On a deterministic approach for the evaluation of gas damping in inertial MEMS in the free-molecule regime

The evaluation of gas dissipation occurring in inertial polysilicon MEMS is addressed focusing the attention on the free-molecule flow. In this regime, which is very often of interest for industrial applications, collisions between molecules can be neglected and the momentum transfer to the moving shuttle can be easily computed. Since the surfaces of silicon MEMS are generally very rough, a complete diffusion model is adopted to describe the wall–molecule interaction. A Boundary Integral Equation approach is proposed and compared to a classical Test Particle Monte Carlo method, pointing out the clear advantages of the former for the applications at hand. It is shown that the introduction of the key assumptions of small perturbations and quasi-static response is crucial in the development of a robust and fast numerical tool. Several examples are presented validating the formulation with analytical and experimental results.     

Analytical model of squeeze film air damping of perforated plates in the free molecular regime

In this paper, an analytical model of squeeze film damping (SQFD) of perforated plates in the free molecular regime is developed, which is based on: (1) the modification of the perforated energy transfer model (P-ETM) (Li and Hu, J Micromech Microeng 21:025006, 2011) by giving the probability of molecules entering the gap through holes; (2) the application of Sumali’s formula (J Micromech Microeng 17:2231–2240, 2007) to relate to the Monte Carlo model (MC) (Hutcherson and Ye, J Micromech Microeng 14:1726–1733, 2004) quantitatively. The analytical model can model the perforation effect on SQFD of plates of various hole sizes. Compared with experiment data and numerical models, the analytical model is proved to be accurate, easy to operate. The effect of gap distance on SQFD of perforated plate in the free molecular regime is discussed. Due to perforation effect, as gap distance increases, the damping constant of non-perforated plate decreases faster than that of perforated plate of the same size.

     

Model-based damping of coupled horizontal and vertical oscillations in a flexible rod

This paper reviews the theory associated with vibrations of angularly accelerated cantilevered beams which display significant gravitational sag (coupling the out-of-plane dynamics of the flexible beam) and formulates a control approach for moving such beams to damp residual first horizontal and vertical modes of oscillation. An experimental implementation of the control strategy using an open-loop, single axis torque that is shaped for simultaneous damping of the horizontal and vertical vibrations is described. The experimental control strategy demonstrates more than a 90% reduction in the coupled residual vibrations.Work Supported by the U.S., Department of Energy at Sandia National Laboratories under Contract DE-AC04-76DP00789.     

A numerical molecular dynamics approach for squeeze-film damping of perforated MEMS structures in the free molecular regime

Accurate determination of the squeeze-film damping in rare air is crucial for the design of high-Q MEMS devices. In the past, for the MEMS structures with no perforations, there have been two approaches to treating the squeeze-film damping in rare air: the approach based on the continuum assumption and the approach using molecular dynamics (MD) method. The amount of squeeze-film damping can be controlled by providing perforations in microstructures. To model perforation effects on squeeze-film damping, many methods have been proposed. However, almost all the previous methods are based on the continuum assumption. Only one paper focuses on analytical modeling of squeeze-film damping of a perforated microplate using the MD method. Hutcherson and Ye (J Micromech Microeng 14:1726–1733, 2004) developed a novel MD method to model the squeeze-film damping in free molecular regime. The method possesses high computational efficiency. However, their work is valid only for non-perforated rectangular microplate. This paper presents a numerical MD approach for calculating the squeeze-film damping of a perforated rectangular plate and a perforated circular plate in free molecular regime. In Hutcherson and Ye’s work, the microplate is non-perforated. After each collision with the non-perforated plate, all the molecules are reflected to the substrate. In this paper, the plate is perforated. For the molecules in the air gap striking the surface of the perforated microplate, some of the molecules are reflected to the substrate. The rest leave the air gap through the perforations. This paper is an extension of the work done by Hutcherson and Ye (J Micromech Microeng 14:1726–1733, 2004). The accuracy of the present numerical MD approach is verified by comparing its results with the experimental results available in the literature and the finite element method results.     

