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Copyright of Journal of Shanghai Jiaotong University (Science) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, we investigated the viscosity, squeeze-film damping, and a SiC-based capacitive micro-accelerometer in rarefied air. A specific expression for the effective viscosity coefficient of the air was derived, and when the air pressure drops from the standard atmospheric pressure, the viscosity of the air will decrease accordingly. Decreases in the air pressure and the viscosity of the air lead to the change in the squeeze-film air damping in the micro-accelerometer, and both the viscous damping force and the elastic damping force of the air film between the moving electrode plate and the fixed electrode plate will also decrease. The damping coefficient and relative damping ratio of the micro-accelerometer in rarefied air were calculated, which was also confirmed by simulations. The changes of the damping coefficient and the relative damping ratio of the system will directly affect the dynamic characteristics of the micro-accelerometer. When the air pressure in the working environment is below the standard atmospheric pressure, the micro-accelerometer will be in an underdamping state. With the decrease in the air pressure, the working bandwidth of the micro-accelerometer will decrease significantly, and the resonant phenomenon may appear. However, the decrease in the air pressure will not have a notable impact on the response time of the micro-accelerometer. Therefore, this work provides a theoretical basis for the study of the performance characteristics of a SiC-based capacitive accelerometer in rarefied air. [ABSTRACT FROM AUTHOR]

• A new coupled framework based on the ALE-DUGKS is introduced to study the nonlinear SFD problem. • Linear and tilting motions of a rigid micro-beam are studied under forced and free oscillations. • The cause of the nonlinear damping phenomenon is investigated. In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic response of the structure is affected greatly by the SFD. In the traditional model, a viscous damping assumption that the damping force is linear with the moving velocity is used. As the nonlinear damping phenomenon is observed for a micro-structure oscillating at a high velocity, this assumption does not hold and will cause error results for predicting the response of the micro-structure. Meanwhile, due to the small size of the device and the low pressure of the encapsulation, the gas in MEMS is usually rarefied gas. Therefore, to correctly predict the damping force, the rarefied gas effect must be considered. To study the nonlinear SFD problem involving the rarefied gas effect, a kinetic method, i.e., discrete unified gas kinetic scheme (DUGKS), is introduced in this paper. Also, based on the DUGKS, two solving methods, i.e., a traditional decoupled method (Eulerian scheme) and a coupled framework (arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods, two basic motion forms, i.e., linear (perpendicular) and tilting motions of a rigid micro-beam, are studied under forced and free oscillations. For a forced oscillation, the nonlinear SFD phenomenon is investigated. For a free oscillation, in the resonance regime, some numerical results at different maximum oscillating velocities are presented and discussed. Besides, the influence of oscillation frequency on the damping force or torque is also studied, and the cause of the nonlinear damping phenomenon is investigated. [ABSTRACT FROM AUTHOR]

• Physics-based modeling of the dynamics of arch resonators for temperature and pressure sensing applications. • Experimental verification of physics-based model of arch microbeams under electric actuation. • Deep learning for simultaneous measurements of temperature and pressure. • Data and network training for the estimation of temperature and pressure from the dynamics of arch resonators. The ability to measure pressure and temperature using a MEMS sensor constitutes a major interest for several engineering applications. In this paper, we present a method and system for simultaneous measurements of pressure and temperature using electrically-actuated arch resonators. The sensor design is selected so that the arch microbeam is sensitive to temperature variations of the surrounding via the inherent thermal stress and to pressure change via the squeeze-film damping resulting from the air flow between the microbeam and the fixed underneath electrode (substrate). A physics-based model is formulated and validated by comparing the static deflection of the microbeam and its natural frequencies under varying temperature to experimental data reported in the literature. We use deep learning to estimate the pressure and temperature from the natural frequencies, quality factors and static deflection of the microbeam. Results show accurate prediction of the temperature and pressure from the quality factors of the arch resonator based on the first three vibration modes. Further improvement is achieved by adding the natural frequencies to the input data. The robustness of the deep learning approach to noise is demonstrated by the small errors obtained using different loss functions when introducing different noise levels to the training data. The proposed approach allows, for the first time, the combination of arch beams dynamics and deep learning techniques for simultaneous sensing of pressure and temperature. [ABSTRACT FROM AUTHOR]

• Physics-based modeling of the dynamics of microcantilevers for fluid sensing applications. • Hydrodynamic interactions of vibrating microcantilevers and incompressible fluid. • Experimental verification of physics-based model of microcantilevers immersed in liquids. • Deep learning for in-situ measurements of viscosity and density of small liquid samples. • Data and network training for the estimation of liquid properties from the dynamic response of microcantilevers. In-situ measurements of the viscosity and density of small volumes of liquids are required in several industrial applications. MEMS sensors deploying vibrating microstructures constitute an attractive alternative given the significant impact of the surrounding liquid on their dynamic behavior. In this work, we combine physics-based modeling approaches and deep learning techniques to simultaneously estimate the density and viscosity of liquids from the resonance frequencies and quality factors of immersed microcantilevers. The physics-based model is first validated by comparing the simulated resonance frequencies and quality factors of immersed microcantilevers to those obtained from experiments conducted on a large variety of liquids. Then, we use the simulations results to train deep neutral networks to learn the mapping from the data space to the parameter space. The deep learning method shows high prediction accuracy provided that there is enough independent input data, shows no bias in the predicted values, and provides the results instantaneously. The optimal accuracy in the estimation of the liquid viscosity and density is achieved when the first resonance frequency and corresponding quality factor are used as inputs. [ABSTRACT FROM AUTHOR]

