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Size-dependent stability analysis of a fully clamped micro-electro-mechanical beam under the effect of shock acceleration pulse is the objective of present paper. The size-dependent Euler–Bernoulli beam model based on the modified couple stress theory (MCST) with von Kármán-type geometric non-linearity is utilized in theoretical formulations. The non-linear governing differential equation of motion is derived using Hamilton’s principle and solved using a simple and computationally efficient single degree-of-freedom (SDOF) approach. The model’s predictions based on the classical theory (CT) are compared with those obtained using the finite element method (FEM) and six modes Galerkin approximations in previous studies and an excellent agreement between them is achieved. It is shown that the present SDOF predictions agree better with the FE results than those obtained using six modes approximations for high shock accelerations. Furthermore, the present model can remove the limitation of previous models in capturing dynamic pull-in instability under enormous shock accelerations. A parametric study is also conducted to show the significant effects of couple stress components on micro-beam motion. It is found that the size effect on both dynamic pull-in voltage and maximum amplitude of micro-beam oscillations is usually negligible, when the ratio of beam thickness to the material length scale parameter is larger than 15. [ABSTRACT FROM AUTHOR]

A micro-grating tilt sensor based on phase diffraction grating with self-calibration capability and direct intensity modulation is proposed. The optical tilt sensor consists of a coherent light source, gold gratings patterned on the transparent substrate, a silicon proof mass supported by the eight symmetrical Al cantilevers. Al membrane is sputtered on the bottom of the proof mass. Both Au and Al membrane serve as electrodes for electrostatic actuation. This can provide the sensitivity adjustment and self-calibration capabilities. Experiments show that the inclinometer provides the maximum incline sensitivity of 90 mV/°, resolution of 0.00006°, a measurement range of ± 5° in the rotational plane that is parallel to the direction of the gravity, and good self-calibration ability with electrostatic actuation. [ABSTRACT FROM AUTHOR]

The paper deals with studying the deflection and pull-in voltages of the carbon nanotubes under electrostatic actuation with various dimensions and boundary conditions. The size-dependent behaviors of the carbon nanotubes (CNTs) are considered via application of the strain gradient theory. The results obtained from the strain gradient theory are compared to those estimated using the classical elasticity. The outcomes reveal that the classical elasticity theory underestimates the pull-in voltages of the carbon nanotubes and strain gradient theorem results in stiffer nano-structures with higher pull-in voltages. Increasing of the deflection due to the higher voltages increases the differences between the results of the strain gradient theory and classical elasticity. Thus, in order to design CNT-based nano-electromechanical systems, researchers should consider the size-dependent theories such as the theorem used in this paper. In addition, the influences of different dimensions on the pull-in voltages are studied in detail. The results proved that longer CNTs with smaller diameters possess lower pull-in voltages than shorter ones with larger diameters. [ABSTRACT FROM AUTHOR]

The experimental study of the stability properties of initially curved micro beams subjected to an axial pre-stressing load and transversal deflection-dependent distributed electrostatic force is presented. The devices were fabricated from single crystal silicon on insulator (SOI) wafer using deep reactive ion etching (DRIE). The in-plane quasi-static beam response was video recorded and analyzed by means of image processing. The beam behavior was theoretically predicted using a reduced order model with the axial pre-stressing force assessed on the basis of the deviation of the beam actual initial curvature from the nominal designed one. The experimental results are consistent with the theoretical symmetric and asymmetric snap-through buckling criteria. [ABSTRACT FROM AUTHOR]

In this paper a novel RF MEMS cantilever type switch with low actuation voltage is presented. The cantilever beam of switch is supported by two L-shaped springs to reduce the spring constant. The switch is simulated using Intellisuite software. The actuation voltage of switch is achieved about 2 volt and the size of the switch is 110×60μ2m, that in compared with other electrostatic cantilever beam switch, it has a small size, low spring constant and as a result low actuation voltage. Its fabrication is simple due to its simple design. The S-parameters of switch have been simulated with HFSS 9.1 that the results show the insertion loss of 0.07 dB, return loss 0f 25 dB and 17 dB isolation till 40 GHz frequency. The results show proper performance of switch in this frequencies band and it had less insertion loss compare pervious work and with these properties of switch, return loss and isolation did not changed much. [ABSTRACT FROM AUTHOR]

