动力学,振动与控制学科未来的发展趋势

对近年来动力学，振动与控制的研究进展作了简要回顾，概述了非线性动力学与振动主动控制这两个研究热点的现状，提出了世纪之初应关注的若干研究前沿，即高维非线性系统的全局摄动法，全局分岔和混沌动力学，高维强非线性系统分岔与混沌动力学的实验研究，非线性时滞系统的动力学，流体－弹性体－刚体耦合系统动力学与控制，碰撞与变结构系统动力学，微机电系统动力学。最后，对我国动力学，振动与控制的发展提出了一些建议。     

考虑微观粘滑的连接梁结构动力响应分析

连接的存在对结构的动力学响应有重要影响.界面的微观/宏观粘滑运动引起结构刚度和阻尼的非线性.传统的结构动力学研究中通常采用等效线性化的方式处理含连接结构的动响应分析问题.本文从连接界面微/宏观滑移运动引起结构非线性和阻尼迟滞的物理机理出发,利用一种弹簧-滑块并联系统模型模拟界面上的微/宏观粘滑行为,以该模型描述的本构关系为基础,推导了能应用于平面梁结构有限元动响应分析的非线性连接单元.利用上述模型和单元研究了含连接平面梁结构的动响应问题.设计了实验件,进行了力锤冲击实验,并将数值计算结果与实验结果进行了对比和分析.结果表明,界面微/宏观粘滑是引起干摩擦阻尼的主要原因,考虑非线性微/宏观粘滑运动对含连接结构的动响应分析至关重要.本文的模型和方法能够有效地预测含连接结构的非线性动力学响应,特别是在瞬态响应的高振幅阶段.     

输液管模型及其非线性动力学近期研究进展

综述了输液管系统的各类物理模型及其相应的数学模型,在流体满足基本假设条件下,对于管道内径远远小于管道长度的直管和曲管,详细叙述了梁模型管动力学数学模型的建模过程以及建模方法,针对在水动压力作用下以及管道短而且薄的情形,综述了壳模型的输液管道的动力学方程.在此基础上,概述了近几年来输液管道的非线性振动、稳定性、分岔与混沌、特别是管道控制的研究现状,并对今后的发展趋势作了分析和预测.综观非线性动力学理论的发展历程可以发现选取研究对象和典型的数学模型是至关重要的.对于低维的非线性系统,常常选用van der Pol、Duffing、Mathieu、Lorenz等典型系统来进行研究工作的.通过本文可以看出,对于研究高维非线性系统动力学,流诱发输液管的动力学问题是非常典型的模型之一,它有着容易理解的工程背景、包含了梁和壳的振动问题,并且它的数学模型相对简单,然而却能包含非常复杂的非线性动力学现象,同时容易解释数学方法得到的结果易对应到工程中的实际现象.本文希望通过对输液管动力学模型及其非线性动力学和控制研究现状的综述,建立高维非线性动力学的分析模型,以便发展高维非线性动力学的分岔与混沌理论,同时建立相应的控制理论基础.      

参数激励下静电驱动MEMS共振传感器的非线性动力特性研究

静电驱动微机电系统(MEMS)共振传感器因其结构简单、应用广泛等优点引起了研究人员广泛的关注,共振传感器件耦合系统在非线性静电力、压膜阻尼、参数激励下呈现出较复杂的非线性振动、不稳定性、分岔与混沌行为.提出参数激励作用下静电驱动微机电系统中梁式微结构共振传感器的动力学模型,采用多尺度方法对微系统的动力学方程进行摄动分析,探讨直流偏置电压、压膜阻尼和交流激励电压幅值对系统频率响应、共振频率的影响规律,结果表明:直流偏置电压和交流电压幅值都具有软化效应,且使共振频率漂移到较小的数值范围,压膜阻尼对共振频率的影响较小,但是增大压膜阻尼会使稳态振幅的峰值明显下降,为静电驱动微机电系统共振传感器的动力学分析与设计提供参考.     

绳索系统的建模、动力学和控制

绳索系统具有无限自由度,当计入非线性因素的作用时,其面内和面外的振动相互耦合,呈现非常丰富的非线性动力学行为.另外,绳索系统经常工作在风、流体、微重力、电磁力等作用下,进一步加剧了其动力学的复杂性.绳索系统的动力学现象引起了工程界和力学界的关注.本文对绳索在重要工程系统中的应用及相应的动力学现象进行概述,给出了柔索的动力学建模过程,对绳索系统的动力学和控制研究进行了总结,并指出了值得进一步关注的若干问题.      