Squeeze-film damping due to compressed thin-film gas comprises both the viscous and elastic effects. Based on the latter, this work reports two capacitively-transduced resonant pressure sensors implemented in a complementary metal oxide semiconductor (CMOS) process to provide sensor miniaturization, integration and sensitivity enhancement. Post-CMOS fabrication is simplified as a sealed membrane in conventional pressure sensors is not required. The squeeze-film elastic effect enhanced by the narrow sub- $\mu \text{m}$ gap leads to improved sensitivity and reduced sensor size. The two designs have resonant plates of $200\times200$ and $100\times 100\,\,\mu \text{m}^{2}$ , and demonstrate sensitivities of 0.77 and 5.34 Hz/Pa, respectively. [ABSTRACT FROM AUTHOR]

We present a unified model of electrostatic sensors comprising cantilever microbeam resonators in fluid media. The model couples Euler–Bernoulli beam equation to the nonlinear Reynolds equation. Static, damped eigenvalue, and dynamic reduced-order models were developed and validated by comparing a nonlinear frequency response of a gas sensor to its experimentally measured counterpart. Experiments were conducted to verify the capability of the developed model to predict the out-of-plane and in-plane natural frequencies of the sensor. The models were also used to investigate the potential operation of electrostatic chemical sensors based on different sensing mechanisms. While in-plane and out-of-plane vibration modes were found to be viable alternatives for resonant gas sensors, only in-plane modes were suitable to implement resonant chemical sensors due to the added mass and damping of liquid media. Similarly, higher-order modes were found more sensitive than lower order modes. Further, evidence was found for elastic interaction between out-of-plane modes and liquids in the channel underneath them but none for in-plane modes. Finally, the model predicts that in-plane modes provide the multi-valuedness necessary to implement bifurcation chemical sensors in liquid media. [ABSTRACT FROM AUTHOR]

We investigate the nonlinear dynamic response of a device made of two electrically coupled cantilever microbeams. The vibrations of the microbeams triggered by the electric actuation lead to the redistribution of the air flow in the gap separating them and induce a damping effect, known as the squeeze-film damping. This nonlinear dissipation mechanism is prominent when encapsulating and operating the microstructure under high gas pressure. We present different modeling approaches to analyze the impact of the squeeze-film damping on the dynamic behavior of the microsystem. We first develop a nonlinear multi-physics model of the device by coupling Euler–Bernoulli beam equations with the nonlinear Reynolds equation and use the Galerkin decomposition and differential quadrature method to discretize the structural and fluidic domains, respectively. We consider also another modeling approach based on approximating the squeeze-film damping force by a nonlinear analytical expression. This approach is widely used in the literature and referred to as partially coupled model in this paper. We conduct a comparative study of the nonlinear dynamic responses obtained from the two models under different operating conditions in terms of electric actuation and applied pressure. The simulated frequency and force-response curves show the limitations of the partially coupled model to capture properly the microsystem dynamics, especially when approaching the onset of the pull-in instability and exciting the microsystem with an AC voltage near resonance. As such, we propose a correction factor to the partially coupled model which is much less computationally demanding to obtain good match with the fully coupled model. The selection of the correction factor depends on the thickness ratio, the ambient pressure, and the excitation frequency. The influence of the ambient pressure and the thickness ratio between the two microbeams were also examined. We observe that operating the microsystem at a reduced ambient pressure or when reducing one of the microbeams' thickness can lead to a premature instability of the dynamic solution which reduces the maximum amplitude of the vibrating microbeams. This feature can be exploited for switching applications but it constitutes an undesirable effect for resonators. [ABSTRACT FROM AUTHOR]

Compressed thin-film gas between the plates produces the squeeze-film damping force that comprises both dissipative and elastic effects. The latter is used in this paper as the mechanism to modify the structural resonance with respect to the change of ambient pressure. Capacitively sensed squeeze-film pressure sensors are implemented in a silicon-based fabrication platform. Nine designs with resonant plate sizes from $200\times 200$ to $800\times 800\,\,\mu \text{m}^{\mathbf {2}}$ , and different natural frequencies for the same size are comprehensively studied. Measured sensitivities range from 94 to 762 Hz/kPa. Both simulations and measurements show the design tradeoff between sensitivity and quality factor. Required critical dimensions such as gap spacing and structural thickness to increase the squeeze-film elastic effect are also analyzed. [ABSTRACT FROM AUTHOR]

