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This research paper offers a simple and original approach to extend the resonant frequency tuning range from high-to-low frequencies in electrostatically actuated microelectromechanical systems (MEMS) based resonators. Typically, it is possible to achieve low frequencies in MEMS through increasing the effective mass or decreasing the mechanical stiffness in micro structures. However, this work intends, assuming a double-sided electrodes design, to control the excited mode of the micro-system in order achieve low frequencies through DC bias voltage variations and possibly eliminating the displacement dependency in capacitive micro-bridges-based structures. The design consists of a flexible microbeam where its equations of motion are derived within the framework of the nonlinear Euler–Bernoulli beam theory. The equations are then solved using the reduced-order modeling based on the Galerkin modal decomposition and while considering the couple-stress theory. Simulations show an improved performance of the micro- structure as compared to previous investigations. In addition, a wider frequency tuning range has been achieved through a proper DC bias voltage arrangement.

Parallel-plates based micro-tunable capacitors are known to have low travel ranges, which deteriorate as going even lower in terms of their initials gap sizes. Such conditions have put strict requirements on the operation of such designs and hence hindering their use in numerous practical applications requiring high tunability. This work is proposed to examine the possibility to implement a closed-loop control strategy to increase the maximum capacitance and therefore tunability of micro tunable capacitors. The suggested control strategy is implemented on an electrostatically actuated parallel-plates (one stationary and one movable) based micro-capacitor and had an objective to stabilize the movable electrode when it is close to the fixed one for the sake of maximizing its maximum capacitance and possibly improving its overall tunability. Robustness of the micro-capacitor to the so-called pull-in phenomenon (short-circuit instability) when using the closed loop control scheme is studied. Indeed, an adaptive sliding mode controller is designed to compensate the effects of uncertainty, disturbance and eliminate any possibility for chattering phenomenon. The controller proficiencies in terms of stabilizing the micro-capacitor and its robustness to uncertainty as well as disturbance have been thoroughly examined. Furthermore, the effects of the control parameters on the behavior of micro-capacitor, such as overshoot, settling time, steady state error, robustness to uncertainty, external disturbances and to the chattering phenomenon, have been completely inspected. The obtained results indicated satisfactory proficiency and trustworthiness of the proposed control strategy to achieve high level of tunability and maximum capacitance.

The nonlinear mechanical response of an electrostatically actuated doubly-clamped micro-actuator assuming a non-contact based actuation arrangement is examined. The electrostatic actuating force is numerically approximated through solving a nonlinear electrical field problem using a finite-elements based analysis. An electro-mechanical model is established within the framework of the Euler–Bernoulli continuous nonlinear beam theory, where both the nonlinear geometric mid-plane stretching and the nonlinear electric forcing effects have been both taken into consideration. Then, assuming a Galerkin’s based modal expansion technique, the structural behavior of the micro-actuator under the effect of the resultant electric out-of-plane fields is solved numerically. The resultant nonlinear reduced-order model equations are examined to get the deflection of the microbeam against an assumed bias voltage for different vertical initial gap sizes. The snap-through and pull-out voltages of the micro-system are calculated for different assumed initial vertical gap separation. Frequency diagrams are analyzed against any applied DC bias voltage through solving a linearized eigenvalue problem. Thorough parametric simulations indicate a prospect of such bi-stable design of the micro-actuator with large stroke and high fundamental frequency enabling it to be potentially useful for MEMS based high frequency energy harvester devices with bi-stable capabilities.

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

The temperature change and size scale dependent effects on the dynamical behaviors of the Carbon nanotube (CNT)-based nano-resonator are investigated in this work. The equation of motion of the CNT-based nano-resonator incorporating the higher-order strain gradient deformation, the geometric nonlinearity due to von Karman nonlinear strain, and the thermal effects is derived. A Galerkin based modal decomposition is used to investigate both the free vibration and forced vibration of the nano-resonator. The temperature variation effect is analyzed by assuming both low and high temperature environments. The results show that when assuming a high temperature in the post buckling regime, the nano-resonator natural frequencies dispersion graph shows possibilities of modes-veering and modes-crossing variation due to the initial buckling of the nano-resonator. From the forced-vibration analysis, the results demonstrate that taking into consideration the higher-order strain gradient deformation in modeling the CNT based nano-resonator completely changes the frequency response of the CNT-based nanoresonator.