压电超声电机的非线性动力学研究进展

压电超声电机 (ultrasonic motor, USM) 是一个具有闭环控制的机电耦合强非线性系统,在大功率情况下,会表现出明显的非线性现象．其非线性因素主要表现为: (1) 定子与动子之间的接触非线性; (2) 定子材料非线性; (3) 温度、磨损等因素引起的缓变因素; (4) 驱动电网络中的非线性因素．由于诸多非线性因素的存在,使得 USM 系统具有跳跃、滞后、共振频率漂移、死区和饱和等非线性现象,同时,给 USM 的非线性动力学建模带来了困难．而 USM 闭环控制要求有一个合理的动力学模型,因此,研究 USM 的非线性动力学建模是 USM 研究中的一个重要内容．针对超声电机系统中普遍存在的非线性因素和非线性动力学建模方法进行了归纳,对已有文献中有关超声电机非线性动力学的研究进行了总结,指出了有关该方面的若干研究方向．      

超磁致伸缩换能器的磁滞非线性动力学仿真

在超磁致伸缩材料输出端位移假设的基础上,建立了以输出顶杆为研究对 象、考虑材料内部磁滞非线性及预压弹簧特性的超磁致伸缩换能器非线性动力学模 型; 并将Simulink仿真系统应用到超磁致伸缩换能器系统动力学仿真中. 仿真结果表 明: 换能器模型系统为稳定周期运动系统,并具有滞回非线性特性;弹簧非线性项中的平方 项是影响换能器模型系统的主要因素. 经验证,数值计算结果与文献给出的试验测试结果吻 合较好.     

用IHB法分析双谐波激励下铰接塔-油轮系统的非线性动力学特性

研究了考虑平方阻尼情况下,铰接塔-油轮系统在双谐波激励下的非线性动力学特性.将该系统简化为单自由度分段线性恢复力,含平方阻尼的运动学分析模型,建立了铰接装载塔系统的分段非线性动力学方程.采用增量谐波平衡法获得系统周期解,使用Floquet理论判断系统的运动稳定性,结合路径跟踪法跟踪系统响应曲线,获得了系统所有可能的亚谐、谐波、组合谐波共振运动.分析了不对称恢复刚度比值对系统亚谐、组合谐波共振和对系统运动倍周期分岔点的影响,比较了考虑平方阻尼和不考虑平方阻尼情况下系统非线性动力学特性,得到了系统的一些重要的非线性动力学特点.     

《强非线性系统周期解的能量法》书评

<正>在自然界和科学技术的实际问题中,非线性是普遍存在的,具有多样性和复杂性.长期以来,人们十分重视开展非线性系统的理论、数值和实验研究.理论分析是非线性研究的最基本方法,大致可分为定性和定量两大类.基于动力系统理论的非线性动力学是定性地分析非线性系统的局部或全局动力学行为的主要工具.非线性     

机电耦联动力学的研究进展

简要介绍了机电系统及机电耦联动力学包含的主要领域．介绍了机电耦合非线性动力学研究中需要解决的两个基本问题．对以电机为核心组成的机电耦联系统中的非线性振动及非线性动力学3个方面的研究成果进行了系统的阐述．最后,对今后研究的方向进行了展望．      

A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage

In this paper, we propose the design of an ohmic contact RF microswitch with low voltage actuation, where the upper and lower microplates are displaceable. We develop a mathematical model for the RF microswitch made up of two electrostatically actuated microplates; each microplate is attached to the end of a microcantilever. We assume that the microbeams are flexible and that the microplates are rigid. The electrostatic force applied between the two microplates is a nonlinear function of the displacements and applied voltage. We formulate and solve the static and eigenvalue problems associated with the proposed microsystem. We also examine the dynamic behavior of the microswitch by calculating the limit-cycle solutions. We discretize the equations of motion by considering the first few dominant modes in the microsystem dynamics. We show that only two modes are sufficient to accurately simulate the response of the microsystem under DC and harmonic AC voltages. We demonstrate that the resulting static pull-in voltage and switching time are reduced by 30 and 45%, respectively, as compared to those of a single microbeam-microplate RF-microswitch. Finally, we investigate the global stability of the microswitch using different excitation conditions.     

