Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Alternating Current ◽  
Electrostatically Actuated ◽  
Current Voltage ◽  
Fringe Effect ◽  
Parametric Frequency

This paper deals with nonlinear-parametric frequency response of alternating current (AC) near natural frequency electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators. The model includes fringe and Casimir effects, and damping. Method of multiple scales (MMS) and reduced order model (ROM) method are used to investigate the case of weak nonlinearities. It is reported for uniform resonators: (1) an excellent agreement between the two methods for amplitudes less than half of the gap, (2) a significant influence of fringe effect and damping on bifurcation frequencies and phase–frequency response, respectively, (3) an increase of nonzero amplitudes' frequency range with voltage increase and damping decrease, and (4) a negligible Casimir effect at microscale.

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Alternating Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Fringe Effect

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY ACTUATED MICRORESONATORS

2011 ◽  
Vol 11 (04) ◽  
pp. 641-672 ◽  
Author(s):  
DUMITRU I. CARUNTU ◽  
MARTIN KNECHT
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated ◽  
Fringe Effect

This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A first-order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The influences of damping, actuation, and fringe effect on the resonator response are found.

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.

Sensitivity of MEMS/NEMS Biosensors Near Twice Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Equation Of Motion ◽  
Direct Approach ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Phase Amplitude

Bio-MEMS/NEMS resonator sensors near twice natural frequency for mass detection are investigated. Electrostatic force along with fringe correction and Casimir effect are included in the model. They introduce parametric nonlinear terms in the system. The partial-differential equation of motion of the system is solved by using the method of multiple scales. A direct approach of the problem is then used. Two approximation problems resulting from the direct approach are solved. Phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors are reported.

Casimir Effect on Simultaneous Resonances of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Natural Frequency ◽  
Bottom Electrode ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Parallel Plates ◽  
Casimir Forces ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Simultaneous Resonances

This paper deals with the influence of Casimir effect on MEMS resonator sensors under double electrostatic actuation and simultaneous resonances. The MEMS cantilever is between two parallel plates (electrodes) under soft AC double actuation. The AC voltage with the bottom electrode is of frequency near half natural frequency of the resonator and the AC voltage with the top electrode is of frequency near natural frequency of the resonator. The method of multiple scales is used to model the behavior of the system. In the model the damping, fringing, voltage, and Casimir forces are taken into consideration and the effects of these parameters on the frequency response are reported. Designing MEMS resonators for applications in fields such as automotive and biomedical can benefit from this work.

On MEMS/NEMS Biosensor Sensitivity Near Half Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Direct Approach ◽  
Mass Detection ◽  
Additional Mass ◽  
Electrostatically Actuated ◽  
Virus Size ◽  
Phase Amplitude

This paper deals with sensitivity of electrostatically actuated Bio-MEMS/NEMS resonator sensors near half natural frequency for mass detection for applications in medicine and biology. Electrostatic force along with fringe correction and Casimir effect are included in the model. They introduce parametric nonlinear terms in the system. The partial-differential equation of motion of the system is solved by using the method of multiple scales. A direct approach of the problem is then used. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors are provided. An additional mass consisting of a film with a thickness of 100 nm (virus size), and a density of 0.43 of the density of the microsensor, has been added to the sensor. The additional mass shifted the amplitude-frequency curve of the sensor to lower frequencies.

Reduced Order Model of Electrostatically Actuated MEMS Resonators Resonance Near Half Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Mems Resonators

This paper uses the Reduced Order Model (ROM) method to investigate the influence of nonlinearities from parametric electrostatic excitation due to soft AC voltage of frequency near half natural frequency of the MEMS cantilever resonator on its frequency response. Most of the analysis in literature investigates pull-in phenomenon, stability, amplitude–frequency relations, or finds time responses of such systems. In this work it is showed that the bifurcation points in the amplitude-frequency response occur at lower frequencies and amplitudes than predicted by the Method of Multiple Scales (MMS), a perturbation method. This result is extremely important for predicting pull-in phenomena. Also the ROM predicts pull-in instability for large initial amplitudes and AC frequencies less than half natural frequency of the resonator. MMS fails to predict this behavior. Increasing the damping and/or decreasing the voltage increases the frequency at which the system undergoes into a pull-in phenomenon.

Electrostatically Actuated MEMS Circular Plate Resonators: Frequency Response of Superharmonic Resonance of Third Order

2019 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Circular Plate ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Damping Force ◽  
Third Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Ground Plate

Abstract This paper deals with the frequency response of superharmonic resonance of order three of electrostatically actuated MicroElectroMechanical Systems (MEMS) circular plate resonators. The MEMS structure in this work consists of an elastic circular microplate parallel to an electrode ground plate. The microplate is elelctrostatically actuated through an AC voltage between the microplate and the ground plate. The voltage is in the category of hard excitations. The AC frequency is near one sixth 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 third 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 Reduced Order Model (ROM) method using two modes of vibration are also utilized to investigate the resonance. ROM is solved numerically integrated using Matlab in order to simulate time responses of the structure, and third, the ROM is used to predict the frequency response using AUTO, a software for continuation and bifurcation analysis. All methods are in agreement for moderate nonlinearities and small to moderate amplitudes. For relatively large amplitudes, when compared to the gap between the microplate and the ground plate, ROM more accurately predicts the behavior of the system. Effects of the parameters of the system on the frequency response are reported.

Near Three Half Natural Frequency Resonance of Electrostatically Actuated MEMS Resonators

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Direct Approach ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Phase Amplitude ◽  
Fringe Effect

This paper investigates electrostatically actuated micro resonators response near three half natural frequency. Electrostatic force including fringe effect and Casimir force are included in the model. These forces introduce parametric nonlinear terms in the system. The partial-differential equation of motion of the system is solved by using the method of multiple scales. A direct approach of the problem is then used. Two approximation problems resulting from the direct approach are solved. Phase-amplitude relationship is obtained. Numerical results for electrostatically actuated uniform micro resonator sensors are provided.

Response Near Twice the Natural Frequency of Electrostatically Actuated Microresonators

2010 ◽  
Author(s):  
Martin Knecht ◽  
Dumitru I. Caruntu
Keyword(s):  
Natural Frequency ◽  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Equation Of Motion ◽  
Direct Approach ◽  
Electrostatically Actuated ◽  
Phase Amplitude ◽  
Fringe Effect

This paper deals with electrostatically actuated micro resonators response near twice natural frequency. Both the electrostatic force (including fringe effect) and the Casimir force are included in the model. They introduce parametric nonlinear terms in the system. The partial-differential equation of motion of the system is solved by using the method of multiple scales. A direct approach of the problem is then used. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors are provided.

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