有界窄带激励柴油机轴系扭振系统主参数共振

研究柴油机轴系扭振强非线性系统在有界窄带激励下的主参数共振响应和稳定性问题。应用改进多尺度法得到在有界窄带随机激励下柴油机轴系扭振系统的幅频响应方程,导出系统的Ito随机微分方程。通过矩法得到系统随机均方响应的近似表达式,分析各个参数对柴油机轴系扭振系统主参数共振均方值的影响。结果表明,主参数共振稳态解稳定的充分必要条件与系统二阶矩稳定的充分必要条件是一样的;随着阻尼值的增大,系统主参数共振振幅的均方值减小;随着曲轴扭转刚度的减小,系统主参数共振的均方响应曲线的斜率增大;随着随机扰动强度的增大,系统时间响应曲线和相图变化微小。     

简谐与随机噪声联合激励下Van der Pol-Duffing系统的响应

研究了Van der Pol—Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数，用多尺度法分离系统的快变项，讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明，当随机激励强度增大时，系统的响应可从一个极限环变为一个扩散的极限环；在一定的条件下，系统可有两个稳定的稳态解及随机跳跃现象。数值模拟表明本文提出的方法是有效的。     

有界窄带激励下的电磁开关系统主共振分析

以电磁开关系统为研究对象,研究电路与磁路耦合系统在有界窄带激励下的强非线性振动问题。建立电磁开关强非线性系统在有界窄带激励下的随机微分方程。应用改进的多尺度法得到系统的幅频响应方程,对窄带激励下系统主共振的稳定性进行计算,并分析系统各参数对系统主共振均方值的影响。结果表明,增大阻尼系数可以减小系统主共振的均方值;增大激励电压可以增大系统主共振的均方值;增大电阻可以减小系统主共振的均方值;增大随机扰动强度,极限环变化不大。     

窄带激励下带有时滞反馈的非线性动力系统的响应

研究了窄带激励下带有时滞反馈的Duffing振子的主共振响应。用多尺度法分离了系统的快慢变量。分析了稳态响应的稳定性和分叉，研究了时滞、调谐参数、噪声带宽和幅值对系统的影响。证明了由于时滞的存在，系统将表现出复杂的动力学行为：时滞会导致分叉、时滞会影响跳跃区域等;发现噪声幅值会导致系统多解或分叉现象的出现，且随着噪声带宽的增大系统非零稳态响应从-极限环变为-扩散的极限环。最后，给出了数值模拟。     

轴向基础窄带随机激励柔性梁的稳定性与Hopf分岔

针对轴向基础窄带随机激励柔性梁而建立的非线性动力学方程，采用多尺度法并结合笛卡尔坐标变换，导出了系统两阶模态间受组合参数共振时的非线性调制方程组。随后，在假设谐和激励下，获得了系统平凡响应稳定性边界条件的解析表达式，相应的Hopf分岔类型及产生的极限环在中心流型定理与数值计算间相互得到了验证。最后，计算了窄带随机激励下系统平凡响应的最大Lyapunov指数，获得了几乎肯定稳定性边界的数值形式，发现带宽的增大导致系统不稳定区域的增大，数值观察了类似的极限环的存在，同时，也发现相应的极限环的厚度随带宽的增大而变厚且存在相应环面趋于杂乱现象。     

窄带随机噪声作用下强非线性系统的响应

研究了Van der Pol-Duffing振子在窄带随机噪声激励下的响应问题。用参数变换法使方程出现小参数，用多尺度法分离了系统的快变项，讨论了系统的阻尼项，非线性项和随机项等参数对系统的影响，理论分析表明，当随机激励强度或带宽增大时系统的响应可从一个极限环变为一扩散的极限环，在一定的条件下系统可有两个稳定的稳态解。数值模拟表明本文提出的方法是有效的。     

外激励作用下输流管道伴随内共振的非线性振动分析

利用多元L-P法研究外部周期激励下两端固定输流管道伴随内共振的非线性受迫振动问题。外激励流固耦合系统固有频率第二阶约为第一阶3倍且激励频率接近前两阶固有频率中间值时会发生伴随强烈内部共振的组合共振,并用多元L-P法求解振动响应,分析前两模态运动及外激励幅值对内共振的影响。数值算例揭示出系统因内共振发生的更丰富、复杂的动力学行为,随激励幅值增大内共振发生趋势降低,响应形式亦发生变化。用多元L-P法研究非线性动力学便捷、高效。     