汽车空气滤清器的模态分析及结构优化

汽车空气滤清器的表面板壳非常薄,高速气流从进气系统流过时将激励薄板结构产生振动,进而辐射出强烈的噪声,提高滤清器结构动态刚度是减小辐射噪声的有效途径,但刚度的提高通常伴随着质量的增加,实际中希望以最低的结构质量获得最大的动态刚度.针对上述问题,建立了空气滤清器的有限元模型,对其进行了模态分析.从前4阶模态分析结果找出了滤清器上下壳体的薄弱环节,然后通过调节上下壳体壁厚及合理布置加强肋的方法进行结构优化.经优化得到了一种壳体壁厚为3.5mm,加强肋厚度为2.5mm的结构优化设计方案.分析结果表明,滤清器的基频从157.1Hz提高到188.7Hz,提高了20.1％.模态测试表明,结构1阶固有频率为184.4Hz,有限元分析误差为2.3％,优化后的结构提高了低阶固有频率,降低了辐射噪声.     

高灵敏度QCM在阻尼介质中的分辨率改进

为改进晶体谐振器在阻尼介质中频率的稳定性和分辨率,研究了分辨率和干扰频率的理论关系,采用D触发器设计混频电路来减小回路的噪音干扰,由此分析了石英晶片上附着微小质量和液体时的等效电路,并制作了QCM传感器,得到了电路响应曲线;取4MHz、10MHz的谐振器在液体中进行了试验。结果表明:提高晶体谐振器的分辨率,减小噪音在谐振器中的出现比提高频率更有效。     

On the construction of free algebras for equational systems

The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop the finitary and transfinite construction of free algebras for equational systems; and to illustrate the use of equational systems as needed in modern applications.     

孔的形状和排列方式对厚孔板微结构压膜空气阻尼的影响分析

本文对微结构上孔的形状和排列方式对压膜空气阻尼的影响进行了理论和模拟分析.理论研究表明对于不同厚度、不同排列方式下的孔单元阵列,若孔的总面积和孔单元面积均为常数,当孔数增加到某一值时有最小阻尼力,并用FEM工具ANSYS证明了该结论的正确性.结果还表明孔数对恒定尺寸微结构空气阻尼的影响随着结构厚度和孔数的增加而变得更加明显.分析结果对比表明在同样的尺寸条件下,孔方形排列微结构的空气阻尼小于孔蜂窝式排列微结构的空气阻尼,该现象随着孔单元面积的增加变得越明显,但是随着孔单元接近微结构的边界,阻尼之间的差距减小.研究结果可以用在高精度MEMS器件如MEMS地震检波器、MEMS光开关和MEMS红外光传感器等的优化设计中去.     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

附加阻尼控制SVC在双馈型风电场中的应用研究

将附加阻尼控制SVC应用于兆瓦级双馈型风电场并网系统,在此基础上研究了系统的暂态过程.首先建立了双馈风电机组的动态模型,水轮发电机组以及附加阻尼控制SVC的数学模型,然后仿真研究了双馈型风电场并网以后对区域系统暂态过程的影响,对比分析了风电场接入和故障情况下采用普通SVC和附加阻尼控制SVC的作用和效果,仿真结果验证了建立模型和采取方法的正确性和有效性.     

Choice of B-splines with free parameters in the flexible discriminant analysis context

Flexible discriminant analysis (FDA) is a general methodology which aims at providing tools for multigroup non linear classification. It consists in a nonparametric version of discriminant analysis by replacing linear regression by any nonparametric regression method. A new option for FDA, consisting in a nonparametric regression method based on B-spline functions, will be introduced. The relevance of the transformation (hence the discrimination) depends on the parameters defining the spline functions: degree, number and location of the knots for each continuous variable. This method called FDA-FKBS (Free Knot B-Splines) allows to determine all these parameters without the necessity of many prior parameters. It is inspired by Reversible Jumps Monte Carlo Markov Chains but the objective function is different and the Bayesian aspect is put aside.     

