Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Casimir effect on the pull-in parameters of nanometer switches. Microsys Technol

The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.

Thermoelastic Damping in Micro- and Nano-Mechanical Systems.

Double-sided electromechanical nano-bridges can potentially be used as angular speed sensors and accelerometers in rotary systems such as turbine blades and vacuum pumps. In such applications, the influences of the centrifugal force and rarefied flow should be considered in the analysis. In the present study, the non-linear dynamic pull-in instability of a double-sided nano-bridge is investigated incorporating the effects of angular velocity and rarefied gas damping. The non-linear governing equation of the nanostructure is derived using Euler-beam model and Hamilton׳s principle including the dispersion forces. The strain gradient elasticity theory is used for modeling the size-dependent behavior of the system. The reduced order method is also implemented to discretize and solve the partial differential equation of motion. The influences of damping, centrifugal force, length scale parameters, van der Waals force and Casimir attraction on the dynamic pull-in voltage are studied. It is found that the dispersion and centrifugal forces decrease the pull-in voltage of a nano-bridge. Dynamic response of the nano-bridge is investigated by plotting time history and phase portrait of the system. The validity of the proposed method is confirmed by comparing the results from the present study with the experimental and numerical results reported in the literature.

Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow

Nano and micro electro-mechanical systems (NEMS and MEMS) have been attracting a large amount of attention recently as they have extensive current/potential applications. However, due to their scale, molecular interaction and size effects are considerably high which needs to be considered in the theoretical modelling of their electro-mechanical behaviour. Both nano- and micro-scale electrically actuated structures are discussed when subjected to constant and time-varying voltages, and different theories and models, introduced in the past few years for modelling such small structures, are discussed. It is highlighted that considering the intermolecular forces and size-dependence effects can change both the static and dynamic behaviours of such systems significantly. This review presents the current stage of the research on electrically actuated NEMS/MEMS by analysing the latest models and studies in this field in the framework of electro-mechanical coupling and small-size effects.

A review on the statics and dynamics of electrically actuated nano and micro structures

This paper presents a high-precision capacitive angular position sensor (CAPS). The CAPS is designed to be excited by a single voltage to eliminate the matching errors of multi-excitations, and it is mainly composed of excitation electrodes, coupling electrodes, petal-form sensitive electrodes and a set of collection electrodes. A sinusoidal voltage is applied on the excitation electrodes, then the voltage couples to the coupling electrodes and sensitive electrodes without contact. The sensitive electrodes together with the set of collection electrodes encode the angular position to amplitude-modulated signals, and in order to increase the scale factor, the sensitive electrodes are patterned in the shape of petal-form sinusoidal circles. By utilizing a resolver demodulation method, the amplitude-modulated signals are digitally decoded to get the angular position. A prototype of the CAPS is fabricated and tested. The measurement results show that the accuracy of the sensor is 0.0036°, the resolution is 0.0009° and the nonlinearity over the full range is 0.008° (after compensation), indicating that the CAPS has great potential to be applied in high-precision applications with a low cost.

https://www.mdpi.com/1424-8220/16/8/1196/pdf

A Novel Single-Excitation Capacitive Angular Position Sensor Design

In this paper, the influence of centrifugal forces on the stability of an electro-statically actuated clamped–clamped micro-beam has been investigated. The non-dimensional governing static and dynamic equations have been linearized using the step by step linearization method (SSLM), then, a Galerkin-based reduced order model has been used to solve the linearized equations. For constant value of a bias DC voltage and different values of angular velocity the equilibrium points of the corresponding autonomous system including stable center points, unstable saddle points and singular points have been obtained using the equivalent mass-spring model. Subsequently the bifurcation diagram has been depicted using the obtained fixed point. The static pull-in voltage value for different values of angular velocity and the static pull-in angular velocity for different values of bias voltage have been calculated. The obtained results are validated using results of previous studies and a good agreement has been observed. The effect of the centrifugal force on the fixed points has been studied using the phase portraits of the system for different initial conditions. Moreover, the effects of centrifugal forces on the dynamic pull-in behavior have been investigated using time histories and phase portraits for different angular velocities.

Bifurcation analysis of an electro-statically actuated micro-beam in the presence of centrifugal forces

On the modeling of a capacitive angular speed measurement sensor

Development of a capacitive angular velocity sensor for the alarm and trip applications

Surface and Nonlocal Effects on the Thermoelastic Damping in Axisymmetric Vibration of Circular Graphene Nanoresonators

In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.

Hadi Azimloo

Papers

Bifurcation analysis of an electro-statically actuated micro-beam in the presence of centrifugal forces

On the modeling of a capacitive angular speed measurement sensor

Development of a capacitive angular velocity sensor for the alarm and trip applications

Surface and Nonlocal Effects on the Thermoelastic Damping in Axisymmetric Vibration of Circular Graphene Nanoresonators

Stability analysis of an electrostatically actuated out of plane MEMS structure