Micro deformable porous mirrors are designed and investigated in this work. Finite element methods are used to analyze mirror deflection induced by electrostatic force. The porous micro mirror is designed by bulk micromachining and bonds with aluminum plate which is ground electrode with photo resist for its good adhesion ability. This design has advantages of avoiding warpage, using less masks, and easily fabricated. It is found mirror boundary types and holes shapes and arrangement in mirror would affect deflection under applying voltage. Spring like boundary will induce larger deflection than traditional clamped boundary condition. However, the effect is more obvious for mirror with round holes in radical direction. Although porous mirror has smaller electrode area and electrostatic force than mirror without holes, yet it has larger displacement. The effect of holes overcomes disadvantage of smaller driving force due to avoiding air resisting force as mirror having airtight bounding. In this study, spring-like boundary has advantages of better performance and easier alignment in mirror fabrication. Therefore, it is useful for mirror design and fabrication in practice. [ABSTRACT FROM AUTHOR]

This paper deals with electrostatically actuated carbon nanotube (CNT) cantilever over a parallel ground plate. Three forces act on the CNTs cantilever, namely electrostatic, van der Waals, and damping. The van der Waals force is significant for values of 50 nm or less of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNTs electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The methods of multiple scales and reduced order model (ROM) are used to investigate the system under soft AC near half natural frequency of the CNT and weak nonlinearities. The frequency-amplitude response and damping, voltage, and van der Waals effects on the response are reported. It is showed that only five terms ROM predicts and accurately predicts the pull-in instability and the saddle-node bifurcation, respectively. [ABSTRACT FROM AUTHOR]

Optical grating-based interferometric sensors have been the subject of prior investigations, with recent work focused on micromachined microphone applications. The silicon structure is similar in construction to capacitive microelectromechanical-system microphones, with the exception that the microphone backplate contains an optical-diffraction grating at the center. The grating serves as a beam splitter in this system, allowing only a portion of the incident light to pass to the diaphragm and back, enabling interferometric readout of diaphragm displacements. A cited advantage of this system is the ability to design highly perforated backplates with low mechanical damping and with the ability to realize low thermal-mechanical noise. Grating backplates, however, have their own unique optical design constraints different from capacitive sensors. This paper details a rigorous finite element computational fluid dynamics model for flow resistance of a grating backplate. The model is validated for a case study backplate fabricated in the epitaxial layer of a 2-μm silicon-on-insulator wafer. The dynamics of the backplate are studied in isolation from other microphone elements by mounting the backplate in close proximity to a rigid optical-reflector and using electrostatic actuation to vibrate the backplate for extraction of compliance, resonance frequency, and quality factor. [ABSTRACT FROM AUTHOR]

A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamic pull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-in instability of electrically actuated CNTs by employing an analytic approach namely He's iteration perturbation method (IPM). The effects of basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on the pull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits. [ABSTRACT FROM AUTHOR]

The nanoscaled electrostatically actuated electromechanical ohmic switch is an emerging device with advanced performance in terms of ON I OFF ratio. It is imperative that compact models accompany such novel devices in order to fully evaluate their potential at the circuit-level. A minimal, yet, adequate compact model is developed and analyzed in this work. Further, the model is used as a compass for switch design space exploration and, simultaneously, a corresponding parameter extraction methodology is compiled. The application on data from numerical simulations and on measurements of fabricated devices, verifies the potential of the model, while circuit-level simulations validate its robustness within an industrial IC design environment. [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]

