微悬臂梁DNA生物传感器纳米力学分析的重力模型及其应用

基于微悬臂梁技术的DNA生物传感器的纳米挠度与核苷长度、嫁接密度、杂交率、重力、盐溶液浓度、时间、温度变化、缓冲液流场特性等诸多因素有关.利用Zhang两变量方法,建立了静态模式中自重作用下微梁正应力、切应力、层间挤压应力及其挠度预测的解析模型.作为应用,采用McKendry实验参数,研究了重力因素对静态纳米挠度的影响,发现参考梁技术中生物层自重对纳米挠度的影响可以忽略,但单梁技术中非生物层自重对纳米挠度的影响不可以忽略;同时,利用DNA生物传感器表面应力的Zhang解析模型,考虑自重和表面应力因素,给出了微梁的最优尺寸,从而可使单梁技术中自重因素对静态挠度的影响降到最低.     

旋转粘弹性夹层梁非线性自由振动特性研究

对旋转粘弹性夹层梁的非线性自由振动特性进行了分析.基于Kelvin-Voigt粘弹性本构关系和大挠度理论,建立了旋转粘弹性夹层梁的非线性自由振动方程,并使用Galerkin法将偏微分形式振动方程化为常微分振动方程.采用多重尺度法对非线性常微分振动方程进行求解,通过小参数同次幂系数相等获得微分方程组,并通过求解方程组及消除久期项来获得旋转粘弹性夹层梁非线性自由振动的一次近似解.用数值方法讨论了粘弹性夹层厚度、转速和轮毂半径对梁固有频率的影响.结果表明:固有频率随转速增大而增大,随夹层厚度增大而减小,随轮毂半径的增大而增大.     

MEMS薄膜平均应力梯度及等效弹性模量在线提取方法

薄膜沿厚度方向的平均应力梯度及薄膜的弹性模量对器件性能有重要影响.提出了一种利用静电作用下悬臂梁的吸合电压提取薄膜沿厚度方向的平均应力梯度及等效弹性模量的方法,该方法的关键在于实现悬臂梁吸合电压的快速精确计算.考虑了悬臂梁由应力梯度引起的沿宽度方向的弯曲及实现其固定端接近理想固支的方法,提高了吸合电压的计算精度.实际模拟表明该测量方法计算速度快、精度高,能够应用于实际工艺过程中材料参数的在线测量.     

光纤光栅测量微挠度的研究

提出一种基于光纤光栅传感技术的微挠度测量系统。将B ragg光纤光栅粘贴于悬臂梁的自由端,当悬臂梁自由端受力发生微挠度弯曲时,光纤光栅将沿轴向发生形变,通过监测B ragg光纤光栅(FBG)传感器反射波长漂移可以测量出悬臂梁的微挠度变化。通过对系统结构理论分析和实验验证,该装置挠度测量范围为0~51μm,测量灵敏度达到0.05μm,线性拟合度达到0.999 7,非线性误差小于0.1%。     

压电微悬臂梁气体传感器静态弯曲模型的研究

压电微悬臂梁是一种灵敏度高、尺寸小的生化传感器.分子或原子在压电微悬臂梁功能化表面的吸附会引起悬臂梁的静态弯曲,通过静态变形可以得到微悬臂梁的表面应力.将表面应力引起的微悬臂梁中性层位置的变化引入建模过程,并与能量法相结合,建立了压电微悬臂梁在单分子层吸附稳定后的静态弯曲理论模型.结果发现在相同吸附表面积和吸附量条件下...     

计及边缘效应的扭转微镜的动态特性分析

基于计及边缘效应的矩形平行板的静电力计算公式,建立了扭转微镜的动力学模型,采用Rom-berg数值积分法计算驱动力,并借助迭代修正齐次扩容精细积分法求解非线性动力方程.数值计算结果表明:电压、微镜和电极的几何尺寸等参数都会影响微镜的边缘效应,从而使微镜的动态响应产生较大的误差,在分析微镜力学性能时应考虑边缘效应的影响.     

开孔变截面微悬臂梁传感器的等效刚度和固有频率

研究新型开孔变截面微悬臂梁传感器的等效法向刚度及其对固有频率的影响.首先,考虑微梁纵截面孔洞结构引起的弯扭耦合效应,利用二次积分法获得在自由端集中载荷作用下悬臂梁的挠度,基于弹性材料的Hooke定律建立了微梁等效法向刚度分析的解析模型.然后,采用Rayleigh法获得了微梁的固有频率.最后,通过比对实验结果和有限元结果对解析模型进行了验证.研究表明:解析模型对于开孔变截面微梁刚度和频率的预测和标定具有较好的精度;微梁的等效刚度和固有频率与跨宽比负相关,却与内外宽度比正相关.有关结论可为新型变截面微纳机械传感器的设计提供理论依据和参考.     