A comparative study of analytical squeeze film damping models in rigid rectangular perforated MEMS structures with experimental results

Several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon our previously reported work by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cell differently as proposed by Mohite et al. We benchmark all these models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. We study the validity of the proposed model over the entire range of perforation ratios (PR) by comparing its results with numerically computed results from 3D Navier-Stokes equation. These results are also compared with other analytical models. The proposed model shows considerably better results than other models, especially for large values of PR.     

One-step approximations for detecting regime changes in the state space model with application to the influenza data

Kim and Nelson [1999. State Space Models with Regime Switching. MIT Press, Cambridge, MA] and others extended the framework of state space models involving independent regime changes to the Markov dependent case. The cost of dealing with state space models with Markov switching is high in computational effort because of the number of the possible paths through the chain. Thus it is necessary to make some approximations in order to obtain a computationally feasible algorithm for estimation. The approximations depend on modified smoothing and filtering recursions that can be easily incorporated into an EM algorithm for maximum likelihood estimation. To investigate the accuracy of approximations, we develop a new method to obtain more exact solutions, and then compare the two methods. We apply both methods to a simulated series. The result shows that employing the approximation-based algorithm not only provides accurate results but also leads to a significant reduction in the computational costs. We also apply the methods to an influenza mortality series, in which we develop a model that is general enough to include most structural models useful in monitoring changes of regime. The model proposed has the flexibility to deal with a wide range of problems involving possible regime shifts in pattern that may be seen to occur in many biological, medical and epidemiological studies.     

On the classification of toppoints in scale space

An algebraic classification scheme for toppoints in scale space is proposed. A critical point is a point whose spatial derivatives are zero, and a toppoint is a critical point in which the Hessian does not have full rank. A critical curve is a curve consisting of critical points. It is proposed that toppoints be classified according to the number of critical curves that intersect at the toppoint.Toppoints are analyzed further when one or two critical curves pass through the toppoint. If the Hessian is of rank one, a single critical curve passes through the toppoint; an extremum and a saddle point meet along a curve with a horizontal tangent at the toppoint. Two possibilities exist in the generic case. Either an extremum and a saddle point approach each other with increasing scale and disappear at the toppoint, or an extremum and a saddle are created at the toppoint and diverge from each other at increasing scale.If two critical curves intersect at a toppoint, there are again two different cases when Gaussian blurring is used. In the first case the Hessian has rank zero and the two curves intersect with horizontal perpendicular tangents. Two subcases occur, depending on the root structure of the cubic form of the Taylor expansion of the image at the toppoint. If this cubic form has a single real root, two extrema and two saddles approach the toppoint from below and disappear at the toppoint. The two extrema approach each other along a tangent from opposite directions. Similarly, the two saddles approach each other along the perpendicular tangent. If the cubic form has three distinct real roots, two saddles approach each other from below along a tangent from opposite directions. Above the toppoint the two saddles separate from each other in the perpendicular direction.In the second case the Hessian has rank one and there also exists another algebraic constraint on the coefficients of the cubic form of the Taylor expansion of the image of the toppoint. Two critical curves intersect at the toppoint. Again, two subcases occur, depending on whether the curves are real or complex. If the curves are real, there are two tangents at the intersection point but they are not horizontal, as in the previous subcase. An extremum and a saddle approach each other from below. Above the toppoint an extremum and a saddle separate from each other. The saddle above the toppoint moves in the same direction as the extremum below the toppoint, and the extremum above the toppoint moves in the same direction as the saddle below the toppoint. If the curves are complex, the toppoint is an isolated point in scale space.     

Time-dependent performance approximation of truck handling operations at an air cargo terminal

This paper provides an analytical solution for the time-dependent performance evaluation of truck handling operations at an air cargo terminal. The demand for loading and unloading operations is highly time-dependent and stochastic for two classes of trucks. Two heterogeneous handling facilities with multiple servers are available to handle trucks assuming exponentially distributed processing times. Trucks are routed to a handling facility depending on the current state of the system upon arrival. To approximate the time-dependent behavior of such heterogeneous queueing systems, we develop a stationary backlog-carryover (SBC) approach. A numerical study compares this approach with simulations and demonstrates its applicability to real-world input data.     

