Amplitude reduction of parametric resonance by dynamic vibration absorber based on quadratic nonlinear coupling

The paper proposes an amplitude reduction method for parametric resonance with a new type of dynamic vibration absorber utilizing quadratic nonlinear coupling. A main system with asymmetric nonlinear restoring force and harmonic excitation causes parametric resonance in the system. In contrast with autoparametric vibration absorber, the natural frequency of the vibration absorber is tuned to be in the neighborhood of twice that of the main system. For such a vibration absorber, we investigate the effect on the amplitude reduction for a parametrically excited main system. Analytical results using the method of multiple scales show that the amplitude of parametric resonance is reduced by the effect of the vibration absorber. The experimental results by a simple apparatus indicate that the parametric resonance is stabilized by the effects of both vibration absorber and Coulomb friction of the main system. Moreover, numerical results considering the Coulomb friction of the main system show that the amplitude of parametric resonance becomes close to zero by the proposed vibration absorber.     

The potential of micro-electro-mechanical accelerometers in human vibration measurements

This paper evaluates the advantages and the drawbacks deriving from the use of MEMS (micro-electro-mechanical systems) accelerometers for hand-arm and whole-body vibration measurements. Metrological performances of different transducers were assessed through the identification of their frequency response function, linearity, floor noise and sensitivity to thermal and electromagnetic disturbances. Experimental results highlighted a standard instrumental uncertainty (including the nonlinearity) lower than 5% with the single frequency calibration procedure, such a value was reduced to 2%. The temperature effect was negligible and the electromagnetic disturbances sensitivity was comparable to that of the piezoelectric accelerometers. The compatibility of measurements obtained with MEMS accelerometers with those of piezoelectric-based measurement chains was verified for two specific applications. An example of direct transducer fixation on the skin for vibration transmissibility measurements is also presented. Thanks to the MEMS peculiarities – mainly small sizes and low cost – since novel approaches in the vibration monitoring could be pursued. For instance, it is possible to include by design MEMS accelerometers in any hand-held tool at the operator interface, or inside the seats structures of cars, tractors and trucks. This could be a viable solution to easily obtain repeatable exposure measurements and could also provide diagnostic signals for the tools or seats of functional monitoring.     

Identification of Iwan distribution density function in frictional contacts

Mechanical contacts affect structural responses, causing localized nonlinear variations in the stiffness and damping. The physical behaviors of contact interfaces are quite complicated and almost impossible to model at the micro-scale. In order to establish a meaningful understanding of the friction effects and to predict the contact behavior, a robust parametric friction model is usually employed. This paper employs an Iwan-type model to predict the nonlinear effects of a frictional contact interface. The Iwan model is characterized by its distribution density function which is commonly identified by double differentiation of the experimentally obtained joint interface restoring force. Direct measurement of restoring forces at the contact interface is impractical and estimating it using an inverse approach introduces considerable uncertainties in identification of the density function. This paper develops a more reliable procedure in identification of the Iwan model by relating the density function to the joint interface dissipated energy. The energy dissipated in a contact interface is easily obtained from measurement and it is shown that the dissipation is uniquely defined using the density function and the vibration amplitude. In an experimental case study Iwan distribution density function in a frictional contact is obtained using measured dissipations at different vibration levels.     

云南龙陵黄龙玉的振动光谱及XRD光谱表征

黄龙玉是云南省龙陵县近年发现的新玉石品种,在国内市场热度较高。目前对其矿物组成和光谱特征还未有报道。在常规的宝石学测试基础上,重点采用激光拉曼光谱仪、红外光谱仪和X射线粉晶衍射(XRD)分析方法,对其振动光谱特征和矿物组成进行了细致的研究。结果表明,黄龙玉显示典型的石英质玉石的振动光谱特征,主要红外吸收谱带位于1 162,1 076,800,779,691,530和466 cm-1处,分别属于Si—O—Si非对称伸缩振动、Si—O—Si对称伸缩振动、Si—O—Si弯曲振动。其中在800 cm-1附近谱带有分裂,表明黄龙玉结晶程度较好。拉曼光谱中,归属Si—O—Si弯曲振动的谱带强度较高,主要拉曼散射峰为463和355 cm-1。XRD结果证实,其矿物组成为较纯的石英,红色样品中还含有微量的赤铁矿,是其产生红色的原因。这是首次系统研究黄龙玉的红外光谱、拉曼光谱及XRD谱学特征,为其鉴定、定名及后续的研究提供科学依据。     