The paper deals with the investigation of nonlinear static and dynamic behaviors of electrostatically actuated carbon nanotubes with different geometries and boundary conditions. The deflection and pull-in properties are studied in detail in the presence of DC and combined DC + AC electrostatic voltages accompanying the interatomic interactions. The considered nano system can be applied in a wide range of nanoelectronics devices such as nano switches, nano resonators, nano transistors, nano capacitors and random access memories. Moreover, a useful mathematical model of the nano sensor application of the studied nano system to sense the stiffness of the nano particles is presented. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic instability of cantilever micro-beam submerged in an incompressible viscous fluid cavity and actuated by electrostatic force. Equivalent squeeze film damping is incorporated in the vibrational equation of the micro-beam to obtain the natural frequencies of the coupled system. Then, imposing various step voltages, dynamic responses, and pull-in conditions of the micro-beam are studied. A parametric study is conducted to evaluate the effect of fluidic confinement on the instability voltage. Dielectric constant of the fluid proves dominantly influential compared with viscosity and density. In addition, values of pull-in voltage are seen to be highly dependent on the vertical position as well as the length of the micro-beam. [ABSTRACT FROM AUTHOR]

Nowadays, electronics face a challenge regarding the power consumption of integrated circuits (ICs). There is a need for new devices that can provide improved switching capabilities. The downscaled electrostatically actuated ohmic switch, as a (re)emerging device, is a promising candidate to meet this need. To bring such a device seamlessly into IC design, it must be accompanied by an accurate, fast and robust analytical compact model. The development and the main characteristics of such a model are described within this paper. Extensive numerical simulations and measurements have been used to validate the model. [ABSTRACT FROM AUTHOR]

Electrostatically driven torsional micromirrors are suitable for optical microelectromechanical systems due to their good dynamic response, low adhesion, and simple structure for large-scale-integrated applications. For these devices, how to eliminate the excessive residual vibration in order to achieve more accurate positioning and faster switching is an important research topic. Because of the known nonlinearity issues, traditional shaping techniques based on linear theories are not suitable for nonlinear torsional micromirrors. In addition, due to the difficulties in calculating energy dissipation, the existing nonlinear command shaping techniques using energy method have neglected the effect of damping. We analyze the static and dynamic behavior of the electrostatically actuated torsional micromirrors. Based on the response of these devices, a multistep-shaping control considering the damping effects and the nonlinearity is proposed. Compared to the conventional closed-loop control, the proposed multistep-shaping control is a feedforward approach which can yield a good enough performance without extra sensors and actuators. Simulation results show that, without changing the system structure, the preshaping input reduces the settling time from 4.3 to 0.97 ms, and the overshoot percentage of the mirror response is decreased from 33.2% to 0.2%. [ABSTRACT FROM AUTHOR]

This paper deals with investigation of fluid flow on static and dynamic behaviors of carbon nanotubes under electrostatic actuation. The effects of various fluid parameters including fluid viscosity, velocity, pressure and mass ratio on the deflection and pull-in behaviors of the cantilever and doubly clamped carbon nanotubes are studied. Furthermore, the effects of temperature variation on the static and dynamic pull-in voltages of the doubly clamped carbon nanotubes are reported. The results reveal that altering the fluid parameters significantly changes the mechanical and pull-in behaviors. Hence, the proposed system can be applied properly as a nano fluidic sensor to sense the various parameters of the fluid. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new solution for electrically actuated micro-beams under mechanical shock is introduced. [•] The results of this new procedure agree better than previous methods with FE model. [•] The present approach does not suffer from long run time. [•] This approach is also able to capture dynamic pull-in instability in every desired loading case. [Copyright &y& Elsevier]