Squeeze-film damping plays a significant role in the performance of micro-resonators because it determines their quality factors. Perforations in microstructures are often used to control the squeeze-film damping in micro-resonators. To model the perforation effects on the squeeze-film damping, many analytical models have been proposed, however, most of the previous models have been concerned with the squeeze-film damping due to the normal motion between the perforated vibrating plate and a fixed substrate, while there is a lack of works that model the squeeze-film damping of perforated torsion microplates, which are also widely used in MEMS devices. This paper presents an analytical model for the squeeze-film damping of perforated torsion microplates. The derivation in this paper is based on a modified Reynolds equation that includes compressibility and rarefaction effects. The pressure distribution under the vibrating plate is obtained using the double sine series. Closed-form expressions for the stiffness and the damping coefficients of the squeeze-film are derived. The accuracy of the model is verified by comparing its results with the finite element method (FEM) results and the experimental results available in the literature. The regime of validity and limitations of the present model are assessed.

The Bernoulli gripper, which is widely employed in automated production lines, is a pneumatic manipulator capable of noncontact suction and gripping. Previous studies of Bernoulli grippers have focussed on its steady state suction force. This study experimentally and theoretically investigates the dynamic characteristics of the Bernoulli gripper. In practical applications, the gripped workpiece is lifted by placing the gripper immediately above the workpiece and then supplying compressed air to the gripper. In our pick-up experiment, the workpiece started to oscillate vertically after lifting, and then, the oscillation amplitude decreased until the workpiece became stable. Based on this experimental observation, we propose a mass-spring-damper model in which the steady state suction force is considered a spring and the squeeze-film flow exerts an additional damping force. Furthermore, the effects of the initial gap height and outer diameter on the motion of the workpiece are individually investigated. It was found that a small initial gap height and a large diameter aids in reducing the oscillation amplitude. In addition, the mass-spring-damper model could accurately predict the motion of the workpiece despite changes in the initial gap height and outer diameter. [ABSTRACT FROM AUTHOR]

This paper reports on the design, fabrication, and characterization of wafer-level-packaged wide-bandwidth capacitive accelerometers with high aspect-ratio nanometer scale gaps utilizing sloped electrode configuration. Narrow gaps defined by the thickness of a sacrificial layer provide an increased electromechanical coupling that enables designing sensors with high operational bandwidth (~15 kHz), while maintaining low-noise performance. Furthermore, by sloping the sense fingers, one can get a larger traveling range for the proof mass than the thickness of the sacrificial layer, allowing for the realization of shock stops without additional fabrication steps. The proposed scheme was incorporated into a 1 mm \times1 mm accelerometer design with 270-nm gap and fabricated on a 40- \mu \text{m} -thick silicon-on-insulator wafer using an high-aspect-ratio combined poly and single-crystal silicon (HARPSS) process, and subsequently wafer-level-packaged at a reduced pressure level of ~10 torr. The damping factor of the device was tailored using dedicated damping electrodes to ensure stable operation of the quasi-static accelerometer at low-pressure. The noise density is measured to be 221~\mu \text{g}/\surd $ Hz at 1 Hz, exhibiting a bias instability of 178~\mu \text{g} , with a scale factor nonlinearity of less than ±0.4% in a full-scale range of ±16 g, and showing an operational bandwidth greater than 8.5 kHz. Furthermore, a number of fabricated sensors were dropped from 1.8 m height to apply shock acceleration levels greater than 1000 g; all of the prototypes remain operational to their specifications after the free-fall test. [2017-0137] [ABSTRACT FROM PUBLISHER]

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Air-film damping, which dominates over other losses, plays a significant role in the dynamic response of many micro-fabricated devices with a movable mass suspended by various bearing mechanisms. Modeling the damping characteristics accurately will be greatly helpful to the bearing design, control, and test in various micromotor devices. This paper presents the simulated and experimental squeeze-film air damping results of an electrostatic bearing for use in a rotary high-speed micromotor. It is shown that the boundary condition to solve the three-dimensional Reynolds equation, which governs the squeeze-film damping in the air gap between the rotor and its surrounding stator sealed in a three-layer evacuated cavity, behaves with strong cross-axis coupling characteristics. To accurately characterize the damping effect, a set of multiphysics finite-element simulations are performed by computing both the rotor velocity and the distribution of the viscous damping force acting on the rotor. The damping characteristics varying with several key structure parameters are simulated and discussed to optimize the device structure for desirable rotor dynamics. An electrical measurement method is also proposed and applied to validate the numerical results of the damping coefficients experimentally. Given that the frequency response of the electric bearing is critically dependent on the damping coefficients at atmospheric pressure, a solution to the air-film damping measurement problem is presented by taking approximate curve fitting of multi-axis experimental frequency responses. The measured squeeze-film damping coefficients for the five-axis electric bearing agrees well with the numerical solutions. This indicates that numerical multiphysics simulation is an effective method to accurately examine the air-film damping effect for complex device geometry and arbitrary boundary condition. The accurate damping coefficients obtained by FEM simulation will greatly simplify the design of the five-axis bearing control system and facilitate the initial suspension test of the rotor for various micromotor devices. [ABSTRACT FROM AUTHOR]