无内共振时的扬声器分谐波

研究了驱动频率低于扬声器辐射体薄壳轴对称模态最低固有频率的扬声器1/2分谐波失真。采用以位敏探测器作为光电传感器的激光三角法实验观测扬声器振膜的振动位移和模态,确定了参与的非轴对称模态的周向波数。采用多尺度法求解了扬声器的非线性模态方程。给出了扬声器分谐波的阈值电压公式。结果表明扬声器辐射体薄壳的分谐波失真源于直接激励的轴对称模态耦合激发了非轴对称模态的振动,这种耦合激励表现为参数激励。增大扬声器振膜材料的损耗因子、杨氏模量和厚度可提高产生分谐波的阈值电压。      

Lie Symmetries,Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations

Abstract

The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik – Novikov – Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation, the (2+1)-dimensional generalization of the nonlinear Schrödinger equation by Fokas as well as the (2+1)-dimensional generalized sine-Gordon equation of Konopelchenko and Rogers. We show that in all these cases the Lie symmetry algebra is infinite-dimensional; however, in the case of the breaking soliton equation they do not possess a centerless Virasorotype subalgebra as in the case of other typical integrable (2+1)-dimensional evolution equations. We work out the similarity variables and special similarity reductions and investigate them.     

On the orthogonalised reverse path method for nonlinear system identification

The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673–708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach – the orthogonalised reverse path (ORP) method – is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.     

扬声器辐射体旋转薄壳的非线性振动方程

推导了扬声器辐射体旋转薄壳的离散非线性振动方程。从虚功原理出发,选用扬声器辐射体旋转薄壳的本征模态对连续体进行离散。薄壳的几何非线性采用Sanders非线性薄壳理论的应变一位移关系。方程系数由有限元方法确定。方程表明轴对称模态由驱动力直接激励,非轴对称模态由轴对称模态非线性耦合激励,该耦合激励表现为参数激励。方程揭示了扬声器非线性失真的机制,可用于分析扬声器辐射体薄壳非线性引起的谐波失真、分谐波失真和互调失真。      

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

扭摆振动实验

为了丰富“非线性系统实验”课程的教学内容,开设了扭摆振动实验,将力学中的非线性现象引入到教学中.在实验内容的设计上,采取线性振动和非线性振动相结合的方式,即:首先研究扭摆的线性振动,如阻尼振动、受迫振动等,先对振动问题有基本的理解,然后再研究扭摆的非线性振动,分别固定驱动频率、改变励磁电流和固定励磁电流、改变驱动频率,观察非线性摆的运动情况.     

Finite element modeling of a micro-drill and experiments on high speed ultrasonically assisted micro-drilling

Modal characteristics of a generic micro-drill and experiments on the micro-drilling with superimposing of longitudinal ultrasonic vibration are presented. Finite element (FE) analysis is used for identification of eigenfrequencies and modes of the drill. Dynamic influence of the drill shank is discussed and a hybrid model is proposed to account for it. The model is proven to be efficient for complicated drill models and advanced analysis. A high speed ultrasonically assisted micro-drilling (UAMD) system is established with air bearings and longitudinally vibrating workpiece. During the experiments the thrust force reduction is studied as well as effects of ultrasonic vibration frequency and rotational speed. A correlation study was conducted between the thrust force measurements and simulations from a nonlinear force model. It can be seen that the current one-dimensional model is not sufficient to describe the complete behavior of the drill. The FE model and force experimental results can be utilized for a full dynamic model of the UAMD system to study vibration and the cutting mechanism in the future.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,拓展非线性振动教学内容.     

光学移相干涉仪抗振系统的鲁棒μ控制器设计

将结构奇异值μ综合鲁棒控制技术应用于主动抗振控制系统中,并用于解决光学移相干涉仪抗振系统的不确定性问题.采用小波分析方法将随机振动信号进行时频分析后得到低频全局信息,随后运用μ综合D-K迭代法设计鲁棒μ控制器对低频振动进行抑制.该方法克服了由模型自身和外部干扰所引起的不确定性,使得控制系统能够有效地抑制抗振模型的不确定性和外部振动的干扰,同时也具有很高的控制准确度和灵敏度.仿真结果表明,该方法使光学移相干涉仪在外部振动的干扰下具有较好的鲁棒稳定性和控制准确度,同时也能较好地抑制低频振动.     

