolutionary excitation. Finally, pertinent numerical examples, including a hardening Duffing and a bi-linear hysteretic oscillator, are considered to demonstrate the reliability of the proposed technique. 相似文献
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Active control of non-stationary response of a two-degree of freedom vehicle model with nonlinear passive suspension elements
is considered in this paper. The method of equivalent linearization is used to derive an equivalent linear model and optimal
control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic
damping and hysteretic type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system
performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the
corresponding passive suspension systems. 相似文献
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Dynamic Response Analysis of Fuzzy Stochastic Truss Structures under Fuzzy Stochastic Excitation 总被引:1,自引:1,他引:1
A novel method (Fuzzy factor method) is presented, which is used in the dynamic response analysis of fuzzy stochastic truss structures under fuzzy stochastic step loads. Considering the fuzzy randomness of structural physical parameters, geometric dimensions and the amplitudes of step loads simultaneously, fuzzy stochastic dynamic response of the truss structures is developed using the mode superposition method and fuzzy factor method. The fuzzy numerical characteristics of dynamic response are then obtained by using the random variable’s moment method and the algebra synthesis method. The influences of the fuzzy randomness of structural physical parameters, geometric dimensions and step load on the fuzzy randomness of the dynamic response are demonstrated via an engineering example, and Monte-Carlo method is used to simulate this example, verifying the feasibility and validity of the modeling and method given in this paper. 相似文献
16.
Yoshiyuki Suzuki 《Sadhana》1995,20(2-4):475-488
A method of stochastic optimal control of hysteretic structural systems under earthquake excitations is presented. Stochastic estimation and control problems are formulated in the form of Itô stochastic differential equations on the basis of the theory of continuous Markov processes. The conditional moment equations given observation data are derived for nonlinear filtering, and are closed by introducing appropriate analytical form of the conditional probability density functions of the state variables. Under the assumption that the admissible controls are expressed as functions of the conditional moment functions the Bellman equation is derived. If the spatial variables of the Bellman equation are defined by a part of the full set of conditional moment functions appearing in the closed moment equations, the resulting Bellman equation is coupled with conditional moment equations both for filtering and for prediction. The Gaussian and non-Gaussian stochastic linearization techniques combined with simple solution techniques to the Bellman equation are examined to solve the Bellman equation or extended Riccati equations without prediction procedures. 相似文献
17.
Stationary response of single-degree-of-freedom (SDOF) bilinear hysteretic system driven by Poisson white noise is investigated via stochastic averaging of energy envelope in this paper. The averaged generalized Fokker–Planck–Kolmogorov (GFPK) equation for SDOF bilinear hysteretic system driven by Poisson white noise is derived and the approximate stationary solutions of the averaged GFPK equation are obtain by using a modified exponential polynomial closure method. The effectiveness and accuracy of the approximate solution are assessed by performing appropriate Monte Carlo simulations. It is found that analytical and numerical results agree well and the effect of non-Gaussianity of the excitation process on stationary probability densities of total energy and displacement of bilinear hysteretic system is predicted successfully via stochastic averaging of energy envelope. 相似文献
18.
An analytical method of stochastic seismic response and reliability analysis of hysteretic structures based on the theory of Markov vector process is presented, especially from the methodological aspect. To formulate the above analysis in the form of stochastic differential equations, the differential formulations of general constitutive laws for a class of hysteretic characteristics are derived. The differential forms of the seismic safety measures such as the maximum ductility ratio, cumulative plastic deformation, low-cycle fatigue damage are also derived. The state equation governing the whole nonlinear dynamical system which is composed of the shaping filter generating seismic excitations, hysteretic structural system and safety measures is determined as the Itô stochastic differential equations. By introducing an appropriate non-Gaussian joint probability density function, the statistics and joint probability density function of the state variables can be evaluated numerically under nonstationary state. The merit of the proposed method is in systematically unifying the conventional response and reliability analyses into an analysis which requires knowledge of only first order (single-time) statistics or probability distributions. 相似文献
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Jie Li Jian‐Bing Chen 《International journal for numerical methods in engineering》2006,65(6):882-903
The probability density evolution method (PDEM) for dynamic responses analysis of non‐linear stochastic structures is proposed. In the method, the dynamic response of non‐linear stochastic structures is firstly expressed in a formal solution, which is a function of the random parameters. In this sense, the dynamic responses are mutually uncoupled. A state equation is then constructed in the augmented state space. Based on the principle of preservation of probability, a one‐dimensional partial differential equation in terms of the joint probability density function is set up. The numerical solving algorithm, where the Newmark‐Beta time‐integration algorithm and the finite difference method with Lax–Wendroff difference scheme are brought together, is studied. In the numerical examples, free vibration of a single‐degree‐of‐freedom non‐linear conservative system and dynamic responses of an 8‐storey shear structure with bilinear hysteretic restoring forces, subjected to harmonic excitation and seismic excitation, respectively, are investigated. The investigations indicate that the probability density functions of dynamic responses of non‐linear stochastic structures are usually irregular and far from the well‐known distribution types. They exhibit obvious evolution characteristics. The comparisons with the analytical solution and Monte Carlo simulation method demonstrate that the proposed PDEM is of fair accuracy and efficiency. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献