In a variety of MEMS applications, the thin film of fluid responsible of squeeze-film damping results to be rarefied and, thus, not suitable to be modeled though the classical Navier-Stokes equation. The simplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinary formulation, by substituting the standard fluid viscosity with an effective viscosity term. In the present paper, some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied by numerical solving a full 3D Navier-Stokes equation, where the effective viscosity is computed according to proper expressions already included in the literature. Furthermore, the same expressions for the effective viscosity are implemented within known analytical models, still derived from the Navier-Stokes equation. In all the considered cases, the numerical results are shown to be very promising, providing comparable or even better agreement with the experimental data than the corresponding analytical results, even at low air pressure. Thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied at low pressure regimes, especially when this is combined with a finite element analysis (FEA).

Our previous report based on a 10 g (gravity) silicon-based inertial micro-switch showed that the contact effect between the two electrodes can be improved by squeeze-film damping. As an extended study toward its potential applications, the switch with a large proof mass suspended by four flexible serpentine springs was redesigned to achieve 5 g threshold value and enhanced threshold accuracy. The impact of the squeeze-film damping on the threshold value was theoretically studied. The theoretical results show that the threshold variation from the designed value due to fabrication errors can be reduced by optimizing the device thickness (the thickness of the proof mass and springs) and then establishing a tradeoff between the damping and elastic forces, thus improving the threshold accuracy. The design strategy was verified by FEM (finite-element-method) simulation and an experimental test. The simulation results show that the maximum threshold deviation was only 0.15 g, when the device thickness variation range was 16⁻24 μm, which is an adequately wide latitude for the current bulk silicon micromachining technology. The measured threshold values were 4.9⁻5.8 g and the device thicknesses were 18.2⁻22.5 μm, agreeing well with the simulation results. The measured contact time was 50 μs which is also in good agreement with our previous work.

Contact time is one of the most important properties for inertial micro-switches. However, it is usually less than 20 µs for the switch with rigid electrode, which is difficult for the external circuit to recognize. This issue is traditionally addressed by designing the switch with a keep-close function or flexible electrode. However, the switch with keep-close function requires an additional operation to re-open itself, causing inconvenience for some applications wherein repeated monitoring is needed. The switch with a flexible electrode is usually fabricated by electroplating technology, and it is difficult to realize low-g switches (<50 g) due to inherent fabrication errors. This paper reports a contact enhancement using squeeze-film damping effect for low-g switches. A vertically driven switch with large proof mass and flexible springs was designed based on silicon micromachining, in order to achieve a damping ratio of 2 and a threshold value of 10 g. The proposed contact enhancement was investigated by theoretical and experimental studies. The results show that the damping effect can not only prolong the contact time for the dynamic acceleration load, but also reduce the contact bounce for the quasi-static acceleration load. The contact time under dynamic and quasi-static loads was 40 μs and 570 μs, respectively. [ABSTRACT FROM AUTHOR]

We report on an accurate analytical model for the squeeze-film damping in laterally oscillating MEMS and MOEMS, which has not been available up to now. The models currently used are not able to correctly predict the damping and underestimate the squeeze- film contribution by a quite large factor of ∼4. This discrepancy was overcome by choosing more appropriate boundary conditions for solving Reynold's lubrication equation which governs the behavior of thin fluid films. The model was tested against numerical FVM computations with the open source software package OpenFOAM as well as measurements of MOEMS test devices with varying width of the squeeze-film gap and is in good agreement with both. This can now be used to increase the efficiency in thedesign step not only of laterally moving microstructures. [ABSTRACT FROM AUTHOR]

Squeeze-film damping and acceleration load are two major issues in the design of inertial micro-switches. In order to deeply and systematically study these two issues, this paper proposes a typical vertically-driven inertial micro-switch, wherein the air and electrode gaps were chosen to design the required damping ratio and threshold value, respectively. The switch was modeled by ANSYS Workbench, and the simulation program was optimized for computational accuracy and speed. Transient analysis was employed to investigate the relationship between the damping ratio, acceleration load, and the natural frequency, and the dynamic properties (including contact bounce, contact time, response time, and threshold acceleration) of the switch. The results can be used as a guide in the design of inertial micro-switches to meet various application requirements. For example, increasing the damping ratio can prolong the contact time of the switch activated by short acceleration duration or reduce the contact bounce of the switch activated by long acceleration duration; the threshold value is immune to variations in the damping effect and acceleration duration when the switch is quasi-statically operated; the anti-jamming capability of the switch can be improved by designing the sensing frequency of the switch to be higher than the acceleration duration but much lower than the other order frequencies of the switch. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical solution to calculate the squeeze-film air damping of circular and elliptical micro-torsion mirrors. To derive the expressions of squeeze-film air-damping torque, the nonlinear Reynolds equation, which governs the air behavior of torsion mirror, is solved by the method of eigenfunction expansions in polar coordinate and elliptical coordinate, respectively. The series solutions are integrated and summed up to deduce the damping torque of circular and elliptical torsion mirrors. The formulas of circular mirror and elliptical mirror are deduced independently, and their results match when the eccentricity of the elliptical mirror approaches zero. Besides, the results of the formulas are consistent with numerical simulation. Both of them verifies the damping torque formulas in this paper. [ABSTRACT FROM AUTHOR]

