scholarly journals Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Multiple Scales ◽  
Dc Voltage ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Subcritical Hopf Bifurcation ◽  
Fold Bifurcation ◽  
Type Change ◽  
Ground Plate ◽  
Dc Bias ◽  
And Shifts

This paper investigates the nonlinear response of microelectromechanical system (MEMS) cantilever resonator electrostatically actuated by applying a soft alternating current (AC) voltage and an even softer direct current (DC) voltage between the resonators and a parallel fixed ground plate. The AC frequency is near natural frequency. This drives the resonator into nonlinear parametric resonance. The method of multiple scales (MMS) is used to solve the dimensionless differential equation of motion of the resonator and find the steady-state solutions. The reduced order model (ROM) method is used to validate the results obtained using MMS. The effect of the soft DC voltage (bias) component on the frequency response is reported. It is shown that the DC bias changes the subcritical Hopf bifurcation into a cyclic fold bifurcation and shifts the bifurcation point (where the system loses stability) to lower frequencies and larger amplitudes.

ROM of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Second Order ◽  
Voltage Response ◽  
Order Model ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Method Effects ◽  
Ground Plate

This paper deals with the voltage-amplitude response (or voltage response) of superharmonic resonance of second order of MEMS resonator sensors under electrostatic actuation. The system consists of a MEMS flexible cantilever above a parallel ground plate. The AC frequency of actuation is near one fourth the natural frequency. The voltage response of the superharmonic resonance of second order of the structure is investigated using the Reduced Order Model (ROM) method. Effects of voltage and damping voltage response are reported.

Electrostatically Actuated Coupled MEMS Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
System Structure ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Beam System ◽  
Mems Resonators ◽  
The Mathematical Model ◽  
Steady State Solutions

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

Amplitude-Frequency Response for Superharmonic Resonance of Fourth Order of Electrostatically Actuated MEMS Cantilever Resonators

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christopher Reyes
Keyword(s):  
Frequency Response ◽  
Fourth Order ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Damping Force ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Homotopy Analysis ◽  
Ground Plate

Abstract This paper deals with the frequency response of superharmonic resonance of order four of electrostatically actuated MicroElectroMechanical Systems (MEMS) cantilever resonators. The MEMS structure in this work consists of a microcantilever parallel to an electrode ground plate. The MEMS resonator is elelctrostatically actuated through an AC voltage between the cantilever and the ground plate. The voltage is in the category of hard excitation. The AC frequency is near one eight of the natural frequency of the resonator. Since the electrostatic force acting on the resonator is proportional to the square of the voltage, it leads to superharmonic resonance of fourth order. Besides the electrostatic force, the system experiences damping. The damping force in this work is proportional to the velocity of the resonator, i.e. it is linear damping. Three methods are employed in this investigation. First, the Method of Multiple Scales (MMS), a perturbation method, is used predictions of the resonant regions for weak nonlinearities and small to moderate amplitudes. Second, the Homotopy Analysis Method (HAM), and third, the Reduced Order Model (ROM) method using two modes of vibration are also utilized to investigate the resonance. ROM is solved through numerical integration using Matlab in order to simulate time responses of the structure. All methods are in agreement for moderate nonlinearities and small to moderate amplitudes. This work shows that adequate MMS and HAM provide good predictions of the resonance.

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

2019 ◽  
Vol 19 (07) ◽  
pp. 1950072 ◽  
Author(s):  
S. K. Lai ◽  
X. Yang ◽  
C. Wang ◽  
W. J. Liu
Keyword(s):  
Free Vibration ◽  
Lower Order ◽  
Forced Vibration ◽  
Analytical Approximation ◽  
Beam Model ◽  
Decomposition Approach ◽  
Dc Voltage ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Resonance Response

This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler–Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a nonautonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge–Kutta method.

Parametric Resonance of Electrostatically Actuated MEMS Cantilever Resonators Using Method of Multiple Scales and Homotopy Perturbation Method

2017 ◽  
Author(s):  
Christopher Reyes ◽  
Dumitru I. Caruntu
Keyword(s):  
Perturbation Method ◽  
Parametric Resonance ◽  
Homotopy Perturbation Method ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Plate Electrode ◽  
Electrostatically Actuated ◽  
Homotopy Perturbation ◽  
Ground Plate

This paper investigates the dynamics governing the behavior of electrostatically actuated MEMS cantilever resonators. The cantilever is held parallel to a ground plate (electrode) with an AC voltage between the plate and the electrode causing the electrostatic actuation (excitation). For the purposes of this paper this is soft excitation. The frequency of the excitation is near the natural frequency of the cantilever leading to what is known as parametric resonance. The electrostatic force in the problem investigated throughout the paper is nonlinear in nature and includes the fringe effect. Two methods are used in investigating this problem: the method of multiple scales (MMS) and the homotopy perturbation method (HPM). The two methods work well for small non-linearities and small amplitudes. The influence of voltage, fringe, damping, Casimir, and Van der Waals parameters will be investigated in this paper using MMS and HPM as a means of verifying the results obtained.