陀螺稳定平台的有限元模态分析

陀螺稳定平台是制导武器的核心部件之一,平台结构性能好坏直接影响制导武器的工作精度和可靠性.应用有限元模态分析理论,对该平台的结构动态特性进行研究,目的是为对平台进行结构动力学修改和结构优化设计提供依据,以便提高平台的工作精度和可靠性.运用uG建立某陀螺稳定平台的三维实体模型,进行合理简化后,建立该平台的有限元模型.采用有限元数值计算方法,计算得到该平台前七阶模态的频率及振型,各阶模态的频率均满足要求.并提出了改善该平台结构动态性能的措施.     

挠性加速度计石英摆片的微运动仿真分析

加速度计石英摆片的微运动仿真分析可以获取帮助提高石英挠性加速度计生产质量的技术手段和途径。从加速度计石英摆片的物理模型入手,用有限元方法对摆式加速度计的关键部件石英摆片进行静力计算与模态分析,直观地显示了石英摆片结构的应力场与形变场,获得了各阶自然频率和阵型。结果表明：采用有限元分析的方法能够辅助提高加速计的性能。     

Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health

Generalized additive models (GAMs) have become the standard tool for the analysis of short-term effects of air pollution on human health. Usually, the confounding effect of seasonality and long-term trend is described by flexible parametric or non-parametric functions of calendar time. Two different modeling strategies, i.e. GAM with penalized regression splines and GAM with regression splines, were compared by means of a simulation study, addressing attention to the inference on air pollutant effect. Simulation results indicated that GAM with regression splines provides negligibly biased estimates of air pollutant effect and it is robust to misspecification of the degrees of freedom of the spline. GAM with penalized regression splines requires a certain amount of undersmoothing in order to reduce the bias of the estimates and to improve the coverage of confidence intervals. These findings agree with asymptotic results developed in the context of partially splined models.     

On the consistency, expressiveness, and precision of partial modeling formalisms

Partial transition systems support abstract model checking of complex temporal properties by combining both over- and under-approximating abstractions into a single model. Over the years, three families of such modeling formalisms have emerged, represented by (1) Kripke Modal Transition Systems (KMTSs), with restrictions on necessary and possible behaviors; (2) Mixed Transition Systems (MixTSs), with relaxation on these restrictions; and (3) Generalized Kripke MTSs (GKMTSs), with hyper-transitions, respectively. In this paper, we investigate these formalisms based on two fundamental ways of using partial transition systems (PTSs) - as objects for abstracting concrete systems (and thus, a PTS is semantically consistent if it abstracts at least one concrete system) and as models for checking temporal properties (and thus, a PTS is logically consistent if it gives consistent interpretation to all temporal logic formulas). We study the connection between semantic and logical consistency of PTSs, compare the three families w.r.t. their expressive power (i.e., what can be modeled, what abstractions can be captured using them), and discuss the analysis power of these formalisms, i.e., the cost and precision of model checking.Specifically, we identify a class of PTSs for which semantic and logical consistency coincide and define a necessary and sufficient structural condition to guarantee consistency. We also show that all three families of PTSs have the same expressive power (but do differ in succinctness). However, GKMTSs are more precise (i.e., can establish more properties) for model checking than the other two families. The direct use of GKMTSs in practice has been hampered by the difficulty of encoding them symbolically. We address this problem by developing a new semantics for temporal logic of PTSs that makes the MixTS family as precise for model checking as the GKMTS family. The outcome is a symbolic model checking algorithm that combines the efficient encoding of MixTSs with the model checking precision of GKMTSs. Our preliminary experiments indicate that the new algorithm is a good match for predicate-abstraction-based model checkers.