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, ) 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, ). 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. [ABSTRACT FROM AUTHOR]

A new principle for gas viscosity sensing using electrostatic pull-in and its implementation using a microstructure are presented in this paper. The sensor is based on viscosity-dependent pull-in time measurement. A nonlinear dynamic analysis of pull-in demonstrates the influence of damping conditions on the pull-in time of devices that are operated at meta-stability (requiring specific damping and electrostatic actuation conditions) with a squeeze-film damping coefficient at low frequencies directly proportional to viscosity. Therefore, the fundamentals of pull-in behavior suggest that pull-in can be used for the implementation in a gas viscosity sensor. Capacitive parallel-plates MEMS structures with squeeze-film dampers have been fabricated and pull-in time measurements have been performed for different gas media. Both pure gases (H2, CH4, CO2, CO and N2) and mixtures (H2N2, CH4N2 and CH4N2CO2) have been tested, with viscosity values in the range between 9 and 18 μPa s. The results show a sensitivity of 2 ms/(μPa s), which can be further increased by manipulating the actuation voltage. Further efforts are necessary to reduce the device sensitivity to external vibration, which translated to a significant amount of noise in the measurements. [ABSTRACT FROM AUTHOR]

While at high pressure, the classical Navier-Stokes equation is suitable for modeling squeeze-film damping, at low pressure, it needs some modification in order to consider fluid rarefaction. According to a common approach, fluid rarefaction can be included in this equation by substituting the standard fluid viscosity with a fictitious quantity, known as effective viscosity, for which different formulations were proposed. In order to identify which expression works better, the results obtained when either formulation is implemented inside the Navier-Stokes equation (that is then solved by both analytical and numerical means) are compared with already available experimental data. At the end, a novel expression is discussed, derived from a computer-assessed optimization procedure. [ABSTRACT FROM AUTHOR]

In a variety of MEMS applications, the thin film of fluid responsible of squeeze-film damping results to be rarefied and, thus, not suitable to be modeled though the classical Navier-Stokes equation. The simplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinary formulation, by substituting the standard fluid viscosity with an effective viscosity term. In the present paper, some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied by numerical solving a full 3D Navier-Stokes equation, where the effective viscosity is computed according to proper expressions already included in the literature. Furthermore, the same expressions for the effective viscosity are implemented within known analytical models, still derived from the Navier-Stokes equation. In all the considered cases, the numerical results are shown to be very promising, providing comparable or even better agreement with the experimental data than the corresponding analytical results, even at low air pressure. Thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied at low pressure regimes, especially when this is combined with a finite element analysis (FEA)

Nonlinear dynamic behaviour of a cantilever microbeam actuated by a combination of DC and AC loading are investigated in presence of squeeze-film damping. A reduced order model formulated accounting for the nonlinearities of the system arising out of electrostatic forces and squeeze-film damping is numerically simulated to observe the large amplitude dynamic characteristics near primary and superharmonic resonances. The emphasis is on the significance of nonlinear damping in capturing the true dynamic characteristics of microsystems formulated as distributed parameter model. The damping nonlinearity is found to considerably affect the dynamics with a profound stabilising effect on the microsystem. Under the effect of large DC bias voltage, frequency–response curves obtained for different amplitudes of AC excitation exhibit local and global bifurcations. Response sensitivity to initial conditions is investigated near bifurcation points. Findings in the superharmonic resonance domain are emphasised. [ABSTRACT FROM PUBLISHER]

Copyright of Fracture & Structural Integrity is the property of Gruppo Italiano Frattura and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A semi-analytical model of an electrostatically actuated damped cantilever microbeam is used to study the response characteristics of small amplitude motion about a statically deflected position. A Euler-beam equation, incorporating the electrostatic force terms and the squeeze-film damping terms, coupled with the linearized compressible Reynolds equation is analyzed under different ambient pressures and DC polarization conditions. The dynamic problem is simulated with the coupled field finite element analysis software ANSYS and results are compared. The applicability of the present model for the range of flow compressibility has been studied through the use of a term called compressibility ratio. [ABSTRACT FROM PUBLISHER]

The literature includes a variety of analytical and semi-analytical models to describe squeeze-film damping in MEMS perforated structures. Even if many of them have been validated by means of numerical simulations, nobody seems to have discussed about the accuracy of numerical approaches in this field. In the present paper, we apply both the main analytical models and a commercial finite element software, COMSOL Multiphysics, to solve a good number of squeeze-film problems. They refer to some cases, which were experimentally investigated during the past by different authors. The tested structures are rigid rectangular plates fabricated with different material, different perforation ratio (i.e., the ratio of the hole side to the holes pitch) and different number of perforations. We compare both the analytical and the numerical results with the available experimental data, in order to have an overview about their effectiveness. Numerical simulations offer in all the considered cases valuable agreement with experiments. [ABSTRACT FROM AUTHOR]