Nonlinear dynamics of a resonant gas sensor

We develop a mathematical model for a resonant gas sensor made up of an microplate electrostatically actuated and attached to the end of a cantilever microbeam. The model considers the microbeam as a continuous medium, the plate as a rigid body, and the electrostatic force as a nonlinear function of the displacement and the voltage applied underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microsystem. The Galerkin method is used to discretize the distributed-parameter model and, thus, approximate it by a set of nonlinear ordinary-differential equations that describe the microsystem dynamics. By comparing the exact solution to that associated with the reduced-order model, we show that using the first mode shape alone is sufficient to approximate the static behavior. We employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations for the limit cycles. The stability of these cycles is determined by combining the FDM discretization with Floquet theory. We investigate the basin of attraction of bounded motion for two cases: unforced and damped, and forced and damped systems. In order to detect the lower limit of the forcing at which homoclinic points appear, we conduct a Melnikov analysis. We show the presence of a homoclinic point for a loading case and hence entanglement of the stable and unstable manifolds and non-smoothness of the boundary of the basin of attraction of bounded motion.     

Numerical analysis of theoretical model of the RF MEMS switches

An improved electromechanical model of the RF MEMS (radio frequency microelectromechanical systems) switches is introduced, in which the effects of intrinsic residual stress from fabrication processes, axial stress due to stretching of beam， and fringing field are taken into account. Four dimensionless numbers are derived from the governing equation of the developed model. A semianalytical method is developed to calculate the behavior of the RF MEMS switches. Subsequently the influence of the material and geometry parameters on the behavior of the structure is analyzed and compared, and the corresponding analysis with the dimensionless numbers is conducted too. The quantitative relationship between the presented parameters and the critical pull-in voltage is obtained, and the relative importance of those parameters is given.     

Isolation of circulating tumor cells under hydrodynamic loading using microfluidic technology(基于微流控技术在流体动力载荷下分离循环肿瘤细胞)

在世界范围内, 癌症的死亡率仍在逐年上升. 循环肿瘤细胞(circulating tumor cells, CTCs) 是指从原发肿瘤脱落并进入血液循环系统的细胞, 可能引发肿瘤转移并入侵其他正常组织和器官. 因此, CTCs 的检测结果可以作为癌症病人疗效和预后的评价指标. 但是CTCs 的数量及其稀少, 使得CTCs 的检测尤为困难. 在癌症转移的病人中, 每毫升血液约含有10-100 个CTCs. 利用经生物活性材料表面修饰的微流控器件, 可以从血液中分离出CTCs. 这是一项跨学科的挑战, 需要来自不同学科背景的专家们共同参与, 如细胞生物学、表面化学、流体力学及微纳加工技术等. 该文首先介绍了CTCs 的细胞生物学基础, 然后总结了当前分离CTCs 的主要微流控技术, 包括基于细胞-- 配体作用、磁力作用和过滤等, 最后综述了基于微流控技术的CTC 检测和计数、在体CTC 成像等最新研究进展.      

Minimum thickness control at various levels for topology optimization using the wavelet method

Especially in microsystem design, maintaining the minimum thickness of each structural member at a certain scale is often as important as achieving the maximum system performance. Several successful methods to suppress one-point hinges or checkerboards in topology optimization have been developed, but an efficient method to control the minimum thickness at a desire scale remains to be developed. The objective of this investigation is to develop a wavelet-based minimum thickness controlling method applicable to topology optimization and to show the effectiveness of the proposed method in MEMS design. The idea behind the thickness controlling method is to extend the wavelet shrinkage method developed for one-point hinge control to any scale-level minimum thickness control. The major difficulties in implementing this idea are the development of an efficient algorithm to detect all undesirable patterns of different scales and the hierarchical application of the wavelet shrinkage method over multiple scales. Some techniques to overcome these difficulties are developed and applied to some MEMS design problems.     

Homogenization of microsystem interconnects based on micropolar theory and discontinuous kinematics

In the present paper, the homogenized mechanical response of an interface in a microsystem interconnection is established on the basis of micropolar theory. The interface is treated as a finite RVE (representative volume element), across which macroscopic discontinuities occur as expressed in terms of the regularized discontinuous displacement and rotation fields. For the microstructure within the interfacial RVE, the micro-macro kinematical coupling is introduced as a second-order Taylor series expansion, along with a fluctuation term representing the microscopic displacement variation. In the second-order term of the expansion a restriction for the curvature is made, which motivates the adopted micropolar kinematics. Explicit expressions for the homogenized traction vector and the couple stress traction, associated with displacement and rotational jumps across the interface surface, are derived. A planar elastic interface is subjected to three basic deformation modes, i.e. the standard modes I, II and a non-conventional rotation mode, which are considered in the numerical examples representing a typical interconnect. A comparison to the results from the Taylor assumption is made, which shows that the Taylor assumption method produces an overstiffening of the interface.     