The influence of Casimir and van der Waals forces on the instability of vibratory micro and nano-bridge gyroscopes with proof mass attached to its midpoint is studied. The gyroscope subjected to the base rotation, Casimir and van der Waals attractions is actuated and detected by electrostatic methods. The system has two coupled bending motions actuated by the electrostatic and Coriolis forces. First a system of nonlinear equations for the flexural-flexural deflection of beam gyroscopes is derived using the extended Hamilton's principle. In modeling, the nonlinearities due to mid-plane stretching, electrostatic forces, including fringing field, Casimir and van der Waals attractions, are considered. The method of homotopy perturbation is used to solve the equations of equilibrium, with the solution validated by numerical methods. In addition, the effect of nondimensional parameters on the instability and deflection of the gyroscope is investigated. The data presented can be used in the design of vibratory micro/nano gyroscopes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the classical and nonlocal elasticity are applied to investigate the deflection and instability of electrostatically actuated carbon nanotubes. The results are presented for different geometries and boundary conditions. They reveal that increasing radius and gap and decreasing length confine to increasing pull-in voltages of the carbon nanotubes. The results prove that application of the nonlocal elasticity theorem leads to stiffer structures with higher pull-in voltages. Thus, in order to obtain more accurate results about the mechanical and electromechanical behaviors of the carbon nanotubes, one should apply the nonclassical elasticity theories such as that applied in this paper. [Copyright &y& Elsevier]

We present an electrostatically actuated rotary stage featuring liquid rings, which serve as both mechanical bearings and electric connections between the rotor and the substrate. The liquid rings are formed by confining a liquid inside hydrophilic grooves and repelling it from the superhydrophobic surfaces outside the grooves. Made of a fluid, the liquid-ring bearing avoids the dry friction of the solid bearings, significantly improving the reliability. Formed as rings, it avoids the resistance of contact-angle hysteresis sliding over droplets, and hence dramatically reducing the static friction. Furthermore, surface tension facilitates the self-alignment of the rotor to the substrate and stator during the assembly and provides the stability against drift and shock during operation. Electrically, each liquid ring passes an independent electric signal, allowing a direct electrical path between the substrate and potential components on the rotor. A three-phase electrostatic rotary stage has been design, fabricated, and tested. The minimum torque to initiate the rotation is ~ 2.5 nN·m-hundreds of times smaller than droplet-based counterparts. The device has operated successfully by applying sequential voltages of 50 VDC between the rotor and the stators. The electric transmission has been verified by powering an LED on a rotating rotor. This is the first report of an electrostatically actuated rotating microdevice with a liquid bearing and a direct power transmission. [ABSTRACT FROM AUTHOR]

A new device resulting from the merging of mechanical and electromagnetic properties of a couple of conductive cantilevered beams is described in this paper. The device, which is based on two metallic clamped-free beams which, at the same time, are the arms of a radio frequency dipole antenna is capable to receive the electromagnetic power radiated from an emitting antenna and transduce it directly in a dc mechanical actuation. A numerical model developed to describe the behavior of the device has been validated through the test of a millimeter scale demonstrator working in the microwave frequency band. [Display omitted] • Novel device called MEMSTENNA. • Flexible dipole antenna. • Direct transduction of microwave radiated power into DC mechanical deflection. • Dipole antenna loaded by a MEMS capacitive actuator. [ABSTRACT FROM AUTHOR]

This paper introduces tunneling current as a sensor to detect and control the displacements of micro- and nanoelectromechanical systems. Because of its extremely small magnitude, the tunneling current cannot be used without an appropriate control strategy. A control methodology involving two feedback loops is proposed to control displacements with an accuracy of 40 pm while also compensating the sensor drift. With this strategy, controlling displacements with an amplitude >1~nm is possible, extending the predicted capabilities of tunneling current by the literature. The overall approach is a solution for the control of macro to nano systems and may be embedded in positioning applications requiring a very high degree of accuracy. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the study of structural noise in a capacitive MEMS microphone, which consists of a fully clamped circular micro-plate. The micro-plate is subjected to a bias DC voltage and sound pressure waves. Due to the nonlinearity and displacement dependency of the electrostatic force, the amplitude of the applicable bias DC voltage has some limitations and also this nonlinearity causes the generation of super or sub-harmonic responses and consequently the initiation of the structural noise in capacitive microphones. In order to determine the amplitude of the generated structural noise in these microphones, the first order multiple scales method is used and asymptotic analytical solution of the dynamic response is presented. The effects of the bias DC voltage value on the fundamental frequency, sensitivity and consequently on the amplitude of the structural noise of the microphone are studied. In addition the effects of the sound pressure frequency and amplitude on the value of structural noise are investigated. [Copyright &y& Elsevier]