Abstract: The experimental evaluation of damping-improved parallel-plate geometries is reported in this paper. An improved damper geometry with air channels was developed to address contradictory design constraints: large sensing parallel-plate area is desirable for a significant readout capacitance as well as reduced damping coefficient. Damping coefficients were measured at different gaps in conventional parallel-plates MEMS and in parallel-plates with air channels. The inertial masses of the fabricated structures were pulled-in and released. From the return to rest position trajectory, the damping coefficients, at each point, were extracted. Results show a significant damping decrease in parallel-plates with air channels without visible reduction in the capacitance value. [Copyright &y& Elsevier]

Abstract: We present a physics-based multi-energy domain coupled macromodel that allows for the efficient simulation of the dynamic response of electrostatically controlled and viscously damped ohmic contact RF-MEMS switches on the system-level. The predictive power of the macromodel is evaluated w.r.t. white light interferometer and laser vibrometer measurements. Furthermore, the macromodel is, concerning accuracy and performance, benchmarked versus two alternative state-of-the-art system-level models. The results obtained with the presented macromodel are in very good agreement with the measured quasi-static pull-in characteristics as well as the pull-in and pull-out transients. Due to its capability to account for multiple structural modes, the presented macromodel produces, among the evaluated models, the result that is closest to the measured phase of initial contact during dynamic pull-in. Moreover, a detailed experimental evaluation of the damping model shows a very good agreement (maximum relative error does not exceed 10%) for ambient pressures ranging from 960hPa down to approximately 200hPa. Compared to other damping models, this constitutes a very good result, especially because the models contain only geometric parameters and no problem-specific fit factors are needed to obtain this accuracy. The resulting macromodel is physics-based and, hence, scalable and predictive. Due to its generic nature it can be – in general – adapted for any electrostatically actuated device working in contact mode. [Copyright &y& Elsevier]

Abstract: The pull-in time (t pi) of electrostatically actuated parallel-plate microstructures enables the realization of a high-sensitivity accelerometer that uses time measurement as the transduction mechanism. The key feature is the existence of a metastable region that dominates pull-in behavior, thus making pull-in time very sensitive to external accelerations. Parallel-plate MEMS structures have been designed and fabricated using a SOI micromachining process (SOIMUMPS) for the implementation of the accelerometer. This paper presents the experimental characterization of the microdevices, validating the concept and the analytical models used. The accelerometer has a measured sensitivity of 0.25μs/μg and a bandwidth that is directly related to the pull-in time, BW=1/2t pi ≈50Hz. These specifications place this sensor between the state of the art accelerometers found both in the literature and commercially. More importantly, the resolution of the measurement method used is very high, making the mechanical–thermal noise the only factor limiting the resolution. The in-depth noise analysis to the system supports these conclusions. The total measured noise floor of 400μg (100μs) is mainly due to the contribution of the environmental noise, due to lack of isolation of the experimental setup from the building vibrations (estimated mechanical thermal noise of 2.8μg/√Hz). The low requirements of the electronic readout circuit makes this an interesting approach for high-resolution accelerometers. [Copyright &y& Elsevier]

The Reynolds equation coupled with an effective viscosity model is often employed to predict squeeze-film damping of plate resonators in a low vacuum. Due to the lack of a sound theoretical foundation, a study is carried out to evaluate the performance of such an approach in the free-molecule regime and results are presented in this paper. An experimentally validated Monte Carlo simulation approach for the simulation of air damping is developed and employed for this study. First, effective viscosity models are developed for a parallel-plate resonator and a rotational resonator based on experimental measurements. These models are then coupled with Reynolds equation and employed to simulate air damping of resonators of the same type but with differing dimensions. The results are compared with Monte Carlo simulation results. It has been found that the modified Reynolds equation approach cannot accurately compute air damping for a general class of resonators and hence cannot serve as a predictive tool. The deficiency lies in the effective viscosity model that is assumed to be a function of Knudsen number only. Possible extensions of the modified Reynolds equation approach in the highly rarefied regime are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Effects of uncertainties in gas damping models, geometry and mechanical properties on the dynamics of micro-electro-mechanical systems (MEMS) capacitive switch are studied. A sample of typical capacitive switches has been fabricated and characterized at Purdue University. High-fidelity simulations of gas damping on planar microbeams are developed and verified under relevant conditions. This and other gas damping models are then applied to study the dynamics of a single closing event for switches with experimentally measured properties. It has been demonstrated that although all damping models considered predict similar damping quality factor and agree well for predictions of closing time, the models differ by a factor of two and more in predicting the impact velocity and acceleration at contact. Implications of parameter uncertainties on the key reliability-related parameters such as the pull-in voltage, closing time and impact velocity are discussed. A notable effect of uncertainty is that the nominal switch, i.e. the switch with the average properties, does not actuate at the mean actuation voltage. Additionally, the device-to-device variability leads to significant differences in dynamics. For example, the mean impact velocity for switches actuated under the 90%-actuation voltage (about 150V), i.e. the voltage required to actuate 90% of the sample, is about 129cm/s and increases to 173cm/s for the 99%-actuation voltage (of about 173V). Response surfaces of impact velocity and closing time to five input variables were constructed using the Smolyak sparse grid algorithm. The sensitivity analysis showed that impact velocity is most sensitive to the damping coefficient whereas the closing time is most affected by the geometric parameters such as gap and beam thickness. [Copyright &y& Elsevier]