含间隙强非线性扭振系统的分岔行为研究

建立了含间隙旋转机械强非线性扭振系统的动力学方程。应用MLP法求解谐波激励下强非线性系统的解析近似解,并运用MLP法与多尺度法结合的方法得到该系统的分岔响应方程。采用奇异性理论研究了系统在非自治情形下的分岔特性,得到不同参数下系统的分岔形态。最后通过具体算例,利用数值模拟的方法得到系统在强非线性项参数变化下的分岔行为,发现随着系统参数变化系统发生周期运动、倍周期运动以及混沌等多种运动形态的复杂动力学行为。研究结果为分析间隙引起的旋转机械传动系统扭振特性提供一定的理论指导和参考。     

输流管道含有内共振的横向受迫振动研究

利用多元L-P法研究外部周期激励下两端铰支输流管道含有内共振的非线性受迫振动问题。对于外激励作用下的流固耦合系统,当第二阶固有频率约为第一阶值的3倍,并且激励频率接近系统固有频率时,系统会发生含有强烈内部共振的主共振。利用多元L-P法求解这种振动响应,并详细分析振动中前两个模态的运动及外激励幅值对内共振的影响。数值算例揭示了系统由于内共振而发生的更加丰富而复杂的动力学行为,并且表明,随着激励幅值的增大,部分内共振的发生趋势将降低并最终消失。研究结果同时证明了多元L-P法在研究非线性动力学方面是便捷而高效的。     

Winkler地基上材料非线性矩形薄板主参数共振研究

研究Winkler地基上材料非线性矩形薄板受参数激励的参数共振动问题。按照弹性力学理论建立Winkler地基上材料非线性矩形薄板受参数激励的动力学方程。利用Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足主参数共振条件的一次近似解，并进行数值计算，分析定常解的稳定性。给出主参数共振系统参数平面的分岔集和幅频响应方程的分岔图。分析激励、调谐值、阻尼系数、非线性参数、几何参数对共振响应曲线的影响。     

Random response of Duffing oscillator to periodic excitation with random disturbance

This paper discusses the random response of a non-linear Duffing oscillator subjected to a periodic excitation with random phase modulation. Effects of uncertainty in the periodic excitation and level of the system non-linearity on the response moments and non-Gaussian nature of the response caused by both the system non-linearity and the non-Gaussian loading are investigated. Results are presented in terms of the second- and the fourth-order moments as well as the excess factor of the response and some results are compared with those from the Monte Carlo simulation. An iterated linearisation technique is proposed to improve the accuracy of the numerical results for strongly non-linear systems.     

求解一类含阻尼的强非线性系统的改进多尺度方法

将改进LP方法参数变换思想直接应用到多尺度方法中,提出一种改进的多尺度方法,对含有阻尼的Duf-fing系统自由振动摄动解进行研究,得出了该类问题摄动解的显示表达式,这是使用MLP方法无法得到的。和数值计算比较的算例表明,所得方法计算结果与数值计算结果非常接近。     

用范式理论研究强非线性振动问题

拓展了范式方法 ,使其可以研究强非线性振动问题。创新之处在于改进了 Nayfeh关于响应频率的选取 ,根据振动过程中基频的变化选取响应的频率。采用本文所提出的方法 ,无论是周期解的稳定性 ,还是渐近解都可以较容易地获得。作为算例 ,用本文提出的方法计算了一般具有平方、立方项强非线性系统的范式及其渐近解、定常解 ,计算结果与数值仿真结果十分吻合     

Computation of response moments of high dimensional MDOF structure excited by stationary non-Gaussian random fields

Output moments of a non-linear dynamical system excited by a non-Gaussian random field can be obtained in practice only by simulation techniques. When the dynamical system can be decomposed in a low dimension non-linear part acting on a high dimension linear part, the original problem reduces to calculate output moments of a high dimension linear system. The proposed method suggests that work should be directed in the frequency domain. Time trajectories are then obtained through Fourier transform. Such a procedure does not introduce any approximation errors due to the time integration numerical scheme nor does it introduce any transient state. Further quasi-static correction terms can be introduced when a truncated modal basis is utilized in order to describe the low frequency dynamic response.     