The paper presents size-dependant mechanical behaviors of carbon nanotubes under electrostatic actuation using modified couple stress theory. The behaviors of the carbon nanotubes with different geometries and boundary conditions are studied in detail. The results reveal that application of this theory results in higher pull-in voltages for both cantilever and doubly clamped boundary conditions. [ABSTRACT FROM AUTHOR]

A closed-loop control methodology is investigated for stabilization of a vibrating non-classical micro-scale Euler-Bernoulli beam with nonlinear electrostatic actuation. The dimensionless form of governing nonlinear Partial Differential Equation (PDE) of the system is introduced. The Galerkin projection method is used to reduce the PDE of system to a set of nonlinear Ordinary Differential Equations (ODE). In non-classical micro-beams, the constitutive equations are obtained based on the non-classical continuum mechanics. In this work, proper control laws are constructed to stabilize the free vibration of non-classical micro-beams whose governing PDE is derived based on the modified strain gradient theory as one of the most inclusive non-classical continuum theories. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme. Also, the results have been compared with those obtained by the classical model of micro-beam. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, another latent capability of SWCNT as a mass sensor is investigated. The relationship between the resonant frequency, dynamic pull-in voltage at the resonance frequency shift, and the attached mass is established by using the nonlocal Euler–Bernoulli beam theory. Using this relationship, a general closed-form nonlinear sensor-equation has been derived for the detection of the mass attached to the SWCNT. The aim of this study and present model is to show the sensitivity of the Cantilevered SWCNT to the values and positions of attached mass. Moreover, the results indicate that by increasing the value of attached mass and considering a single non-local scaling parameter (e 0), the values of dynamic pull-in voltage at the resonance frequency shift are decreased. Because of the small scaling parameter (e 0), the mass sensitivity of carbon nanotube increases, when the position of the attached mass is in the tip of a Cantilevered SWCNT length. The authority and the accuracy of these formulas are examined with other pull-in sensor equations in literatures. The results demonstrate that the new sensor equation can be applied for CNT-based mass sensors with rational accuracy. [Copyright &y& Elsevier]

Abstract: We report on the results of characterization and modeling of electrostatically actuated meso scale beams. The beams with clamped ends were 5000μm long, 150μm thick and 10, 12 and 15μm wide and were operated by a parallel plate electrode located at the distance of 20μm from the beam. The devices were fabricated using deep reactive ion etching (DRIE) from a silicon on insulator (SOI) wafer with 150μm thick device layer. The beams were operated in ambient air conditions and the voltage–displacement dependence was built using image processing. In addition, pull-in behavior of the beams was modeled using several approaches, starting from geometrically nonlinear shallow Euler–Bernoulli beam model and up to fully coupled nonlinear large deflection three-dimensional anisotropic elasticity finite elements simulations. Excellent agreement between the results provided by the models and the experimental data was observed. The results of the work demonstrate an ability to achieve large displacements in simple meso scale beam structures and provide a reliable experimental reference for double clamped beams actuated by a parallel-plate electrode. [Copyright &y& Elsevier]

This paper presents the design, fabrication, and characterization of a MEMS actuator with large static deflection as a waveguide-mounted variable millimeter-wave phase shifter. The actuator is composed of a pair of interdigitated microplates actuated by vertical comb-drives and suspended by SU-8 torsional springs. The SU-8 spring possesses a thin metallization top layer and a reverse-T-shaped cross-section enabling low torsional stiffness and high in-plane stability. A maximum mechanical deflection of 10.3^\circ is obtained under a dc actuation voltage of 35 V. The dynamic characterization of the device shows that the resonance frequency of the torsional mode is well separated from the other three bending modes, confirming the designed low torsional stiffness and high in-plane stability. The torsional viscoelastic creeping is measured as a function of time at different loads and shows a maximum of 0.5^\circ for an applied voltage of 27.5 V. A high operation cycle test is conducted and the metalized SU-8 spring withstands 800 million cycles without showing fatigue. RF measurements show that a variable mechanical deflection angle between 0^\circ and 8.2^\circ results in a variable transmission phase shift up to 58.0^\circ. The measured insertion loss is always below 5.1 dB at 98 GHz, corresponding to a figure of merit of 11.5^\circ/dB. [2012-0338] [ABSTRACT FROM PUBLISHER]

