多自由度非线性随机参数振动系统响应分析的概率摄动有限元法

提出了一般概率摄动有限元法，并用以解决了具有向量值和矩阵值函数的多自由度非线性随机结构系统承受随机激励的响应分析问题，应用Kronecker代数，矩阵微分理论，向量值和矩阵值函数的二阶矩技术，矩阵摄动理论和概率统计方法系统地扩展了国际上通用的随机有限元法，随机变量和系统导数很方便地排列到二维矩阵中，得到了优美的数学表达式。     

Random Vibration of Strongly Nonlinear Systems

Procedures developed recently to extend the quasi-conservativeaveraging method to the case of non-white broad-band excitations arefurther extended and presented in a unified framework. The excitationscan be stationary or nonstationary with known evolutionary spectra, andthey can be additive, or multiplicative, or both. Relative merits ofthese procedures are compared, and their accuracies are substantiated byMonte Carlo simulations.     

Performance of Nonlinear Vibration Absorbers for Multi-Degrees-of-Freedom Systems Using Nonlinear Normal Modes

Linear vibration absorbers are a valuable tool used to suppressvibrations due to harmonic excitation in structural systems. Whilelimited evaluation of the performance of nonlinear vibrationabsorbers for nonlinear structures exists in the literature forsingle mode structures, none exists for multi-mode structures.Consequently, nonlinear multiple-degrees-of-freedom structures areevaluated. The theory of nonlinear normal modes is extended toinclude consideration of modal damping, excitation and smalllinear coupling, allowing estimation of vibration absorberperformance. The dynamics of the N +1-degrees-of-freedom system areshown to reduce to those of a two-degrees-of-freedom system on afour-dimensional nonlinear modal manifold, thereby simplifying theanalysis. Quantitative agreement is shown to require a higher-order model which is recommended for future investigation.     

求非线性转子－轴承系统周期响应的一种计算方法

本文把求非线性转子－轴承系统瞬态响应的分块Ｎｅｗｍａｒｋ方法与打靶法结合求系统的周期解，该方法利用了分块Ｎｅｗｍａｒｋ方法求解速度快的优点和Ｊａｃｏｂｉ矩阵求解时每步不需迭代的特点。本文首先给出周期解的求解公式，然后用一个算例，讨论了周期解的稳定性及失稳后的分岔行为。     

非线性振动一种稳定的模糊控制方法研究

由于非线性振动系统的非线性本质,在于传统控制理论的线性控制器用于非线性振动控制效果不佳。本文针对非线性振动系统提出了一种模糊自适应滑模控制方案。     

柔性作动器驱动的非线性系统随机振动的最优有界控制

柔性作动器具有低刚度、大变形等特征,这一方面使主结构具备了强的环境适应性,另一方面也使主结构易受外界微扰影响,从而降低其操作精度．本文以介电弹性体作动器驱动的单自由度非线性系统为研究对象,通过即时微调电压,抑制系统在平衡位置附近的随机振动．通过随机平均法降低系统维数,将原系统的控制问题转化为关于慢变过程的控制问题;结合随机动态规划原理及控制约束导出最优有界控制策略．该策略具干摩擦形式,具有能量耗散本质,在抑制系统振动的同时提高了系统的稳定性．数值研究表明：最优有界控制策略具有良好的控制效果、控制效率及较高的鲁棒性．     

Nonlinear Frequency Response of Nonisothermal Adsorption Systems

A general method for the investigation of adsorption kinetics of nonlinear,nonisothermal systems, based on frequency response analysis, ispresented. It is based on the definition of higher-order frequency response functions (FRFs) on the adsorber and on the particle level. FRFs on the adsorber level can be estimated from experimentally measuredadsorber FR and used to calculate FRFs on the particle level,which can be further used for model identification, by comparison withtheoretical particle FRFs. The general procedure for calculation of particle FRFs from those of adsorber is given. Also, the generalprocedure for theoretical derivation of particle FRFs is given andillustrated with an example of nonisothermal adsorption governed bymicropore diffusion and film resistance heat transfer, as well as theprocedure for calculating unmeasured adsorber FRFs, which isillustrated with an example of a batch adsorber with volume modulation.     

Response of Systems Under Non-Gaussian Random Excitations

The approach of nonlinear filter is applied to model non-Gaussian stochastic processes defined in an infinite space, a semi-infinite space or a bounded space with one-peak or multiple peaks in their spectral densities. Exact statistical moments of any order are obtained for responses of linear systems jected to such non-Gaussian excitations. For nonlinear systems, an improved linearization procedure is proposed by using the exact statistical moments obtained for the responses of the equivalent linear systems, thus, avoiding the Gaussian assumption used in the conventional linearization. Numerical examples show that the proposed procedure has much higher accuracy than the conventional linearization in cases of strong system nonlinearity and/or high excitation non-Gaussianity. An erratum to this article is available at .     

不确定非线性动力系统的稳定性分析

本文讨论渐近稳定的非线性名义动力系统在非线性时变扰动下的鲁棒稳定性问题。应用Ｌｙａｐｕｎｏｖ稳定性定理及其推广定理得出了非线性动力系统鲁棒稳定的若干判别准则，并给邮了应用所得准则的实际算例。     

Equivalent Linearization Method Based on Energy-to-cth-Power Difference Criterion in Nonlinear Stochastic Vibration Analysis of Multi-Degree-of-Freedom Systems

Basic equations of energy-to-cth-power difference criterion were derived for multi-degree-of-freedom (MDOF) systems subjected to stationary Gaussian excitations with non-zero mean. Modal transform technique was used in order to reduce unknowns. Main computational formulae were presented and suggested values of c were given. Numerical results show that the method of this paper prevails over equation difference criterion both in accuracy and in simplicity.     