轴向可伸缩复合材料悬臂梁的非线性振动研究

以航空领域中可变体机翼的伸缩变形过程为研究对象,对可伸缩悬臂复合材料层合梁的时变非线性振动进行理论研究.建立可伸缩悬臂复合材料层合梁在外载荷作用下的非线性动力学模型;根据时变系数非线性动力学方程研究时变非线性振动特性.分析可伸缩悬臂复合材料层合梁在外伸与收缩变形过程中的非线性动力学特性.从数值结果上看:模型的外伸速度、飞行速度对振动的影响较大,初值对振动的影响较小.     

航空发动机叶片非线性动力学分析

论文研究了航空发动机叶片的非线性振动问题,将叶片简化为功能梯度材料薄壁悬臂梁,考虑几何大变形的影响,基于一阶活塞气动力理论,利用Hamilton原理建立了叶片的非线性偏微分运动方程.综合运用Galerkin方法、多尺度方法和数值方法对叶片模型进行了非线性动力学分析,通过相图、波形图和频谱图分析了不同气流流速情况下旋转叶片的动态响应.结果表明:随着气流流速的增加,系统呈现倍周期运动和混沌运动等多种复杂动力学行为.     

微张力测量模型设计与实验研究

对差分结构的霍尔式张力测量模型进行了研究,基于线性霍尔元件和悬臂梁设计了挠度参变量和转角参变量两种微张力测量模型.应用悬臂梁系统将待测张力转换为位移和转角的变化,并以它们为中间参变量,建立了张力与霍尔电压的线性关系,实现了用线性霍尔元件以磁敏的方式测量张力.模型的对称互补式设计,不仅抵消了非线性变量对测量的影响,还能提高信号输出幅度.模型的差分式电压输出,能够抑制共模干扰和零点漂移.两种模型均能实现单一线性变量测量,实验结果符合理论结论.对比实验研究表明,挠度参变量微张力测量模型的灵敏度和线性度均优于转角参变量微张力测量模型,论述了设计原理并给出了理论计算.     

An effective method of determining the residual stress gradients in a micro-cantilever

A method of determining the micro-cantilever residual stress gradients by studying its deflection and curvature is presented. The stress gradients contribute to both axial load and bending moment, which, in prebuckling regime, cause the structural stiffness change and curving up/down, respectively. As the axial load corresponds to the even polynomial terms of stress gradients and bending moment corresponds to the the odd polynomial terms, the deflection itself is not enough to determine the axial load and bending moment. Curvature together with the deflection can uniquely determine these two parameters. Both linear analysis and nonlinear analysis of micro-cantilever deflection under axial load and bending moment are presented. Because of the stiffening effect due to the nonlinearity of (large) deformation, the difference between linear and nonlinear analyses enlarges as the micro-cantilever deflection increases. The model developed in this paper determines the resultant axial load and bending moment due to the stress gradients. Under proper assumptions, the stress gradients profile is obtained through the resultant axial load and bending moment.     

基于Matlab GUI编程的大圆弧长中点求解

在Matlab GUI编程的基础上,利用迭代法解非线性方程组的原理,结合Matlab中的丰富的符号工具箱中的函数功能,设计了求解两点间大圆弧长中点及大圆距离的问题的软件。结果证明：运用本软件来计算,解决了传统的手工图解法计算的困难,提高了效率,并能使计算精度提高两位有效数字。     

Pull-In Analysis of Torsional Scanners Actuated by Electrostatic Vertical Combdrives

This paper presents pull-in analysis of torsional MEMS scanners actuated by electrostatic vertical combdrives with general comb gap arrangements and cross sections. The analysis is based on a 2-DOF actuator with a single voltage control. Three failure modes of the scanners are identified as in-plane twist, transversal motion, and out-of-plane twist. For each failure mode, analytical expressions of pull-in deflection are obtained by applying 2D analytical capacitance models to the derived pull-in equations. From these, the dominant pull-in mechanism is shown to be in-plane twist for scanners with high-aspect-ratio torsional springs. The analytical calculations for both symmetric and asymmetric capacitances are shown to be in good agreement with simulation results. The optimum scanner design is achieved when the pull-in deflection matches the capacitance maximum angle. The condition can be expressed in terms of the ratio of the comb thickness to the comb gap, which is smaller than the typical aspect ratio of deep reactive ion etching. The optimum tradeoff between the maximum deflection angle and the number of movable combs is achieved by adjusting the overlap of the movable and fixed combs and the distance of the comb sets from the axis of the rotation.     

A hybrid algorithm for approximate optimal control of nonlinear Fredholm integral equations

In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given.     