The comb fingers of high aspect ratio structures fabricated by micromachining technology are usually not parallel. Effects of the inclination of the fingers and edge effect on the capacitance, driving electrostatic force, and electrostatic spring constant are studied. The complex nonlinear air damping in the 3-D resonators is also determined accurately. The governing equations are presented to describe the complex dynamic problem by taking both linear and nonlinear mechanical spring stiffness constants into account. The dynamic responses of the micro-resonator driven by electrostatic combs are investigated using the multiscale method. Stability analysis is presented using the maximum Lyapunov index map, and effects of vacuum pressure on the frequency tuning and stability are also discussed. The comparisons show that the numerical results agree well with the experimental data reported in the literature, and it verified the validity of the presented dynamic model. The results also demonstrate that the inclination of the fingers causes the resonance frequency to increase and the electrostatic spring to harden under applied dc voltage. Therefore, it can provide an effective approach to balance the traditional resonance frequency decreasing and stiffness softening from driving electrostatic force. The inclination of the fingers can be helpful for strengthening the stability of the MEMS resonators, and avoiding the occurrence of pull-in. [2012-0354] [ABSTRACT FROM PUBLISHER]

This paper describes ultrasound enhanced electrostatic batch assembly (U2EBA) as a low-cost, batch microassembly method to assemble 3D microsystems. U2EBA involves placing the die in an external DC electric field perpendicular to the substrate and actuating the die with an off-chip, bulk-piezoelectric ceramic. The foremost advantages of this method are the simplicity of the assembly setup, applicability to a broad range of surface micromachining processes, lack of any additional fabrication steps or unusual materials, and fully off-chip nature that requires no electrical or mechanical contact to the assembled microstructures. After an investigation of the forces involved in U2EBA, experiments aiming to quantify the anti-stiction effect of ultrasonic actuation are described. Yield rates reaching up to 100% are reported from 8×8 arrays of hinged mirror/paddle structures with dimensions of 97μm×180μm. Reasons of failure for the unassembled structures and the maximum limit for the electrostatic assembly forces are discussed. Experiments on different hinged microstructures allowed comparison of design parameters and revealed a 22% improvement in the assembly yield due to the addition of dimples over the paddle region of the microstructures. [ABSTRACT FROM AUTHOR]

In the present study, the dynamic pull-in instability and free vibration of circular microplates subjected to combined hydrostatic and electrostatic forces are investigated. To take size effects into account, the strain gradient elasticity theory is incorporated into the Kirchhoff plate theory to develop a nonclassical plate model including three internal material length scale parameters. By using Hamilton's principle, the higher-order governing equation and the corresponding boundary conditions are obtained. Afterward, a generalized differential quadrature (GDQ) method is employed to discritize the governing differential equations along with simply supported and clamped edge supports. To evaluate the pull-in voltage and vibration frequencies of actuated microplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. Also, a comparison between the pull-in voltages predicted by the strain gradient theory and the degenerated ones is presented. It is revealed that increasing the dimensionless internal length scale parameter or decreasing the applied hydrostatic pressures leads to higher values of the pull-in voltage. Moreover, it is found that the value of pull-in hydrostatic pressure decreases corresponding to higher dimensionless internal length scale parameters and applied voltages. [ABSTRACT FROM AUTHOR]