The mechanical behavior of MEMS/NEMS based-actuators has been studied in this work while considering the effect of both electrostatic and van der Waals forces. The assumed structural model was constructed based on an Euler–Bernoulli beam continuous nonlinear model, where both the mid-plane stretching (geometric nonlinearity) and the electric fringing-fields effects have been taken into consideration. The nonlinear equation of motion of the actuator governing its static behavior has been derived. An original Galerkin expansion based reduced-order model has been developed to avoid problem arising from all the possible nonlinearities in the nonlinear differential equation. The obtained reduced-order model equations have been resolved mathematically using the so-called Newton-Raphson technique. The developed numerical method was shown to be powerful in examining the basic pull-in design parameters such as the electric load amplitude and the beam static deflection at the pull-in instability state. The model also proved its capability in capturing the effect of the actuator parameter on its detachment length due to the attractive van der Waals forces. Some of the obtained numerical outcomes have been compared with other numerical approaches such as finite-elements and finite-difference methods. The assessment revealed acceptable agreement among all assumed numerical techniques.

In this paper, we investigate the effects of electric fringing-fields on the structural behavior of a MEMS shallow arch. We consider the Galerkin method-based reduced-order modeling to discretize the governing nonlinear equation and obtain a lumped-parameter model of the system. We then assume two most well-known models for demonstrating the fringing-fields effects, that is the Palmer’s and the Mejis-Fokkema models. Using the discretized model, we investigate the system nonlinear behavior assuming the two electric fringing-fields models. The presented results show that for these particular cases of arch configuration, fringing-fields effects should be considered since it improves the prediction of corresponding voltages for both snap-through and pull-in structural instabilities as well as the overall static deflection of the MEMS arch. Comparisons of the acquired numerical results with some available experimental data as well as ANSYS® based finite-elements simulations confirm that neglecting the fringing-fields effects in MEMS arches can represent a significant source of error which should be avoided using much more accurate modeling techniques.

In this work, we propose to investigate the micro-electromechanical post-buckling response of an electrostatically-actuated curled cantilever microbeam. The analytical/numerical model is based on a nonlinear differential governing equation, derived via assuming a continuous Euler---Bernoulli beam model, combined with a multi-modes Galerkin decomposition of the beam deflection. The pull-in voltages which govern the stability of the micro-curled beam actuator are also obtained analytically. These approximate solutions show excellent agreements compared to solutions obtained by other computationally expensive numerical methods as well some previously reported experimental data, for a wide range of the microbeam length. The derived expressions of these analytical approximate solutions are easy to implement, quick to solve, and could be conveniently used by MEMS designers for quick estimations of the effects of the various micro-actuator parameters on its structural stability.

In this work, we investigate the structural behavior of a micro-electromechanical system arch microbeam actuated by electric fringing-fields where the electrodes are located at both side of the microbeam. In this particular configuration, the electrostatic actuating force is caused by the asymmetry of the fringing electric fields acting in a direction opposite to the relative deflection of the microbeam. A reduced-order model is derived for the considered system using the so-called Galerkin decomposition and assuming linear undamped mode shapes of a straight beam as basis functions in the decomposition process. A static analysis is performed to investigate the occurrence of any structural instability. The eigenvalue problem is then investigated to calculate the fundamental as well as higher natural frequencies variation of the microbeam with the applied DC load. A bifurcation analysis is then implemented to derive a criterion for whether symmetric or asymmetric bifurcation is occurring during the static structural instability. The results show elimination of the so-called pull-in instability in this kind of systems as compared to the regular case of parallel-plates electrostatic actuation. The bifurcation analysis shows that the arch goes for asymmetric bifurcation (symmetry breaking) with increase in initial elevation without the occurrence of symmetric bifurcation (snap-through) for any initial elevation.