Dynamic Study of a Capacitive MEMS Switch with Double Clamped-Clamped Microbeams

We study a capacitive MEMS switch composed of two clamped-clamped exible microbeams. We first develop a mathematical model for the MEMS switch where the upper microbeam represents the ground transmission line and the lower one represents the central transmission line. An electrostatic force is applied between the two microbeams to yield the switch to its ON and OFF states. We derive the equations of motion of the system and associated boundary conditions and solve the static and dynamic problems using the differential quadratic method. We show that using only nine grid points gives relatively accurate results when compared to those obtained using FEM. We also examine the transient behavior of the microswitch and obtain results indicating that subsequent reduction in actuation voltage, switching time, and power consumption are expected along with relatively good RF performances. ANSYS HFSS simulator is used in this paper to extract the RF characteristics of the microswitch. HFSS simulation results show that the insertion loss is as low as −0.31 dB and that the return loss is better than −12.41 dB at 10 GHz in the ON state. At the OFF state, the isolation is lower than −23 dB in the range of 10 to 50 GHz

Modeling and design of an ultra low-power NEMS relays: application to logic gate inverters

International audienceIn this work we propose a design based on a nanoelectromechanical relay acting as a logic gate inverter. The proposedinverter is made of a double cantilever nanobeam actuated by a fixed central electrode carrying the input signals. The staticand dynamic behaviors of the ohmic nanoinverter gate are investigated using an electromechanical mathematical modelthat fully incorporates nonlinear form of the electrostatic force and the ohmic contact of the nanobeams’ tip with the fixedoutput electrode. The derived electromechanical model is used for electrical and energy analysis. Simulations are used toconfirm the functionality of the inverter. The analysis of the switching energy showed very low power consumptioncompared to classical CMOS inverters. It is shown that the proposed inverter dissipates only 0.45 fJ to code a ‘‘1’’ logicstateand 0.023 fJ to code a ‘‘0’’ logic-state

Modeling and parametric analysis of a piezoelectric flexoelectric nanoactuator

With the development of nanotechnology, nanoactuators have recently re-stimulated a surge of scientific interests in research communities. One of the interesting transduction mechanisms that showed high efficiency at the nanoscale was flexoelectricity. In fact, the flexoelectric effect in dielectric solids couples polarization and strain gradient, rather than polarization and strain for piezoelectricity, to convert mechanical stimulus into electricity and vice cersa. The objective of the current work is to develop a complete comprehensive electromechanical model of a nanobeam whose for piezoelectrically-actuated nanocantilever sensor in which both the flexoelectricity and piezoelectricity effects will be tzken into consideration. Starting from the enthalpy density function, the Hamilton’s principle is applied to drive the governing coupled equations with appropriate boundary conditions. Then, we investigate the free vibration of the mechanism by formulating the eigenvalue problem associated with the coupled partial differential equations. Using the Galerkin procedure we develop both the static and dynamic of our structure. The results show that a certain aspect ratio flexoelectric effect significantly increases the performance of the nanoactuator

Modeling and parametric analysis of a piezoelectric flexoelectric nanoactuator

With the development of nanotechnology, nanoactuators have recently re-stimulated a surge of scientific interests in research communities. One of the interesting transduction mechanisms that showed high efficiency at the nanoscale was flexoelectricity. In fact, the flexoelectric effect in dielectric solids couples polarization and strain gradient, rather than polarization and strain for piezoelectricity, to convert mechanical stimulus into electricity and vice cersa. The objective of the current work is to develop a complete comprehensive electromechanical model of a nanobeam whose for piezoelectrically-actuated nanocantilever sensor in which both the flexoelectricity and piezoelectricity effects will be tzken into consideration. Starting from the enthalpy density function, the Hamilton’s principle is applied to drive the governing coupled equations with appropriate boundary conditions. Then, we investigate the free vibration of the mechanism by formulating the eigenvalue problem associated with the coupled partial differential equations. Using the Galerkin procedure we develop both the static and dynamic of our structure. The results show that a certain aspect ratio flexoelectric effect significantly increases the performance of the nanoactuator