The impetus of this study is to investigate the nonlinear chaotic dynamics of a clamped-clamped micro-beam exposed to simultaneous electrostatic and piezoelectric actuation. The micro-beam is sandwiched with piezoelectric layers throughout its length. The combined DC and AC electrostatic actuation is imposed on the micro-beam through two upper and lower electrodes. The piezoelectric layers are actuated via a DC electric voltage applied in the direction of the height of the piezoelectric layers, which produces an axial force proportional to the applied DC voltage. The governing differential equation of the motion is derived using Hamiltonian principle and discretized to a nonlinear Duffing type ODE using Galerkin method. The governing ODE is numerically integrated to get the response of the system in terms of the governing parameters. The results show that the response of the system is greatly affected by the amounts of DC and AC electrostatic voltages applied to the upper and lower electrodes. The results show that the response of the system can be highly nonlinear and in some regions chaotic. Evaluating the K-S entropy of the system, based on several initial conditions given to the system, the chaotic response is distinguished from the periodic or quasiperiodic ones. The main objective is to passively control the chaotic response by applying an appropriate DC voltage to the piezoelectric layers. [ABSTRACT FROM AUTHOR]

Abstract: Stability of a functionally graded (FG) micro-beam, based on modified couple stress theory (MCST), subjected to nonlinear electrostatic pressure and thermal changes regarding convection and radiation, is the main purpose of this paper. It is assumed that the functionally graded beam, made of metal and ceramic, follows the volume fraction definition and law of mixtures, and its properties change as an exponential function through its thickness. By changing the ceramic constituent percent of the bottom surface, five different types of the micro-beams are investigated. The static pull-in voltages in presence of temperature changes are obtained by using step-by-step linearization method (SSLM) and, by adapting Runge–Kutta approach, the dynamic pull-in voltages are obtained numerically. Though the temperature distribution through the thickness of FG micro-beam (due to its too small measurement) is considered uniform, owing to the different thermal expansions of layers, temperature changes cause deflection in the micro-beam, and consequently affect pull-in values. Hence the profound effects of different material constituent over the pull-in voltages are illustrated and it is graphically displayed that how in some cases neglecting components of the couple stress leads to inaccurate results. [Copyright &y& Elsevier]

The present work is concerned with the nonlinear dynamic analysis of a vibrating beam microgyroscope composed of a rotating cantilever beam with a tip mass at its end. The rigid mass is coupled to two orthogonal electrodes in the drive and sense directions, which are attached to the rotating base. The microbeam is driven by an AC voltage in the drive direction, which induces vibrations in the orthogonal sense direction due to rotation about the microbeam axis. The electrode placed in the sense direction is used to measure the induced motions and extract the underlying angular speed. A reduced-order model of the gyroscope is developed using the method of multiple scales and used to examine its dynamic behavior. [ABSTRACT FROM PUBLISHER]

To study electrostatic actuation, researchers commonly use a setup proposed by G. I. Taylor in [Proc. R. Soc. Lond. Ser. A, 306 (1968), pp. 423–434]. It consists of soap film held at a distance h above a rigid plate so that when a voltage difference is applied between the two components, the top film deflects towards the bottom plate. The most striking feature of this system is when the voltage difference exceeds a critical value V*, the electrostatic forces dominate the surface forces and the soap film gets ‘pulled-into’ or collapses onto the bottom plate. This so-called ‘pull-in’ instability is a ubiquitous feature of electrostatic actuation and as a result, has been the subject of many studies. Recently, Siddique et al. [J. Electrostatics, 69 (2011), pp. 1–6] measured the value of V* as a function of the separation distance and found that the standard prediction breaks down as h increases. Here, we continue the work done in [N. D. Brubaker and J. A. Pelesko, European J. Appl. Math., 22 (2011), pp. 455–470] by investigating the cause of this discrepancy. Specifically, we model the effect of gravity on the generalized version of Taylor's model and study whether it provides the proper correction to the predicted value of V*. In doing so, we derive two nonlinear eigenvalue value problems and investigate their solutions sets. [ABSTRACT FROM AUTHOR]

Highlights: [•] The nonlinear spring effect of the thin-film poly-Si torsion bar was characterised. [•] Theoretical model considered bending, stretching, and shear stress effects. [•] The spring constant of the torsion bar was observed to increase by 6.25 times. [•] The experimental results validate the accuracy of the theoretical model. [Copyright &y& Elsevier]