Closed-loop pull-in time operated devices are a good alternative for high sensitivity accelerometers. This paper proposes the use of time measurement as the transduction mechanism for the realization of a high-precision accelerometer. The key feature is the existence of a metastable region that dominates pull-in behavior, thus making pull-in time very sensitive to external accelerations. The main design challenges for a pull-in time parallel-plate capacitive microelectromechanical system (MEMS) accelerometer are related to the damping and the associated tradeoff between sensitivity and noise is discussed. Parallel-plate MEMS structures designed and fabricated in a 25 \mum-thick SOI micromachining process (SOIMUMPS) are used to demonstrate the accelerometer time-based approach and experimental results demonstrate a sensitivity of 0.25 \mus/\mug. [ABSTRACT FROM PUBLISHER]

Squeeze-film damping on microresonators is a significant damping source even when the surrounding gas is highly rarefied. This article presents a general modeling approach based on Monte Carlo (MC) simulations for the prediction of squeeze-film damping on resonators in the free-molecule regime. The generality of the approach is demonstrated in its capability of simulating resonators of any shape and with any accommodation coefficient. The approach is validated using both the analytical results of the free-space damping and the experimental data of the squeeze-film damping on a clamped–clamped plate resonator oscillating at its first flexure mode. The effect of oscillation modes on the quality factor of the resonator has also been studied and semi-analytical approximate models for the squeeze-film damping with diffuse collisions have been developed. [ABSTRACT FROM AUTHOR]

Abstract: The design and theoretical modelling of an oscillating micro-mechanical viscometer designed for the measurement of whole unadulterated human blood, is described. The proposed device utilises the dependence of the squeeze-film damping ratio on properties of the surrounding fluid to measure fluid viscosity using an oscillating plate structure. The optimum geometrical configuration for the device structure has been investigated and a methodology for defining the optimum configuration of the micro-mechanical sensor identified. This is then applied to calculate the predicted noise equivalent viscosity change . It was found that the device performance is limited by electronic noise within the detection circuitry rather than thermal-mechanical noise. An electronic noise limited measurement resolution of , is predicted for measurement over a shear range of , at a measurement bandwidth of . The linearity of response of the micro-mechanical viscometer is considered and the device is predicted to provide a linear measurement response. [Copyright &y& Elsevier]

We report on finite element (FE) modeling and simulation of effect of squeeze-film damping on flexible microstructure operating in ambient air in close proximity to a fixed surface, which is a common case in many MEMS devices. A coupled fluidic-structural problem is solved by applying a nonlinear compressible Reynolds equation, which is derived from the Navier-Stokes equations, transformed into weak form and added to commercial FE modeling software. The proposed model enables investigation of influence of surrounding air on dynamics of different microstructures taking into account air rarefaction and air compressibility effects. The paper presents results of numerical analysis, which aim was to study the phenomenon of natural frequency shifting in the case of free and forced vibrations of the cantilever microstructure. Simulations demonstrate that squeeze-film damping may result in the increase of natural frequency of the microstructure due to system stiffening caused by air compression. The magnitude of this effect is determined by such parameters as ambient air pressure, air-film thickness, vibration frequency and lateral dimensions of the microstructure. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper provides results of dynamic numerical analysis of nonlinear electromechanical and vibro-impact interactions in electrically-actuated contact-type microactuator, which is a common component in such devices as microswitches. Mathematical modeling was performed by means of finite element method, representing microactuator as a 3D cantilever microstructure and taking into account influence of bending forces generated by electrostatic field, damping forces due to squeezed air-film in the gap as well as bouncing of the microactuator tip upon its contact with substrate. Electrostatic-structural simulations were performed in order to predict actuation (pull-in) voltages of fabricated microswitches as well as to study influence of various system parameters on the value of the voltage. Results of these simulations were compared with experimental findings obtained by using electrical probe measurements of fabricated microswitches. Numerical analysis of free impact vibrations was carried out and allowed determination of effect of ambient air pressure and intermolecular adhesive interactions on the phenomenon of contact bouncing. [ABSTRACT FROM AUTHOR]

