Design of a nonlinear vibration absorber using three-to-one internal resonances

A weakly nonlinear vibration absorber is designed to attenuate the primary resonance vibrations of a single-degree-of-freedom weakly nonlinear oscillator having cubic nonlinearity. The linearised natural frequency of the nonlinear absorber is tuned to be approximately one-third the linearised natural frequency of the primary nonlinear oscillator. The low frequency mode for the absorber is favourably considered based on the fact that the nonlinear absorber can be easily realised in practice by using a light-weight mass attachment with small values of linear and nonlinear stiffness of coupling. For a given primary nonlinear oscillator and absorber mass, implementation of three-to-one internal resonances requires the smallest value of the absorber linear stiffness among three options for utilising internal resonances to design nonlinear absorber. The method of multiple scales is used to obtain the averaged equations that determine the amplitudes and phases of the first-order approximate solutions to the vibrations of the primary nonlinear oscillator and nonlinear absorber. It is found that the absorber response may admit either forced vibration having the forcing frequency or a combination of forced vibration and free-oscillation term having one third the forcing frequency. The nonlinear absorber can effectively suppress the amplitude of primary resonance response and eliminate saddle-node bifurcations occurring in the frequency-response curves of the primary nonlinear oscillator. Numerical results are given to show the effectiveness of the nonlinear absorber for suppressing nonlinear vibrations of the primary nonlinear oscillator under primary resonance conditions.     

弹性体非线性振动系统参数辨识的一种时域法

提出了对弹性体非线性振动系统参数辨识与预测的一种时域模型法。它可视为时间序列分析中的 AR模型法在非线性领域内的一种推广。该方法首先将非线性振动系统中的非线性恢复力和非线性阻尼力用某一函数级数(例如幂级数 )表示 ,然后 ,先用线性模型来逼近原系统 ,应用线性系统辨识方法确定系统阶次 ,再确定系统中非线性恢复力、阻尼力的结构 ,建立非线性模型并辨识各项参数 ,最后进行预测。算例表明 ,用该方法建立的模型能够较好地反映系统的非线性特性 ,并能提高模型预测的准确性。     

非线性弹性碰摩转子周期运动稳定性分析

在同时考虑轴承油膜力、转轴非线性弹性力和碰摩发生时转静件间的相对速度对非线性摩擦力的影响基础上,构造了具有碰摩故障转子-轴承系统的动力学模型。利用求解非线性非自治系统周期解的延拓打靶法和Floquet理论,研究了系统周期运动的稳定性,分析了非线性摩擦力对系统动力学特性的影响。     

Evaluation of transmissibility for a class of nonlinear passive vibration isolators

In this study, the concept of Output Frequency Response Functions (OFRFs) is applied to represent the transmissibility of nonlinear isolators in frequency domain. With the OFRFs estimated from numerical simulation responses, an explicit analytical relationship between the transmissibility and the nonlinear characteristic parameters is derived for a wide class of nonlinear isolators that have nonlinear anti-symmetric damping characteristics and a comprehensive pattern about how the nonlinear damping characteristic parameters might affect the force and displacement transmissibility is built for the vibration isolators. The results reveal that it is reasonable to analyze the force and displacement transmissibility of the nonlinear isolators by simply investigating the fundamental harmonic components of the force and displacement outputs of the nonlinear isolators, and the introduction of a nonlinear anti-symmetric damping into vibration isolators can significantly suppress both the force and displacement transmissibility over the resonant frequency region, but has almost no effect on the transmissibility at non-resonant regions. These conclusions are of significant importance in the analysis and design of the nonlinear vibration isolators with nonlinear anti-symmetric damping.     

用渐进摄动法对具有二次非线性项的多自由度系统摄动分析

考虑大挠度几何非线性和剪切变形的影响,工程中机械柔性板壳结构的非线性动力学运动控制方程经常被转化为二阶模态的、包含有二次和三次非线性项和外激励的非线性常微分方程,由于二次非线性项的存在,常用的多尺度法进行摄动分析时,需要复杂的运算才能将其包含进来。相比之下,基于傅里叶扩展和时间尺度的渐进摄动法可以较容易地将非线性动力学微分方程中的平方项考虑进来。通过引进适当的尺度变换,利用渐进摄动法对该系统在二阶模态之间发生1:2内共振、主参数共振、1/2亚谐共振时进行摄动分析,得到自治系统下的平均方程。数值结果发现4自由度自治系统存在复杂的周期运动、倍周期运动、概周期运动。该非线性系统为量纲一后的结果,对于与该系统类似的多自由度非线性机械系统可以直接用此平均方程进行全局分叉和混沌动力学研究。     

