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     

轴向加速运动黏弹性梁受迫振动中的混沌动力学

研究了黏弹性轴向运动梁在外部激励和参数激励共同作用下横向振动的混沌非线性动力学行为. 引入有限支撑刚度, 并考虑黏弹性本构关系取物质导数, 同时计入由梁轴向加速度引起的沿径向变化的轴力, 建立轴向运动黏弹性梁横向非线性振动的偏微分-积分模型. 通过Galerkin截断方法研究了外部激励的频率和因速度简谐脉动引起的参数激励的频率在不可通约关系时轴向运动连续体的非线性动力学行为, 并对不同截断阶数的数值预测进行了对比. 基于对控制方程的Galerkin截断, 得到离散化的常微分方程组, 使用四阶Runge-Kutta方法求解. 基于此数值解, 运用非线性动力学时间序列分析方法, 通过Poincaré 映射, 观察到轴向运动梁随扰动速度幅值的倍周期分岔现象, 并比较了有无外部激励对倍周期分岔的影响. 分别在低速以及近临界高速运动状态下, 从相平面图、Poincaré 映射以及频谱分析的角度识别了系统中存在的准周期运动形态. 关键词： 轴向运动梁 非线性 混沌 分岔     

非线性声场下包膜微泡动力学与频率响应分析

包膜微泡在非线性声场下的响应对高强度聚焦超声治疗具有重要意义.本文通过耦合Gilmore-AkulichevZener模型与脂质包膜的非线性模型,采用KZK方程仿真非线性声场,分析在不同超声频率、不同声压以及不同包膜材料的黏弹性下的微泡动力学行为和微泡振荡频率,并进一步对比了实际测量声场与KZK方程仿真声场下的微泡动力学行为和频率响应.研究结果表明:非线性声场会导致微泡壁的瞬时运动速率减小,声压和频率的改变对微泡动力学的影响与在线性声场中类似;包膜材料的不同可以使振荡频率中的谐波分量发生改变,其中包膜材料的弹性对微泡的频率响应影响较小,包膜的初始黏性和初始表面张力对微泡的振荡频率分布影响较大,当初始黏性越小时,二次分谐波的峰值越高,当初始表面张力越大时,主频的峰值越高.本研究进一步阐明非线性超声激励包膜微泡的微泡动力学,为包膜微泡在非线性声场下的频率响应分析奠定理论基础.     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性. 关键词： 相对转动 准周期参激 时滞反馈 极限环     

有界噪声与谐和激励联合作用下Duffing-Rayleigh振子的Melnikov混沌

研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果. 关键词： 有界噪声 随机Melnikov过程 混沌运动 周期运动     

抗磁悬浮振动能量采集器动力学响应的仿真分析

分析了微型抗磁悬浮振动能量采集器中悬浮磁体的受力特性,发现了能量采集器的单稳态和双稳态现象,研究了能量采集器在不同工作状态下该两种稳态类型时的动力学响应特性.当能量采集器处于非工作的单稳态状态时,其动力学响应是在线性系统的基础上加入非线性扰动、幅频响应曲线向右偏转;热解石墨板间距越大,非线性扰动越强烈,右偏现象则越显著.当能量采集器处于非工作的双稳态状态时,其动力学响应比较复杂,出现倍周期、4倍周期以及混沌等非线性系统特有的现象.当能量采集器处于工作状态的双稳态状态时,其振动频率和外界激励频率保持一致,进行周期振动.该研究对抗磁悬浮振动能量采集器的结构设计具有重要的参考价值,为提高能量采集器的响应特性和输出性能提供了理论指导.     

振动声调制技术下微裂纹的非线性响应分析

采用非线性弹簧模型对振动声调制技术下微裂纹产生的非线性调制效应进行解释。从理论上分析了振动声调制技术下微裂纹产生非线性调制现象的原理,将微裂纹的开合状态等效为非线性弹簧。利用有限元软件构建并仿真微裂纹非线性弹簧模型,分别观察不同激励下裂纹界面的开合状态及混合声波的传播特性。结果表明,微裂纹界面随低频声波呈周期性开合,使得通过裂纹界面的高频声波与低频声波相互调制而产生非线性现象。在以上研究基础上,开展振动声调制实验研究。对比仿真结果,非线性调制系数R在实验条件下和仿真随低频激励幅值的变化趋势相同,证明了该模型的正确性。该模型为振动声调制技术应用于微裂纹的超声非线性检测提供了理论依据。     

基于Matlab/Simulink的三弹簧谐振子微振动的仿真实验

建立了三弹簧振子耦合系统微振动的实验模型,利用Matlab/Simulink仿真软件对该实验进行仿真建模,讨论系统在不同实验参数下从周期振动到混沌的各种动力学状态。仿真实验结果表明,参数的选取对系统微振动的动力学行为有着很大的影响。     