A Sequential Tensile Method for Rapid Characterization of Extreme-value Behavior in Microfabricated Materials

A high-throughput sequential tensile test method has been developed to characterize the fracture strength distribution of microfabricated polycrystalline silicon, the primary structural material used in microelectromechanical systems (MEMS). The resulting dataset of over 1,000 microtensile tests reveals subtle extreme-value behavior in the tails of the distribution, demonstrating that the common two-parameter Weibull distribution is inferior to a three-parameter Weibull model. The results suggest the existence of a cut-off or threshold stress (1.446 GPa for this particular material) below which tensile failure will not occur. The existence of a cut-off stress suggests that the material’s flaw size distribution and toughness distribution are both also bounded. From an application perspective, the cut-off stress provides a statistically-sound basis for reliable design. While the sequential method is demonstrated here for tensile strength distributions in polycrystalline silicon MEMS, the technique could be extended to a wide range of mechanical tests (bending strength, elastic modulus, fracture toughness, creep, etc.) for both microsystem and conventional materials.     

On-Chip Electrostatically Actuated Bending Tests for the Mechanical Characterization of Polysilicon at the Micro Scale

The issue of mechanical characterization of polysilicon used in micro electro mechanical systems (MEMS) is discussed in this paper. An innovative approach based on a fully on-chip testing procedure is described; two ad hoc designed electrostatically actuated microsystems are here used in order to determine experimentally the Young’s modulus and the rupture strength of polysilicon. The first device is based on a rotational test structure actuated by a system of comb-finger capacitors which load up to rupture a couple of tapered beams under bending in the plane parallel to the substrate. The second microsystem is based on a large plate with holes. It constitutes with the substrate a parallel plate capacitor moving in the direction orthogonal to the substrate itself. A couple of tapered beams placed at the centre of the plate is loaded up to rupture in bending in the plane orthogonal to the substrate. By means of the two devices, experimental data are obtained: they allow for a careful determination of Young’s modulus and rupture strength. The rupture values are interpreted by means of the Weibull approach; statistical size effects and stress gradient effect are taken into account thus allowing for a direct comparison between the data obtained from the two test structures.     

Non-linear vibrations and frequency response analysis of piezoelectrically driven microcantilevers

Microcantilevers have recently received widespread attentions due to their extreme applicability and versatility in both biological and non-biological applications. Along this line, this paper undertakes the non-linear vibrations of a piezoelectrically driven microcantilever beam as a common configuration in many scanning probe microscopy and nanomechanical cantilever biosensor systems. A part of the microcantilever beam surface is covered by a piezoelectric layer (typically ZnO), which acts both as an actuator and sensor. The bending vibrations of the microcantilever beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in the piezoelectric materials. The non-linear terms appear in the form of quadratic expression due to presence of piezoelectric layer, and cubic form due to geometrical non-linearities. The Galerkin approximation is then utilized to discretize the equations of motion. In addition, the method of multiple scales is applied to arrive at the closed form solution for the fundamental natural frequency of the system. An experimental setup consisting of a commercial piezoelectric microcantilever attached on the stand of a state-of-the-art microsystem analyzer for non-contact vibration measurement is utilized to verify the theoretical developments. It is found that the experimental results and theoretical findings are in good agreement, which demonstrates that the non-linear modeling framework could provide a better dynamic representation of the microcantilever than the previous linear models. Due to microscale nature of the system, excitation amplitude plays an important role since even a small change in the amplitude of excitation can lead to significant vibrations and frequency shift.     

Homogenization of delamination growth in an ACA flip-chip joint based on micropolar theory

In the present paper the delamination mechanism of a typical internal structure of the anisotropic conductive adhesive (ACA) interconnect for electronic packaging is modeled on the basis of micropolar theory and computational homogenization. The interface is treated as a finite Representative Volume Element (RVE), across which the macroscopic deformation is expressed in terms of regularized strong displacement and rotational discontinuities. For the microstructure of the RVE, the micro-macro kinematical coupling is considered as a Taylor series expansion in the regularized macroscopic discontinuities, and, connected to that, a discontinuous fluctuation field representing the microstructural variation is included to describe delamination on the microlevel. As to the microlevel delamination modeling, on the basis of the discontinuous fluctuation field, a damage coupled to slip and dilation formulation is used to model the interface degradation. The constitutive relations are established in a thermodynamic setting, where the interfacial free energy involves internal variables of damage and plastic deformation. The parameters of the interface are calibrated so that a predefined amount of fracture energy is dissipated in mode I. In the numerical example, the response of a planar interface is considered when it is subjected to the basic modes I-II and also the non-conventional rotational discontinuity mode. Case studies on fracture and geometry parameters have also been carried out. Finally, an uncoupled thermomechanical analysis of a microsystem involving a representative ACA microstructure has been made for the understanding of the microscopic delamination during a thermal cycling procedure.