On Electrostatically Actuated CNT Bio-Sensors

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Cone S. Salinas Trevino
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate ◽  
Frequency Phase

This paper deals with electrostatically actuated Carbon NanoTubes (CNT) cantilevers for bio-sensing applications. There are three kinds of forces acting on the CNT cantilever: electrostatic, elastostatic, and van der Waals. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT dynamics is nonlinear parametric. The method of multiple scales is used to investigate the system under soft excitations and/or weakly nonlinearities. The frequency-amplitude and frequency-phase behavior are found in the case of primary resonance. The CNT bio-sensor is to be used for mass detection applications.

Reduced Order Model on DC Bias Effect on the Frequency Response of Electrostatically Actuated Biosensor Microplates

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Alternate Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Bias Effect ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Dc Bias

This paper investigates the frequency response of microplates under electrostatic actuation. The microplate is parallel to a fixed ground plate. The electrostatic force that actuates the system is given by both Alternate Current (AC) and Direct Current (DC) voltages. The AC frequency is set to be near half natural frequency of the structure. Damping influence is also investigated in this paper. The method of investigation is Reduced Order Model. The effects of various parameters on the response of the structure are reported.

Subcritical bifurcation and bistability in thermoacoustic systems

2013 ◽  
Vol 715 ◽  
pp. 210-238 ◽  
Author(s):  
Priya Subramanian ◽  
R. I. Sujith ◽  
P. Wahi
Keyword(s):  
Hopf Bifurcation ◽  
Linear Stability ◽  
Multiple Scales ◽  
Landau Equation ◽  
Linear Instability ◽  
Numerical Continuation ◽  
Rijke Tube ◽  
Subcritical Hopf Bifurcation ◽  
Fold Bifurcation ◽  
Parameter Values

AbstractThis paper analyses subcritical transition to instability, also known as triggering in thermoacoustic systems, with an example of a Rijke tube model with an explicit time delay. Linear stability analysis of the thermoacoustic system is performed to identify parameter values at the onset of linear instability via a Hopf bifurcation. We then use the method of multiple scales to recast the model of a general thermoacoustic system near the Hopf point into the Stuart–Landau equation. From the Stuart–Landau equation, the relation between the nonlinearity in the model and the criticality of the ensuing bifurcation is derived. The specific example of a model for a horizontal Rijke tube is shown to lose stability through a subcritical Hopf bifurcation as a consequence of the nonlinearity in the model for the unsteady heat release rate. Analytical estimates are obtained for the triggering amplitudes close to the critical values of the bifurcation parameter corresponding to loss of linear stability. The unstable limit cycles born from the subcritical Hopf bifurcation undergo a fold bifurcation to become stable and create a region of bistability or hysteresis. Estimates are obtained for the region of bistability by locating the fold points from a fully nonlinear analysis using the method of harmonic balance. These analytical estimates help to identify parameter regions where triggering is possible. Results obtained from analytical methods compare reasonably well with results obtained from both experiments and numerical continuation.

Influence of Timestep and Mesh Sizes on Numerical Simulations of Boundary Value Problem Model of Electrostatically Actuated MEMS Resonators

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Boundary Value Problem ◽  
Numerical Simulations ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mesh Size ◽  
Problem Solver ◽  
Time Step ◽  
Problem Model ◽  
Electrostatically Actuated ◽  
Mems Resonators

Abstract This paper deals with the effects of mesh size and time step on the numerical simulations using bvp4c, a Matlab Boundary Value Problem solver, on the time response of electrostatically actuated MEMS resonators. These results are compared to the reduced order model as well as the method of multiple scales to test how accurate these results are at lower amplitudes. The refinement of mesh size leads to more accurate results to a certain extent, as it eventually reaches a convergence. It should be said that the larger the mesh size, the longer the calculations take. A similar result occurs with timestep size. The smaller the timestep the more accurate the results. However, the CPU time increases significantly. However, beyond a certain timestep, any smaller time step would not yield any noticeable differences. Thus it can be said convergence has been reached.

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Reduced Order Model ◽  
Lagrange Equations ◽  
Order Model ◽  
Reduced Order ◽  
Dc Voltage ◽  
Ground Plate

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.

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