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.

ROM of Electrostatically Actuated MEMS Resonators Under Simultaneous Resonances

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Electrostatic Actuation ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Simultaneous Resonances

This paper deals with MEMS resonator sensors under double electrostatic actuation. The system consists of a MEMS cantilever between two parallel fixed plates. The frequencies of actuation are near natural frequency and near half natural frequency. The frequency response of the simultaneous resonance of the structure is investigated using Reduced Order Model (ROM) method.

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.

Voltage Response of MEMS Resonators Under Simultaneous Resonances

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Natural Frequency ◽  
Electrostatic Actuation ◽  
Voltage Response ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Simultaneous Resonances

This paper deals with MEMS resonator sensors under double electrostatic actuation. The system consists of a MEMS cantilever between two parallel fixed plates. The frequencies of actuation are AC near natural frequency, and AC half natural frequency. The voltage response of the structure is investigated, and parameter influences reported.

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.

Simultaneous Resonance of Soft AC Doubly Actuated MEMS Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Natural Frequency ◽  
Phase Difference ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
The Other ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Voltage Phase

This paper deals with electrostatically actuated microelectromechanical (MEMS) cantilever resonators under soft AC double actuation. The cantilever is between two parallel ground plates. The two AC frequencies are one near half natural frequency, and the other near natural frequency. There is a phase difference between the two voltages. The system undergoes a simultaneous resonance. The voltage-amplitude response is investigated. The effects of the second voltage, phase difference between voltages, and frequency on the response are reported. The method of multiple scales is used in this paper.

Response of Electrostatically Actuated Sensors Near Half of the Natural Frequency

2009 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Governing Equation ◽  
Multiple Scales ◽  
Equation Of Motion ◽  
Casimir Forces ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Micro Sensor ◽  
Phase Amplitude

A cantilever micro-resonator electrostatically actuated near half of the natural frequency is investigated. Hamilton’s principle is used to derive the partial-differential equation of motion for a general non-uniform sensor. Nonlinearities arise due to the electrostatic and Casimir forces. The electrostatic actuation introduces parametric coefficients in both linear and nonlinear parts of the governing equation. A direct approach is taken using the method of multiple scales resulting in a phase-amplitude relationship for the system. Numerical results for a uniform capacitive resonator micro-sensor are provided and tested numerically using a reduced-order model of the governing equation of motion.

Simultaneous Resonances of Electrostatically Actuated MEMS Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Electrostatic Actuation ◽  
The Other ◽  
Electrostatically Actuated ◽  
Mems Resonators ◽  
Simultaneous Resonances

This paper deals with simultaneous resonance of MEMS cantilever resonator sensors under double electrostatic actuation. The system consists of a MEMS cantilever between two parallel fixed plates. The two frequencies of actuation are one near natural frequency, and the other near half natural frequency. The frequency response of the structure is investigated, and parameter influences reported.

Electrostatically Actuated M/NEMS With Casimir Effect: Primary Resonance — Comparison Between Three Methods

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio S. Beatriz ◽  
Christian Reyes
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Boundary Value ◽  
Primary Resonance ◽  
Initial Value ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Modes Of Vibration

This paper deals with electrostatically actuated micro- and nano-electromechanical systems (M/NEMS) cantilever resonator under electrostatic actuation. The model includes Casimir effect. Three different methods are used to investigate the primary resonance of the MEMS resonator. The first two methods are based on a Galerkin approach in which the initial value and boundary value problem, given by the partial differential equation (PDE) of motion and the initial and boundary conditions, is transformed into an initial value problem of one ordinary differential equation (ODE) or a system of ODEs depending on how many modes of vibrations are considered in the model. The first method used is the Method of Multiple Scales (MMS) which is an approximate analytical method used to solve the model using one mode of vibration. The second method referred to as Reduced Order Model (ROM) solves the model using two to five modes of vibration using numerical integration. The third method is different than the first two in the sense that the initial value and boundary value problem describing the MEMS resonator is transformed into a boundary value problem (BVP) by using finite differences tor time derivatives. For this Matlab built-in function bvp4c is used to solve the problem. This built-in function is used for two different versions of the same equation. One which involves Taylor expansions of the nonlinear terms, and the other which does not. Results between the methods are in agreement. Thus any of these methods can be used to accurately predict the behavior of the MEMS resonator. For the ROM, two equations are also used, one for Casimir and one for without. The influence of damping, Casimir, and voltage parameter are also shown.

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.

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.

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