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.     

非线性系统参数辩识的一种频域模型

本文基于对非线性系统的可分离性假设，将非线性弹性力和阻尼力分别分解为物理坐标下各点间相对位移和相对速度的幂级数函数，导出了一般多自由度非线性系统在恒幅激励下的广义频率响应函数与输入输出之间的迭代关系式，提出了非线性系统中基本线性部分的概念，进而了一种在实验条件下的系统物理参数辩识方法。     

Response of Uncertain Nonlinear Vibration Systems with 2D Matrix Functions

This paper extends the response of uncertain nonlinear vibration systems to vector-valued and matrix-valued functions. Random variables and system derivatives are conveniently arranged into 2D matrices. The method is based on a second order expansion of the governing equations and matrix calculus, Kronecker algebra are used in the mathematical development. The results derived are easily amenable to computational procedures.     

Nonlinear Response of a Parametrically Excited System Using Higher-Order Method of Multiple Scales

Two fundamentally different versions of the method of multiple scales (MMS) are currently in use in the study of nonlinear resonance phenomena. While the first version is the widely used reconstitution method, the second version is proposed by Rahman and Burton [1]. Both versions of the second-order MMS are applied to the differential equation obtained for a parametrically excited cantilever beam with a lumped mass at an arbitrary position. The bifurcation and stability of the obtained response show the difference between the two versions. While the Hopf bifurcation phenomena with no jump is found in the case of second-order MMS version I, both jump-up and jump-down phenomena are observed in second-order MMS version II, which closely agree with the experimental findings. The results are compared with those obtained by numerically integrating the original temporal equation.     

Nonlinear Dynamic Response of a Rotor Bearing System Due to Surface Waviness

In this paper, the radial vibrations of a rigid rotor supported by ball bearings are studied. In the analytical formulation, contacts between the balls and races are considered as nonlinear springs whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark- with the Newton-Raphson method is used to solve the nonlinear differential equations iteratively. The effect of bearing running surface waviness on the vibrations of rotor is investigated. The formulation predicts discrete spectrum with specific frequency components for each order of waviness. Numerical results obtained from the simulation are validated with respect to those of prior researchers.     

一类非线性周期系统响应的精细积分法

对于一类非线性周期／变系数微分方程,提出基于精细积分法的数值解法,处理非线性周期／变系数微分方程系统的响应问题,其积分策略是：采用精细积分格式处理常系数部分;采用线性插值格式处理非线性周期／变系数部分,既继承精细积分方程高度准确的特点,又保证足够的精度与较小的计算量。通过数值算例,与以往与用的微分方程直接数值积分法（如预估－校正哈明法）求得的解加以比较表明,对于给定的精度要求,精细积分法更经济有效     

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。     

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.     

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

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局部结构动力修改的频率响应函数方法

本文提出一种计算结构修改后振动特性的频率响应函数方法。此法考虑结构修改时振动系统的物理参数矩阵(质量、刚度、阻尼)的同时变化,利用位置矩阵,将局部修改时产生的物理参数矩阵的增量部分分解表示。推导出修改后振动系统的频率响应函数矩阵,进而拟合出模态参数。此法对物理参数的改变量的大小可以任意,且计算过程简单。     

基于非线性双路光耦的光耦放大器频响分析

频率响应是光电耦合隔离放大器的一个重要参数。首先介绍了光敏三极管光电导工作模式和集成运放宏模型,然后利用该原理对使用双路光耦设计的线性光耦隔离放大器电路进行了深入研究,分析并推导了电路频响的计算公式。对该电路的频响与电路中元件参数的关系进行了仿真和实验,最终得出结论。     

Explorations of the Phase-Space Linearization Method for Deterministic and Stochastic Nonlinear Dynamical Systems