周期驱动下半导体动力学行为及控制

从nGaAs载流子非线性输运理论出发,建立物理模型,推导其动力学方程,分析系统随外场变化出现的复杂分支情况.数值模拟表明,在输入场幅值和频率变化的一定范围内,该系统具有周期、准周期和混沌特性,计算了表征混沌特性的物理量.利用间隙脉冲驱动法控制混沌得到预期的周期轨道 关键词： 分支 混沌 负微分电导     

Nonlinear dynamics of higher-dimensional system for an axially accelerating viscoelastic beam with in-plane and out-of-plane vibrations

In this paper, the bifurcations and chaotic motions of higher-dimensional nonlinear systems are investigated for the nonplanar nonlinear vibrations of an axially accelerating moving viscoelastic beam. The Kelvin viscoelastic model is chosen to describe the viscoelastic property of the beam material. Firstly, the nonlinear governing equations of nonplanar motion for an axially accelerating moving viscoelastic beam are established by using the generalized Hamilton’s principle for the first time. Then, based on the Galerkin’s discretization, the governing equations of nonplanar motion are simplified to a six-degree-of-freedom nonlinear system and a three-degree-of-freedom nonlinear system with parametric excitation, respectively. At last, numerical simulations, including the Poincare map, phase portrait and Lyapunov exponents are used to analyze the complex nonlinear dynamic behaviors of the axially accelerating moving viscoelastic beam. The bifurcation diagrams for the in-plane and out-of-plane displacements via the mean axial velocity, the amplitude of velocity fluctuation and the frequency of velocity fluctuation are respectively presented when other parameters are fixed. The Lyapunov exponents are calculated to identify the existence of the chaotic motions. From the numerical results, it is indicated that the periodic, quasi-periodic and chaotic motions occur for the nonplanar nonlinear vibrations of the axially accelerating moving viscoelastic beam. Observing the in-plane nonlinear vibrations of the axially accelerating moving viscoelastic beam from the numerical results, it is found that the nonlinear responses of the six-degree-of-freedom nonlinear system are much different from that of the three-degree-of-freedom nonlinear system when all parameters are same.     

The evolution of stiction repair for microelectromechanical system cantilevers using periodic excitation

In some recent experiments, it has been shown that structural vibrations are an efficient means to repair (i.e., unstick) stiction failed microcantilever beams. The analysis that accompanied these experiments identified excitation parameters (amplitude and frequency) that successfully initiated the debonding process between the microcantilever and the substrate. That analysis relied on coupling a static fracture model to a vibration model. However, that analysis could not describe what happened after the debonding process was initiated. For example, the repair could be partial, where the debonding begins but then arrests—or it could be total, where the beam is returned to its free-standing shape. The present paper examines the post-initiation behavior of stiction failed microcantilevers. A new, coupled fracture/vibration model is formulated and used to track the evolution of the repair, in order to determine the extent of the repair under various conditions. Moreover, this model successfully predicts some unusual (but explainable) behavior seen in the previous experiments, regarding partial and complete vibration repair.     

Output response identification in a multistable system for piezoelectric energy harvesting

In this paper we examine in detail the multiple responses of a novel vibrational energy harvester composed of a vertical bistable beam whose complex non-linear behavior is tuned via magnetic interaction. The beam was excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric element. The bistable laminate beam coupled to the piezoelectric transducer showed a variety of complex responses in terms of the beam displacement and harvested power output. The range of vibration patterns in this non-linear system included single-well oscillations and snap-through vibrations of periodic and chaotic character. Harvested power was found to be strongly dependent on the vibration pattern with nonlinearities providing a broadband response for energy harvesting. Wavelet analysis of measured voltage, displacement and velocity time histories indicated the presence of a variety of nonlinear periodic and also chaotic phenomena. To measure the complexity of response time series we applied phase portraits and determine stroboscopic points and multiscale entropy. It is demonstrated that by changing parameters such as the magnetic interaction, the characteristics of the bistable laminate harvester, such as the natural frequency, bandwidth, vibration response and peak power can be readily tailored for harvesting applications.     

Nonlinear vibration of micromachined asymmetric resonators

In this paper, the nonlinear dynamics of a beam-type resonant structure due to stretching of the beam is addressed. The resonant beam is excited by attached electrostatic comb-drive actuators. This structure is modeled as a thin beam-lumped mass system, in which an initial axial force is exerted to the beam. This axial force may have different origins, e.g., residual stress due to micro-machining. The governing equations of motion are derived using the mode summation method, generalized orthogonality condition, and multiple scales method for both free and forced vibrations. The effects of the initial axial force, modal damping of the beam, the location, mass, and rotary inertia of the lumped mass on the free and forced vibration of the resonator are investigated. For the case of the forced vibration, the primary resonance of the first mode is investigated. It has been shown that there are certain combinations of the model parameters depicting a remarkable dynamic behavior, in which the second to first resonance frequencies ratio is close to three. These particular cases result in the internal resonance between the first and second modes. This phenomenon is investigated in detail.     