Use of Higher-Order Frequency Response Functions for Identification of Nonlinear Adsorption Kinetics: Single Mechanisms under Isothermal Conditions

The concept of higher-order frequency response functions(FRFs), which is based on Volterra series expansion of nonlinearfunctions, is used for analysis of kinetics of nonlinear adsorptionsystems. Four different kinetic mechanisms: Langmuir kinetics, filmresistance control, micropore diffusion control and pore-surfacediffusion control were analyzed and the results were compared. It wasshown that, contrary to the linear frequency response characteristicfunctions, the higher-order FRFs corresponding to different mechanismsdiffer in shape. This result offers great potential for theidentification of the adsorption-diffusion mechanism governing theprocess. It is shown that the second order FRFs give sufficientinformation for distinguishing different mechanisms.     

Nonlinear System Identification of Systems with Periodic Limit-Cycle Response

A nonlinear system identification methodology based on the principle of harmonic balance and bifurcation theory techniques like center manifold analysis and normal form reduction, is presented for multi-degree-of-freedom systems. The methodology, called Bifurcation Theory System IDentification, (BiTSID), is a general procedure for any nonlinear system that exhibits periodic limit cycle response and can be used to capture the bifurcation behavior of the nonlinear systems. The BiTSID methodology is demonstrated on an experimental system single-degree-of-freedom system that deals with self-excited motions of a fluid-structure system with a sub-critical Hopf bifurcation. It is shown that BiTSID performs excellently in capturing the stable and unstable limit cycles within the experimental regime. Its performance outside the experimental regime is also studied. The application of BiTSID to experimental multi-degree-of-freedom systems has also been very successful. However in this study only the results of the single-degree-of-freedom system are presented.     

多自由度分段光滑非线性系统的近似解——-中华文物龙洗的自激振动

建立了由干摩擦引起的两个弹性体之间自激振动的数学模型. 利用平均法 求出了由干摩擦引起的多自由度分段光滑非线性动力系统的近似解析解，分析了搓动速度、 振动频率与振幅的关系曲线，相位角与搓动速度的关系曲线，分析结果与数值解基本吻合. 为研究多自由度分段光滑非线性系统提供了一种有效的近似解析分析方法.     

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)     

Nonlinear Random Response of Cylindrical Panels to Acoustic Excitations Using Finite Element Modal Method

This paper investigates large amplitude multi-mode free vibration andrandom response of thin cylindrical panels of rectangular planform usinga finite element modal formulation. A thin laminated composite doublycurved element is developed. The system equation in structural nodal DOFis transformed into the modal coordinates by the using the modes of theunderlying linear system. The nonlinear stiffness matrices are alsotransformed into nonlinear modal stiffness matrices. Numericalintegration is employed to determine free vibration and random response.Single-mode free vibration results are compared with existing classicalanalytical solutions to validate the nonlinear modal formulation.Nonlinear random analysis results for cylindrical panels have shown thatthe root mean square of panel deflections could be larger than thoseobtained using the linear structure theory. Time histories, probabilitydistribution functions, power spectral densities, and phase plane plotsare also presented.     

大型转子-基础-地基系统的非线性动力分析

针对实际工程中的大型机组，在线性理论分析基础上，引入转子系统的非线性油膜力项，采用子结构模态综合法，形成一个比较接近实际大型汽轮发电机组的包括陀螺转子-非稳态非线性油膜转承-弹性基础-地基系统的非线性系统计算模型。通过对系统方程进行分块直接积分求解，得到了不同位置的轴承在不同转速和不同转子偏心量下引起的系统非线性动力学现象，为大机组的非线性分析和改进提供较完善的理论分析和计算的基础。     

迟滞系统受随机激励的响应计算

首先为随机激励设计了具有较高精度的滤波器，把迟滞系统受有色噪声激励的随机振动问题转化为由迟滞系统与滤波器组成的扩阶系统受白噪声激励的随机振动问题，然后详细论述了等效线性化法对此问题的具体求解，着重推导了高斯随机变量联合矩的递推关系和李亚普诺夫方程解法的实现，最后根据数字模拟结果分析了等效线性化法的精度和误差来源，给出了迟滞减振系统参数设计的有关建议。     

Stability of Singularly Perturbed Systems with Structural Perturbations. General Theory

Singularly perturbed systems with structural perturbations are analyzed for stability. New sufficient conditions of asymptotic stability and uniform asymptotic stability are established. The systems in question are widely used in control theory, engineering, etc     

正弦波纹扁球壳的非线性强迫振动

波纹壳是传感器弹性元件的一类重要形式,也是精密仪器仪表弹性元件中的一类重要形式。由于波纹壳形状复杂、参数众多、厚度薄,对其进行非线性分析非常重要同时也是十分困难的。本文考虑一种在传感器弹性元件中有重要应用价值的正弦波纹浅球壳体,将这种壳体视为结构上的圆柱正交异性扁球壳,根据Andryewa的思想,分别得到了正弦波纹壳径向、环向在拉伸、弯曲下的等价的四个各向异性参数;建立了正弦波纹扁球壳的非线性强迫振动微分方程;得到了正弦波纹扁球壳非线性强迫振动的共振周期解及幅频特性曲线。     

Investigation of Random Response of Rotational Shell When Considering Geometric Nonlinear Behaviour

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