A Bearing Fault Diagnosis Method Based on PAVME and MEDE

When rolling bearings have a local fault, the real bearing vibration signal related to the local fault is characterized by the properties of nonlinear and nonstationary. To extract the useful fault features from the collected nonlinear and nonstationary bearing vibration signals and improve diagnostic accuracy, this paper proposes a new bearing fault diagnosis method based on parameter adaptive variational mode extraction (PAVME) and multiscale envelope dispersion entropy (MEDE). Firstly, a new method hailed as parameter adaptive variational mode extraction (PAVME) is presented to process the collected original bearing vibration signal and obtain the frequency components related to bearing faults, where its two important parameters (i.e., the penalty factor and mode center-frequency) are automatically determined by whale optimization algorithm. Subsequently, based on the processed bearing vibration signal, an effective complexity evaluation approach named multiscale envelope dispersion entropy (MEDE) is calculated for conducting bearing fault feature extraction. Finally, the extracted fault features are fed into the k-nearest neighbor (KNN) to automatically identify different health conditions of rolling bearing. Case studies and contrastive analysis are performed to validate the effectiveness and superiority of the proposed method. Experimental results show that the proposed method can not only effectively extract bearing fault features, but also obtain a high identification accuracy for bearing fault patterns under single or variable speed.     

A nonlinear energy sink with an energy harvester: Transient responses

This paper investigates energy harvesting using nonlinear energy sink. First a novel apparatus is described in detail outlining how the essential nonlinearity and energy harvesting are achieved. Then the system modeling is addressed, including the equations of motion for the mechanical system and the electromechanical system, and a formula for the transduction factor. The experimental identification is conducted to determine several key parameters and relationships. Using the established models, a computer simulation is carried out to investigate the apparatus?s performance under transient responses in terms of vibration absorption and energy harvesting. Finally experiments are conducted to validate the simulation results. It is shown that the system performs well, being capable of energy localization as well as broad band vibration absorption. The system is also shown to be capable of harvesting energy.     

高功率超声脉冲激励下金属板的非线性振动现象研究

对高功率超声脉冲作用下金属板中的超谐波、次谐波、准次谐波以及混沌等非线性振动现象进行了实验和理论研究.在实验中,高功率超声换能器产生脉冲调制的高频振动激励金属板产生非线性振动,利用激光测振技术测量不同尺寸和不同固定方式下金属板复杂的非线性振动情况,并对其进行了时序分析、频谱分析以及相空间分析.根据实验条件,提出包含非线性接触阻尼的振动-碰撞动力学模型,用以研究强超声振动-碰撞作用下的板非线性振动机制,并进行了相应的理论计算.计算结果表明,超声换能器的变幅杆与金属板之间的间歇性高频碰撞作用是金属板强非线性振 关键词： 非线性板振动 强超声脉冲激发 振动-碰撞动力学     

Large amplitude vibration of an initially stressed cross ply laminated plates

In this paper, nonlinear equations of large amplitude vibration for a laminated plate in a general state of nonuniform initial stress are derived. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration behaviour of an initially stressed cross-ply laminated plate is studied. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge-Kutta method is used to obtain the nonlinear to linear frequencies. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, aspect ratio, thickness ratio, modulus ratio, stack sequence, layer number and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.     

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.     

地塞米松磷酸钠和倍他米松磷酸钠两种差向异构体的FTIR,FT-Raman和SERS光谱研究

检测了地塞米松磷酸钠和倍他米松磷酸钠两种差向异构体的红外光谱(FTIR), 固体和饱和溶液的常规拉曼光谱(NRS)及以银胶为基底的表面增强拉曼光谱(SERS)。通过红外和拉曼光谱的结合,对其各基团的振动模式进行解析,并对峰进行归属和比较。结果表明：两种物质的主要区别是地塞米松磷酸钠的CH₃非对称伸缩振动和对称面内变形振动的拉曼位移较大;依据SERS作用机理和规律,推测两种物质在银胶上主要是通过P—O键、羧基和五元环与银胶垂直吸附。建立了两种差向异构体基于银纳米粒子的吸附模式,实现了对两种物质进行快速鉴别与区分的方法,为进一步研究肾上腺皮质激素类药物提供了十分重要的信息和可靠的参考。     

Neural net pattern recognition based auscultation of croup cough and pertussis using phase portrait features

Cough signal analysis for understanding the pathological condition has become important from the outset of the exigency posed by the epidemic COVID-19. The present work suggests a surrogate approach for the classification of cough signals - croup cough (CC) and pertussis (PT) – based on spectral, fractal, and nonlinear time-series techniques. The spectral analysis of CC reveals the presence of more frequency components in the short duration cough sound compared to PT. The musical nature of CC is unveiled not only through the spectral analysis but also through the phase portrait features – sample entropy (S), maximal Lyapunov exponent (L), and Hurst exponent (H_b). The modifications in the internal morphology of the respiratory tract, giving rise to more frequency components associated with the complex airflow dynamics, get staged through the higher fractal dimension of CC. Among the two supervised classification tools, cubic KNN (CKNN) and neural net pattern recognition (NNPR), used for classifying the CC and PT signals based on nonlinear time series parameters, NNPR is found better. Thus, the study opens the possibility of identification of pulmonary pathological conditions through cough sound signal analysis.