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

Carbon nanotubes (CNTs) are promising mechanical structures at the nano-scale which have attracted increasing attention due to their amazing mechanical, chemical, thermal, and electrical properties. To take into account size dependence of such small sized structures, the use of nonlocal continuum theory is proposed where intrinsic length scales is taken into account. Based on the Eringen theory, a nonlinear nonlocal model of a clamped-clamped CNT is developed in this study. Static and free vibration responses are simulated and analyzed. The main objective of this work is to study the influence of CNT size and length scale parameter on the static and free vibration response to better understand their effect on the general behavior of the CNT. It has been found that the nonlocal effect can largely influence the performance of the CNT and change qualitatively its nonlinear response

Nonlocal modeling of a Carbon Nanotube actuated by an electrostatic force

Carbon nanotubes (CNTs) are promising mechanical structures at the nano-scale which have attracted increasing attention due to their amazing mechanical, chemical, thermal, and electrical properties. To take into account size dependence of such small sized structures, the use of nonlocal continuum theory is proposed where intrinsic length scales is taken into account. Based on the Eringen theory, a nonlinear nonlocal model of a clamped-clamped CNT is developed in this study. Static and free vibration responses are simulated and analyzed. The main objective of this work is to study the influence of CNT size and length scale parameter on the static and free vibration response to better understand their effect on the general behavior of the CNT. It has been found that the nonlocal effect can largely influence the performance of the CNT and change qualitatively its nonlinear response

Nonlinear Analysis of Electrically Actuated Carbon Nanotube Resonator Using a Novel Discretization Technique

Static as well as dynamic analyses have been performed on clamped-clamped carbon nanotube (CNT) resonator. The nonlinear CNT model is investigated with a novel discretization technique: a differential quadrature method (DQM) to discretize the spatial variables and a finite difference method (FDM) for limit-cycle solutions. Parametric study is performed by varying the electric load, as well as the initial curvature (due to fabrication). It is found that the pull-in voltage decreases nonlinearly with initial curvature and linearly with residual stresses. The eigenvalue problem is also solved to obtain the bending natural frequencies of the system as function of the DC voltage as well as the initial curvature of the CNT. Frequency-response curves near some selected resonant frequencies are plotted to better understand the nanotubes' dynamic behavior. Different linear and nonlinear phenomena are depicted such as dynamic pull-in, hardening, and softening behavior and veering of the odd modes. We have found that even when exciting the CNT near its first natural frequency, the vibration mode located at the veering process significantly alters the CNT's motion and hence may decrease its overall quality factor

Nonlinear dynamics of parametrically excited carbon nanotubes for mass sensing applications

International audienceIn this paper, a computational model for large amplitude vibrations of a parametrically excited carbon nanotube (CNT) is developed. The continuous model includes geometric and electrostatic nonlinearities. The Galerkin discretization is used to transform the nonlinearpartial differential equation to a finite degrees of freedom system which is numerically solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The influence of higher modes on the nonlinear dynamics of the considered resonatoris investigated in order to retain the number of modes which will be used by the HBM+ANM procedure. It is shown that at least two modes are required in order to predict accurately the CNT frequency responses

Effects of Squeeze Film and Initial Deflection on the Resonance Frequencies and Modal Damping of Circular Microplates

International audienceWe investigate the effects of squeeze air film and initial deflection on the resonance frequencies and modal damping of capacitivecircular microplates. The equation of motion of a circular microplate, which are derived from the von k´arm´an plate theory, coupled with the Reynolds equation are discretized using the Differential Quadrature Method (DQM). The eigenvalues and eigenvectors of the multiphysical problem are determined by perturbing the system of equations around a static solution. Therefore, the resonance frequencies, modal damping coefficients and mode shapes of the plate and the fluid can be determined. The advantage of using DQM is that the solution of the system can be obtained with only few grid points. The obtained numerical results are compared with the experimental data for the case of a capacitive circular microplates with an initial deflection. The increase of the static pressure leads to a shift in the resonance frequencies due to the increase in the stiffness of the plate. Also the initial deflection change the resonance frequencies due to the change in the effective gap distance. The developed model is an effective tool to predict the dynamic behavior of a microsystem under the effect of air film and with initial deflection