Dynamical analysis and anti-oscillation-based adaptive control of the FO arch MEMS with optimality

Nonlinear Dynamics - This paper mainly investigates dynamical analysis and anti-oscillation-based adaptive control issues of the fractional-order (FO) arch microelectromechanical system (MEMS) with...     

Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation

Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been an active research subject over the past few years. Despite the importance of the topic, robust knowledge is still missing in the understanding of the role of various physical parameters affecting the natural frequencies, such as the stretching of doubly clamped CNTs, the DC electrostatic force, and the initial curvature of slack CNTs. In this investigation, we use a 2D nonlinear curved beam model in the form of an arch to simulate the coupled in-plane and out-of-plane motions of a CNT with curvature. We calculate the variation of its natural frequencies and mode shapes with the level of slackness and the DC electrostatic load. Towards this end, we derive a reduced-order model using a multimode Galerkin procedure. We show various scenarios of mode crossing and mode veering as the levels of slackness and DC load are varied. Finally, we tackle the forced vibration problem of a curved CNT when actuated by small DC and AC loads. The results show the transfer of energy among the vibration modes involved in the veering phenomenon.     

On using the dynamic snap-through motion of MEMS initially curved microbeams for filtering applications

Numerical and experimental investigations of the dynamics of micromachined shallow arches (initially curved microbeams) and the possibility of using their dynamic snap-through motion for filtering purposes are presented. The considered MEMS arches are actuated by a DC electrostatic load along with an AC harmonic load. Their dynamics is examined numerically using a Galerkin-based reduced-order model when excited near both their first and third natural frequencies. Several simulation results are presented demonstrating interesting jumps and dynamic snap-through behavior of the MEMS arches and their attractive features for uses as band-pass filters, such as their sharp roll-off from pass-bands to stop-bands and their flat response. Experimental work is conducted to test arches realized of curved polysilicon microbeams when excited by DC and AC loads. Experimental data of the micromachined curved beams are shown for the softening and hardening behavior near the first and third natural frequencies, respectively, as well as dynamic snap-through motion.     

Dynamic response of slacked single-walled carbon nanotube resonators

This paper presents an investigation of the dynamics of electrically actuated single-walled carbon nanotube (CNT) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear shallow arch model is utilized. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNTs of higher and lower aspect ratio. Results of the perturbation method are verified with those obtained by numerically integrating the equations of a multi-mode reduced-order model based on the Galerkin procedure. The effective nonlinearity of the CNT is calculated as a function of the slack level and the DC load. To handle computational problems associated with CNTs of small radiuses, results based on a nonlinear cable model are also demonstrated. The results have indicated that the quadratic nonlinearity due to slack has dominant effect on the dynamic behavior of the CNT.     

Local nonlinear dynamics of MEMS arches actuated by fringing-field electrostatic actuation

Nonlinear Dynamics - The nonlinear dynamic behavior of a resonant MEMS arch microbeam actuated by fringing electric actuation is investigated in this paper. The arch microbeam is loaded with DC and...     

Nonlinear dynamics of a resonant gas sensor

We develop a mathematical model for a resonant gas sensor made up of an microplate electrostatically actuated and attached to the end of a cantilever microbeam. The model considers the microbeam as a continuous medium, the plate as a rigid body, and the electrostatic force as a nonlinear function of the displacement and the voltage applied underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microsystem. The Galerkin method is used to discretize the distributed-parameter model and, thus, approximate it by a set of nonlinear ordinary-differential equations that describe the microsystem dynamics. By comparing the exact solution to that associated with the reduced-order model, we show that using the first mode shape alone is sufficient to approximate the static behavior. We employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations for the limit cycles. The stability of these cycles is determined by combining the FDM discretization with Floquet theory. We investigate the basin of attraction of bounded motion for two cases: unforced and damped, and forced and damped systems. In order to detect the lower limit of the forcing at which homoclinic points appear, we conduct a Melnikov analysis. We show the presence of a homoclinic point for a loading case and hence entanglement of the stable and unstable manifolds and non-smoothness of the boundary of the basin of attraction of bounded motion.     

Bifurcation analysis and nonlinear dynamics of a capacitive energy harvester in the vicinity of the primary and secondary resonances

Nonlinear Dynamics - The objective of the present study is to examine the effect of nonlinearity on the efficiency enhancement of a capacitive energy harvester. The model consists of a cantilever...     

The dynamic behavior of MEMS arch resonators actuated electrically

In this paper, we investigate the dynamic behavior of clamped-clamped micromachined arches when actuated by a small DC electrostatic load superimposed to an AC harmonic load. A Galerkin-based reduced-order model is derived and utilized to simulate the static behavior and the eigenvalue problem under the DC load actuation. The natural frequencies and mode shapes of the arch are calculated for various values of DC voltages and initial rises. In addition, the dynamic behavior of the arch under the actuation of a DC load superimposed to an AC harmonic load is investigated. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response of the arch due to DC and small AC loads. Results of the perturbation method are compared with those obtained by numerically integrating the reduced-order model equations. The non-linear resonance frequency and the effective non-linearity of the arch are calculated as a function of the initial rise and the DC and AC loads. The results show locally softening-type behavior for the resonance frequency for all DC and AC loads as well as the initial rise of the arch.