强超声脉冲激励下金属板超谐波和次谐波振动的有限元分析

针对实验中观察到金属板在强超声脉冲作用下的超谐波和次谐波振动现象,采用显式有限元方法建立有限元模型,并对其进行瞬态动力学分析。在模型中压电结构的热弹性类比方法和界面接触-碰撞算法分别用来模拟换能器激励以及变幅杆与板之间的相互作用。通过分析计算得到板的振动速度的波形和频谱以及接触力的波形和频谱,可知在换能器工作条件下,变幅杆与金属板之间的接触力波形畸变是导致板超谐波振动的原因,而变幅杆与金属板之间的间歇性接触运动引起板的次谐波振动,有限元数值模拟与实验结果相符。     

Chaos in atomic force microscopy

Chaotic oscillations of microcantilever tips in dynamic atomic force microscopy (AFM) are reported and characterized. Systematic experiments performed using a variety of microcantilevers under a wide range of operating conditions indicate that softer AFM microcantilevers bifurcate from periodic to chaotic oscillations near the transition from the noncontact to the tapping regimes. Careful Lyapunov exponent and noise titration calculations of the tip oscillation data confirm their chaotic nature. AFM images taken by scanning the chaotically oscillating tips over the sample show small, but significant metrology errors at the nanoscale due to this "deterministic" uncertainty.     

光梯度力驱动纳谐振器的非线性动力学特性研究

光梯度力作为纳谐振器的一种新型驱动方式,得到了广泛关注.本文研究了光梯度力的固有非线性特性,建立了光梯度力驱动圆环与辐条谐振系统的动力学模型.揭示了入射光功率以及几何参数对系统的非线性动力学响应的影响规律.研究表明:光梯度力会引起系统呈现刚度软化效应,随着入射光功率增大,系统主共振峰值明显增大,且谐振频率随着振幅增大而产生较大偏移;两环初始间隙增大,系统振动幅值和谐振频率均下降;辐条厚度越大,系统主共振峰值和谐振频率均减小.因此,可以通过调节入射光功率来实现圆环辐条谐振器的频率调节,为光梯度力驱动纳谐振器动力学设计和性能预测提供理论参考.     

Dynamics of high quality factor force microscope microcantilevers operated in contact mode

In AFM system with contact mode operation, the surface structure is determined by measuring the variation of the microcantilever tip deflection as the tip scans across the sample. Therefore, the dynamic characteristics of the microcantilever, including the stability, rapidity and accuracy performances, are extremely important parameters in determining the performance of AFM. In this paper, we obtain the analytical expressions of the deflection, overshoot, and adjustment time of the cantilever by using the Laplace transform theorem. The influence of the intrinsic parameters on the system dynamics is discussed in detail, which provides theoretical guidance for selecting samples in the experiments. Moreover, we propose a new control method based on the velocity feedback control in order to enhance the dynamic features of the system. The results indicate that the new control method can effectively improve the dynamic characteristics of the microcantilever.     

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibration absorber is thus employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions. The values of the spring stiffness and mass of the vibration absorber are significantly lower than their counterpart of the forced nonlinear oscillator. Vibrational energy of the forced nonlinear oscillator is transferred to the attached light mass through linked spring and damper. As a result, the nonlinear vibrations of the forced oscillator are greatly reduced and the vibrations of the absorber are significant. The method of multiple scales is used to obtain the averaged equations that determine the amplitude and phases of the first-order approximate solutions to primary resonance vibrations of the forced nonlinear oscillator. Illustrative examples are given to show the effectiveness of the dynamic vibration absorber for suppressing primary resonance vibrations. The effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibrations are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.     

Modal interaction in chaotic vibrations of a shallow double-curved shell-panel

Experimental results and analytical results are presented on chaotic vibrations of a shallow double-curved shell-panel subjected to gravity and periodic excitation. Modal interactions in the chaotic responses are discussed. The shell-panel with square boundary is simply supported for deflection. In-plane displacement at the boundary is elastically constrained. In the experiment, time histories of the chaotic responses at the spatial multiple positions of the shell-panel are measured for the inspection of modal interaction. In the analysis, the shallow shell-panel is assumed to have constant curvatures along to orthogonal directions and geometric initial imperfection. The Donnell-Mushtari-Vlasov type equation is used as governing equation with lateral inertia force. Assuming deflection with multiple modes of vibration, the governing equation is reduced to a set of nonlinear ordinary differential equations by the Bubnov-Galerkin procedure. Chaotic responses are integrated numerically. The chaotic responses, which are obtained by the experiment and the analysis, are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. Contribution of modes of vibration to the chaotic responses is analyzed by the principal component analysis, i.e., Karhunen-Loève transformation.