Micromechanical structures that have squeeze-film damping as the dominant energy dissipation mechanism are of interest in this paper. For such structures with narrow air gap, the Reynolds equation is used for calculating squeeze-film damping, which is generally solved with trivial pressure boundary conditions on the side walls. This procedure, however, fails to give satisfactory results for structures under two important conditions: 1) for an air gap thickness comparable to the lateral dimensions of the microstructure and 2) for nontrivial pressure boundary conditions such as fully open boundaries on an extended substrate or partially blocked boundaries that provide side clearance to the fluid flow. Several formulas exist to account for simple boundary conditions. In practice, however, there are many micromechanical structures such as torsional microelectromechanical system (MEMS) structures that have nontrivial boundary conditions arising from partially blocked boundaries. Such boundaries usually have clearance parameters that can vary due to fabrication. These parameters, however, can also be used as design parameters if we understand their role on the dynamics of the structure. We take a MEMS torsion mirror as an example device that has large air gap and partially blocked boundaries due to static frames. We actuate the device and experimentally determine the quality factor Q from the response measurements. Next, we model the same structure in ANSYS and carry out computational fluid dynamics analysis to evaluate the stiffness constant K, the damping constant D, and the quality factor Q due to the squeeze film. We compare the computational results with experimental results and show that without taking care of the partially blocked boundaries properly in the computational model, we get unacceptably large errors. [ABSTRACT FROM AUTHOR]

Abstract: The squeeze-film damping in perforated structures is modelled using a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green’s function. The solution thus obtained adds an additional term to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting , one recovers Blech’s formulae. We compute the squeeze film forces using these new formulae and compare the computed forces with the solution of 3D Navier–Stokes equation solved using ANSYS for different perforation ratios (ratio of hole to cell dimensions). The results match very well. The approximate limit of maximum frequencies under which the formulae give reasonable results is also discussed. Although the main result is derived for a rigid plate under transverse motion, we discuss the effect of flexibility of the structure by deriving results for a flexible plate under a specified set of boundary conditions and comparing the results with that of a suitably modified rigid plate result. For small amplitude motion, the results show that a suitably modified rigid plate model can capture the effect of flexibility through a simple scaling factor. [Copyright &y& Elsevier]

Abstract: We describe the theoretical modelling of an infrared (IR) sensor based on an oscillating bi-material cantilever in which the beam is quantified as a function of the squeeze-film damping ratio, by measurement of the forced damped resonance frequency or phase angle. The structure under consideration is composed of a silicon nitride cantilever beam, coated with an upper gold absorbing layer. A detailed description of the optimisation of the cantilever geometry is described, with the gap height being identified as the critical parameter. The influence of the length, width, absorber gap and thickness of the two layers on signal-to-noise ratio (snr) is also discussed and an optimum configuration identified for each parameter. Phase modulation measurement techniques are found to provide the highest measurement resolution, with a thermal mechanical noise-limited performance of NEΔT=0.21mK, and an electronic noise-limited performance of NEΔT=4mK, being predicted for a 100×100μm cantilever at 1kHz measurement bandwidth. [Copyright &y& Elsevier]

In this paper, we present a single-crystal-silicon (SCS) continuous membrane deformable mirror (DM) as a corrective adaptive-optics (AO) element for space-based telescopes. In order to correct the polishing errors in large aperture (~8 m) primary mirrors, a separate high-quality surface DM array must be used. Up to 400000 elements and a mirror stroke of ~100 nm are required for the correction of these polishing errors. A continuous membrane mirror formed by the the SCS device layer of a silicon-on-insulator (SOI) wafer is used to achieve a high-quality optical surface and to minimize the additional diffractive effects in the optical system. To achieve substantial local deformation needed to correct high-order errors, we use a highly deformable silicon membrane of 300-nm thickness. This thin membrane is able to deform locally by 125 nm at an operating voltage of 100 V with a pixel pitch of 200 mum. The resonance frequency of a pixel is 25 kHz with a low Q-factor of 1.7 due to squeeze-film damping. The device is fabricated by processing the microelectromechanical system (MEMS) and electronic chips separately and then combining them by flip-chip bonding. This allows optimization of the MEMS and electronics separately and also allows the use of an SOI layer for the mirror by building the MEMS bottom up. A small prototype array of 5times5 pixels with 200-mum pitch is fabricated, and we demonstrate single pixel and multiple pixel actuation [ABSTRACT FROM PUBLISHER]

Abstract: The damping characteristics of a packaged high-g accelerometer have been investigated in this paper. Firstly, a multi-segments-plates-approximate (MSPA) model on curved surface damping suitable for this component has been established to obtain the relationship between the parallel-shift-distance (PSD) of curved stop and the damping of component. Subsequently, not only the effect of the PSD of curved protection but also the impact of the characteristics of damping media on the dynamic shock response of the component has been studied with ANSYS FEM technology. Results show that the dynamic output responses of component were in reality the superposition of both the forced vibration under acceleration shock and the vibration of cantilever in its inherent frequency. With the increase of PSD, the inherent frequency vibration became outstanding in output response and both the peak output voltage and displacement of beam end increased linearly whereas its corresponding time decreased nonlinearly. The effects of damping media on the dynamic response characteristics of the component were attributed to the difference of viscosity coefficient of damping medium. Under the same other conditions, with increment of viscosity coefficient, the output response curve become smoother except for lower peak voltage. Therefore, the PSD of curved stop should be controlled between 0.5 and 0.65μm during the fabrication of chip and if the PSD was about 0.5μm, air would be the most suitable damping media in the packaging of the component. [Copyright &y& Elsevier]