A new numeric-analytic phase-space linearization (PSL) schemefor a class of nonlinear oscillators with continuous vector fields isinvestigated in this study. The essence of the PSL method is to replacethe nonlinear vector field by a set of conditionally linear ones, eachvalid either over a short segment of the evolving trajectory or(equivalently) over a sufficiently small interval of time. This conceptmay be usefully exploited to arrive at certain explicit and implicitintegration schemes for analyses and simulations. The explicit schemes,which are found to have ready extensions to systems under stochasticinputs, are first numerically implemented for a few oft-used nonlineardynamical systems under (deterministic) sinusoidal inputs. An estimateof an upper bound to the local error in terms of the chosen time stepsize is provided. The explicit scheme of local linearization is nextextended to nonlinear oscillators under stochastic excitations, namelywhite noise processes, which are formal derivatives of one or acombination of Gauss–Markov processes. Since the PSL approach is todecompose the nonlinear operator into a set of linear operators, theprinciples of linear random vibration may be suitably exploited toarrive at a faster Monte-Carlo scheme for computing the responsestatistics, both in stationary and nonstationary regimes. A fewexamples, based on Ueda's and Duffing–Holmes' oscillators, arepresented and compared with exact solutions, whenever available, toverify the correctness and versatility of the proposed schemes.     

一种诊断复合材料层合板损伤的频响方法

本文首先选取对故障比较敏感,又能反映结构动力学特性的频响函数作为诊断故障的参数。通过计算无损板在给定模态下各单元的模态能量,求得每个单元对该阶模态下全板能量的贡献,并由模态实验得到损伤前后频响函数在各阶共振峰处的变化。分析发现两者之间存在内在联系,从而得到一种分析小损伤位置和范围的新方法。     

非线性转子的低频振动失稳机理分析

包括两部分内容：１）材料内阻作用下转子自激振动的局部分岔分析；２）考虑湍流因素的滑动轴承油膜力作用下转子轴承系统油膜失稳机理的全面分析。结果表明，非线性转子的自激振动表现出复杂的动力学现象，这些低频振动现象的揭示，为工程上转子故障的识别和预防提供了理论依据。     

钢筋混凝土剪力墙单元非线性分析模型及其应用

本文简要评述了几种常见的钢筋混凝土剪力墙非线性宏观单元模型后，着重对多垂直杆剪力墙非线性单元模型的几个重要问题如剪力变形的考虑方法，单元刚度矩阵的形式，垂直拉压杆及剪切弹簧的恢复力模型等进行了探讨与改进，最后给出了一个算例，并与试验结果比较，表明非线性宏观墙单元模型具有较好的计算精度。     

双参数地基上环板的非线性动力响应

研究双参数地基上环板的大挠度动力响应问题，给出了求解该问题的一种有效方法，即在空间域上运用摄动微分求积法处理非线性边值问题，在时间域上则以三点递推格式的Ｎｅｗｍａｒｋ－β法计算其动力响应。文中同时讨论了不同形式地基对环板在均布阶跃载荷作用下动力响应的影响。     

On the Implementation of the Eigenvalue Method for Limit Cycle Determination in Nonlinear Systems

In many practical systems, limit cycles can be predicted with suitable precision by frequency domain methods using describing functions. Within such an approach, limit cycles can be predicted using the “eigenvalue method” [Somieski, G., Nonlinear Dynamics 26(1), 2001, 3–22]. This contribution presents a novel and advantageous implementation of this method, using singular value instead of eigenvalue calculations, and enhancing computational efficiency by avoiding a so called “frequency iteration”. An erratum to this article is available at .     

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

I. INTRODUCTION The composite material and the composite structure are liable to generate damage during manufactureand under load, which will lead to a decrease of the material and structure’s mechanical properties.It is accepted that there exist four…     

Experimental Investigation of the Nonlinear Response of a Hanging Cable. Part II: Global Analysis

The nonlinear dynamics of the same experimental model of an internally resonant hanging elastic cable considered in Part I [1] are addressed here from the point of view of the global system behaviour in the control parameter space. Synthetic results of systematic response measurements, made at different amplitudes of the support motion in frequency ranges including meaningful external resonance conditions, are reported and discussed. Attention is devoted to the detection of the most robust classes of motion. Quite complicated overall pictures of regular response regions with variable contributions from different planar and nonplanar cable modes are observed, as well as several regions of quasiperiodic and chaotic responses. Sample quantitative characterizations of nonregular motions are presented. Some experimental results are also observed against the background of the nonlinear dynamic phenomena exhibited by a theoretical model of a continuous cable with four-degrees-of-freedom.