基于包络法的正交面齿轮齿廓尖化研究

提出了一种新型的3P-6SS并联机构,计算了其运动学反解。制作了这种并联机构的实物样机,并搭建了该并联机构的控制系统。基于数字信号处理器（DSP）编写了控制程序,并使用3P-6SS并联机构的实物样机进行了实验。在无抬笔、落笔控制的情况下,该并联机构写出了有联笔的字母“BUPT”;在有抬笔、落笔控制时,该机构写出了无连笔的数字“2008”。实验结果表明了反解算法的正确性和控制系统的有效性。     

一类迟滞非线性振动系统建模新方法

用理论和试验相结合的手段研究一类迟滞非线性振动系统的动力建模, 提出一种新的建模方法, 用此方法建立非线性模型用来描述这类系统的动态特性。该模型用非线性刚度和非线性阻尼机理构造, 刚度和阻尼机理由理论和试验推出, 模型中的参数由试验数据辨识。用所建模型重构恢复力——位移迟滞环, 结果表明, 该模型能很好描述这类非线性振动系统的特性, 模型中各参数的重要性得到展示, 提出的建模方法实用且有效。     

On the distribution of nonlinear effects in locally nonlinear one-dimensional chain type structures

Nonlinear effect is a typical phenomenon for nonlinear systems, which is characterized as the energy of the system input transferred from the frequency modes in the input to the output frequency locations, which are either below or above the input frequency band. The present work is devoted to investigating the distribution of nonlinear effects in one-dimensional chain type structures with local nonlinearity in which only one or few components are of nonlinear property. The results reveal that the positions of both the nonlinear components and the external input play crucial roles in determining the distribution of nonlinear effects in the locally nonlinear structures, and provide a new insight into the complex dynamic of nonlinear systems in frequency domain. The results are of great significance to the analysis, design and control of the mechanical systems whose few components are of nonlinear property.     

Dynamic analysis of harmonically excited non-linear structure system using harmonic balance method

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear structural systems. This method is based on the substructure synthesis formulation and a harmonic balance procedure, which is applied to the analysis of nonlinear responses. A complex nonlinear system is divided into substructures, of which equations are approximately transformed to modal coordinates including nonlinear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the nonlinear solution for the system is obtained. Based on the harmonic balance method, the proposed procedure reduces the size of large degrees-of-freedom problem in the solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated using the study of the nonlinear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to nonlinear response prediction when compared with other conventional methods.     

Time-frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems

Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.     

NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS

In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation. However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process. Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis. A nonlinear data reconciliation method based on KPCA is proposed. The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space. Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel. The data reconciliation method based on KPCA is applied to ternary distillation column. Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.     

具有模糊可靠性的齿轮传动优化设计

针对齿轮传动设计中一些设计参数的随机性和强度判据的模糊性，本文提出了齿轮动的模糊可靠性设计理论和方法，建立了模糊可靠性优化设计的数学模型，并给出了优化设计实例。     

基于ANFIS的温度传感器非线性校正方法

介绍了用神经网络进行传感器非线性误差校正的原理与方法,分析了自适应神经模糊推理系统(ANFIS)的基本原理。通过模糊聚类和混合学习算法,ANFIS可以逼近高阶输入输出非线性系统,将该算法用于两个典型非线性系统建模,均能获得满意结果。之后,将ANFIS算法用于温度传感器非线性校正中,试验结果表明该方法与基于CMAC网络和BP网络的校正方法相比,校正的精度高于以上两种校正方法。     

基于最小二乘支持向量机的传感器非线性动态补偿

提出了一种基于最小二乘支持向量机的非线性传感器动态测量误差的校正方法，使得通过该方法补偿的传感器具有理想的输入输出特性。先将传感器的非线性动态系统分解成线性动态子环节和非线性静态子环节串联；与之对应，非线性动态补偿过程也包含2个阶段：线性动态补偿和非线性静态校正。然后，通过函数展开将补偿器的非线性传递函数转换为等价的类线性形式一中间模型；再通过LS-SVM回归算法求取中间模型参数；最后，推导出中间模型参数与补偿器2个子模型参数之间的关系，并通过该关系实现非线性静态校正和线性动态补偿环节的同时辨识。与常规非线性动态补偿方法比较，该方法优点是明显的：（1）只需进行一次动态标定实验；（2）能给出非线性动态补偿器的数学解析表达式；（3）充分利用LS—SVM的优点，使辨识的补偿器具有更好的抗干扰能力。仿真与实际实验结果均表明该传感器非线性动态补偿方法有效。     