A triangular finite difference scheme for large deflection problems

A lumped triangular element formulation is developed based on a finite difference approach for the large deflection analysis of plates and shallow shells. The presented formulation is independent of the boundary condition (unlike the finite difference formulation) and uses energy principles to derive a set of nonlinear algebraic equations which are solved by using an incremental Newton-Raphson iterative procedure. A study of the large deflection behaviour of thin plates is made for various edge conditions and aspect ratios, and the results obtained are compared with those using a finite element scheme. Representative nondimensional solutions for deflections and stresses are presented in the form of graphs.     

Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators

In this paper, the influence of the van der Waals force on two main parameters describing an instability point of cantilever type nanomechanical switches, which are the pull-in voltage and deflection are investigated by using a distributed parameter model. The fringing field effect is also taken into account. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. The integral equation is solved analytically by assuming an appropriate shape function for the beam deflection. The detachment length and the minimum initial gap of the cantilever type switches are given, which are the basic design parameters for NEMS switches. The pull-in parameters of micromechanical electrostatic actuators are also investigated as a special case of our study by neglecting the van der Waals force.     

Numerical analysis on snapping induced by electromechanical interaction of shuffling actuator with nonlinear plate

When a voltage is applied between two electrodes consisting of a rigid ground and a deformable rectangular plate that has two parallel free edges, and one movable edge and one fixed edge, the plate bends under the electrostatic force generated in it. Accompanying to the bending deformation, the movable edge of the plate results in some displacement along the movable direction, which is the main clue of the MEMS actuator of shuffling movement. As the control voltage is applied up to a critical value, the phenomenon of snapping occurs at the plate electrode under the interaction of electromechanical coupling such that the shuffling displacement is obtained as possibly as large. Based on the nonlinear theory of plates with the von Karman’s type deformation and the electrostatic theory, a theoretical analysis for the snapping behavior is quantitatively displayed in this paper. For this purpose, a numerical code is proposed by associating the increment finite element methods for deformation with the moment method for electrostatic fields as well as the arc-length control approach in the quantitative calculations. The numerical results for some case studies show that the path of bending deformation from stability into instability passing through the snapping criterion can be tracked well by this numerical code, while the characteristic curves of the maximum deflection in the plate and the shuffling displacement versus the control voltage, which are mainly concerned in the design of the MEMS shuffling actuator, are obtained additionally.     

基于非线性迭代滑模的欠驱动UUV三维航迹跟踪控制

为实现欠驱动无人水下航行器(Unmanned underwater vehicle, UUV)在未知海流干扰作用下的三维航迹跟踪控制, 提出一种基于工程解耦思想设计的非线性迭代滑模航迹跟踪控制器. 基于虚拟向导的方法,建立UUV空间航迹跟踪误差方程;采用迭代方法设计非线性滑模控制器, 无需对UUV模型参数不确定部分和海流干扰进行估计,避免了舵的抖振现象以及减小了稳态误差与超调问题. 仿真实验表明,设计的控制器对欠驱动UUV系统的模型参数摄动及海流干扰变化不敏感、 且设计参数易于调节,可以实现三维航迹的精确跟踪.     

Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers

In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nanocantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the analytical study are verified by numerical solution of the BVP. The centerline of the beam under the effect of electrostatic and Casimir forces at small deflections and at the point of instability is obtained numerically to test the validity of the shape function assumed for the beam deflection in the analytical investigation. Finally, the large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of nano-canilevers.     

Nonlinear structural behavior of a size-dependent MEMS gyroscope assuming a non-trivial shaped proof mass

In this paper, a size-dependent based non-classical mechanics model for the structural behavior of a MEMS (micro-electro-mechanical systems) gyroscope is investigated. The micro-cantilever based gyroscope is possessing a proof mass at its free end, assumed to hold a non-negligible length as compared to the micro-cantilever’s length. The proof mass is triggered through an actuating electrode and at the same time is assuming a sensing electrode together assuming parallel-plates capacitive arrangements. The governing equations of the micro-gyroscope system are derived within the framework of a modified couple stress non-classical mechanics theory. Based on the resulting equations, the static and dynamic analyses of the system are performed to estimate the pull-in instability voltages, natural frequency, and dynamic responses of the sensing electrodes near primary resonance that are caused by the use of point mass assumption and classical theory. A mixed based method involving both the Galerkin modal expansion procedure along with the method of multiple scales (MMS) technique is utilized to carry out the micro-gyroscope primary resonance analysis through plotting its respective frequency responses near its fundamental mode. Simulated results show that the proof mass dimension and its respective size effects play a substantial role in drastically changing the initiation of the system pull-in instability along its actuation direction, its fundamental natural frequency, and accordingly its dynamic amplitude along its corresponding sensing direction.