E-paper based on the interferometric principle is gaining popularity as a result of the success of Qualcomm's Mirasol technology. We report an interferometric modulator that realizes primary colors through analog modulation by actuating the movable mirrors in suspension with designated locations and orientation. Colors can be temporally modulated and stiction problems can be avoided. [ABSTRACT FROM AUTHOR]

The objective of this work is to create an analytical framework to study the static pull-in and also equilibrium behavior in electrostatically actuated torsional micromirrors. First the equation governing the static behavior of electrostatic torsion micromirrors is derived and normalized. Perturbation method, the method of straight forward expansion is utilized to find the pull-in angle of the mirror. Comparison of the presented results with numerical ones available in the literature shows that the proposed second order perturbation expansion gives very precise approximations for the pull-in angle of the mirror. Then straightforward perturbation expansion method is used again to analytically simulate the voltage dependent behavior in electrostatic torsion micromirrors. The results are compared with numerical and experimental findings and excellent agreement is observed. [ABSTRACT FROM AUTHOR]

We report a study of the electrical and mechanical effects of the inclusion of a thin layer of multiwalled carbon nanotubes (MWCNTs) into the surface of polydimethylsiloxane (PDMS) as a method of creating an electrically actuated, flexible microfluidic valve. Samples of PDMS with various surface loadings of MWCNTs were prepared and tested using a uniaxial tension tester, combined with a four-point probe electrical test. In contrast to other works reporting the inclusion of MWCNTs in the bulk of the material, we have found that inclusion of the MWCNTs on the surface only has no discernible effect on the mechanical properties of the PDMS samples, but causes a significant and repeatable change in the electrical performance. We have found that a loading of 4.16 g m−2 results in an electrical resistivity of 7.31 × 10−4 Ω cm, which is 200% lower than that previously reported for bulk inclusion samples. The microstructure of the MWCNTs was found to consist of both individual fibers and spherical clumps of fibers. We suggest that, due to the microstructure of the MWCNTs used in this study, the mechanical properties can be modeled as a thin layer of particulates, while the electrical properties can be modeled as a thin bed of bulk MWCNTs. © 2012 Society of Chemical Industry [ABSTRACT FROM AUTHOR]

This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators. [ABSTRACT FROM AUTHOR]

In this article stability and parametrically excited oscillations of a two stage micro-shaft located in a Newtonian fluid with arrayed electrostatic actuation system is investigated. The static stability of the system is studied and the fixed points of the micro-shaft are determined and the global stability of the fixed points is studied by plotting the micro-shaft phase diagrams for different initial conditions. Subsequently the governing equation of motion is linearized about static equilibrium situation using calculus of variation theory and discretized using the Galerkin's method. Then the system is modeled as a single-degree-of-freedom model and a Mathieu type equation is obtained. The Variational Iteration Method (VIM) is used as an asymptotic analytical method to obtain approximate solutions for parametric equation and the stable and unstable regions are evaluated. The results show that using a parametric excitation with an appropriate frequency and amplitude the system can be stabilized in the vicinity of the pitch fork bifurcation point. The time history and phase diagrams of the system are plotted for certain values of initial conditions and parameter values. Asymptotic analytically obtained results are verified by using direct numerical integration method. [ABSTRACT FROM AUTHOR]

This paper presents a noncontact drop-on-demand three-layer microdroplet generator based on electrostatic actuation. The dispenser is actuated via a deformable membrane that isolates the electrical field from the working fluid. The dispenser controlled droplet formation, frequency, size, and velocity within the ranges tested. Prototypes were fabricated using three-step deep reactive-ion etching and polydimethylsiloxane (PDMS) plasma activated bonding. Experiments verified stable droplet dispensing with a variance in subsequent droplet volume of less than 15% between droplets. The frequency of stable generation was 20 Hz, and the average volume of dispensed droplet was 1 nL. The dispenser operating range and the nondestructive actuation make it suitable for biological applications.\hfill[2012-0009] [ABSTRACT FROM AUTHOR]