基于位移加载控制的金属橡胶弹性元件试验建模研究

基于电液材料试验机精确的位移加载控制,对圆环形金属橡胶弹性元件进行了动态力学试验,结果表明,金属橡胶材料具有明显的迟滞非线性性质,其阻尼由多种成分组成。根据动态试验结果建立迟滞回线拟和分解的高次弹性复合阻尼模型,该模型用非线性刚度和非线性复合阻尼机理构造,模型中的参数由试验数据辨识。用所建模型重构恢复力一位移迟滞回线．结果表明,该模型能很好描述这类非线性振动系统的特性,为进一步理论分析提供了依据。     

齿轮全齿磨损的胞映射全局动力学分析

含故障齿轮非线性系统的全局性态分析是对齿轮正确故障诊断的状态依据,运用能够反映非线性系统复杂全局性态的简单胞映射方法,把故障齿轮非线性系统所处的状态空间转化为胞空间,对齿轮非线性系统在不同程度磨损故障状态下的动力系统的全局特性进行了分析,通过对比不同程度故障下系统的吸引域及其吸引胞,得到磨损故障齿轮非线性系统全局特性的变化规律,为齿轮非线性系统的故障诊断提供了另一种研究思路和方法。     

液压挖掘臂关节伺服系统非线性动态特征研究

为有效分析挖掘臂关节伺服控制系统,提高控制精度,通过机理建模分析了系统存在的非线性特性——比例阀死区、阀控非对称液压缸动态特性不对称特性、液压缸非线性摩擦力、非线性液压弹簧力及挖掘臂关节非线性动力学。通过实验验证了系统中各项非线性特性对其控制性能的影响。结果表明,以上几种非线性特性对系统动态响应均存在不利影响。     

Nonlinear parameter identification of partial rotor rub based on experiment

To model and understand the physics of partial rub, a nonlinear rotor model is sought by applying a nonlinear parameter identification technique to the experimental data. The results show that the nonlinear terms of damping and stiffness should be included to model partial rotor rub. Especially, the impact and friction during the contact between rotor and stator are tried to explain with a nonlinear model on the basis of experimental data. The estimated nonlinear model shows good agreements between the numerical and the experimental results in its orbit. Also, the estimated nonlinear model could explain the backward whirling orbit and jump phenomenon, which are the typical phenomena of partial rub.     

Decoupling analysis on nonlinear system based on the modified generalized frequency response functions

This paper presents a nonlinear decoupling approach based on the Modified Generalized Frequency Response Functions (MGFRFs) and the nonlinear feature of phase invariance, for the pure nonlinearity-input nonlinear system. The MGFRFs are defined by combining the ‘homotopy’ GFRFs and phase information of the system input. The nonlinear feature of phase invariance is extracted based on MGFRFs. The decoupling approach is proposed based on MGFRFs and extended from the pure tone excitation to the multi-tone excitations by considering phase invariance. Numerical simulation and experimental investigation were carried out, whose results have shown that nonlinear feature of phase invariance is correct and reasonable and the proposed decoupling approach is valid and feasible. The proposed decoupling approach can be employed to identify the excitation sources and to estimate nonlinear system parameters for the pure nonlinearity-input nonlinear vibration system.     

基于不同相控聚焦模式的非线性超声阵列成像方法研究

发展一种用于缺陷定位的非线性超声阵列成像方法。研究聚焦声场的时间-空间传播特点以及形成扩散声场的条件,分析并行聚焦和顺序聚焦的扩散声场声动能与非线性效应的关系,提出利用超声阵列在两种聚焦模式下激励带宽内(基波)声动能差值表征的非线性超声成像方法。进一步研究时延及时间窗宽对两种检测模式的扩散声动能及非线性成像的影响,优化出有效的非线性成像参数。结果表明:时延的选择对成像结果影响较大,时间窗宽的选择对成像结果影响较小;在一定时延范围内,均可以形成稳定的扩散声场,在该时延范围内可以较好实现微裂纹检测。利用提出的非线性超声阵列成像方法很好地实现了结构中微裂纹检测及成像。