An interval random perturbation method for structural‐acoustic system with hybrid uncertain parameters

An interval random model is introduced for the response analysis of structural‐acoustic systems that lack sufficient information to construct the precise probability distributions of uncertain parameters. In the interval random model, the uncertain parameters are treated as random variables, whereas some distribution parameters of random variables with limited information are expressed as interval variables instead of precise values. On the basis of the interval random model, the interval random structural‐acoustic finite element equation is constructed, and an interval random perturbation method for solving this interval random equation is proposed. In the proposed method, the interval random matrix and vector are expanded by the first‐order Taylor series, and the response vector of the structural‐acoustic system is calculated by the matrix perturbation method. According to the linear monotonicity of the response vector, the lower and upper bounds of the response vector are calculated by the vertex method. On the basis of the lower and upper bounds, the intervals of expectation and standard variance of the response vector are obtained by the random interval moment method. The numerical results on a shell structural‐acoustic model and an automobile passenger compartment with flexible front panel demonstrate the effectiveness and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust optimization of structures subjected to stochastic earthquake with limited information on system parameter uncertainty

The optimization of structures subjected to stochastic earthquake and characterized by uncertain parameters is usually posed in the form of non-linear programming with stochastic performance measures where the uncertain parameters are modelled as random variables. Such an approach, however, cannot be adopted in many real life situations when the limited information about uncertainty can be only modelled as of the uncertain but bounded (UBB) type. A robust optimization strategy for stochastic dynamic systems characterized by UBB parameters is proposed in the present study in the framework of the response surface method (RSM). In evaluating the stochastic constraints, repeated computations of the dynamic responses are avoided by applying an adaptive RSM based on the moving least squares method. Numerical results are presented to highlight the effectiveness of the proposed procedure. The effect of parameter uncertainty is also studied by comparing the results obtained from the proposed optimization approach with the conventional stochastic optimization results.     

色噪声与确定性谐波联合激励下Bouc-Wen动力系统响应的统计线性化方法

提出了一种用于求解色噪声和确定性谐波联合作用下单自由度Bouc?Wen系统响应的统计线性化方法.基于系统响应可分解为确定性谐波和零均值随机分量之和的假定,将原滞回运动方程等效地化为两组耦合的且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.利用谐波平衡法求解确定性运动方程,利用统计线性化方法求解色噪声激励下的随机运...     

Stochastic analysis of strongly non-linear elastic impact system with Coulomb friction excited by white noise

The stochastic response of frictionally damped strongly non-linear elastic impact oscillator subjected to white noise excitation and its stochastic bifurcation are considered. By the stochastic averaging method based on generalized harmonic function, one can obtain the stationary probability density function of this system. The effects of system parameters on the responses are investigated and the analytical results were verified by comparing with numerical results from Monte Carlo simulations. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that the coefficient of friction, damping constant of the elastic impact force respectively, can be treated as bifurcation parameters.     

宽带激励下非线性振动系统响应的最小化控制

将一种基于广义谐和函数的随机平均法和随机动态规划原理相结合，提出了一种非线性随机最优控制方法，可以为受宽带激励的单自由度强非线性振动系统设计最优控制规律，以使得系统的稳态响应最小化。方法中的随机平均法用来得到受控系统位移幅值的Ito随机微分方程；用随机动态规划原理为系统稳态响应最小化建立动态规划方程；在控制力为有界的条件下，从动态规划方程中可以导出最优控制规律；通过求解FPK方程得到受控系统的响应。本文用一个具体的例子阐述了这一控制方法的实施过程。     

The geometry of random vibrations and solutions by FORM and SORM

The geometry of random vibration problems in the space of standard normal random variables obtained from discretization of the input process is investigated. For linear systems subjected to Gaussian excitation, the problems of interest are characterized by simple geometric forms, such as vectors, planes, half spaces, wedges and ellipsoids. For non-Gaussian responses, the problems of interest are generally characterized by non-linear geometric forms. Approximate solutions for such problems are obtained by use of the first- and second-order reliability methods (FORM and SORM). This article offers a new outlook to random vibration problems and an approximate method for their solution. Examples involving response to non-Gaussian excitation and out-crossing of a vector process from a non-linear domain are used to demonstrate the approach.