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.

Reduced Order Model of Frequency Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Ground Plate

This paper deals with superharmonic resonance of electrostatically actuated MEMS resonator sensors. The system consists of a MEMS cantilever on top of a parallel ground plate. An AC voltage of frequency near one fourth the natural frequency of the resonator provides the electrostatic force of actuation. The frequency response of the superharmonic resonance of the structure is investigated using two term Reduced Order Model (ROM) method.

Frequency Response of Electrostatically Actuated MEMS Resonators Under Superharmonic Resonance Using MMS

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Second Order ◽  
Voltage Response ◽  
Order Problem ◽  
Plate Electrode ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator

This work investigates the voltage response of superharmonic resonance of second order of electrostatically actuated Micro-Electro-Mechanical Systems (MEMS) resonator cantilevers. The results of this work can be used for mass sensors design. The MEMS device consists of MEMS resonator cantilever over a parallel ground plate (electrode) under Alternating Current (AC) voltage. The AC voltage is of frequency near one fourth of the natural frequency of the resonator which leads to the superharmonic resonance of second order. The AC voltage produces an electrostatic force in the category of hard excitations, i.e. for small voltages the resonance is not present while for large voltages resonance occurs and bifurcation points are born. This solution is then used in the first-order problem to find the voltage-amplitude response of the structure. The influences of frequency and damping on the response are investigated. This work opens the door of using smaller AC frequencies for MEMS resonator sensors. The frequency response of the superharmonic resonance of the structure is investigated using the method of multiple scales (MMS).

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.

Superharmonic Resonance of Third Order of Electrostatically Actuated MEMS Circular Plates: Effect of AC Frequency on Voltage Response

2020 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Multiple Scales ◽  
Voltage Response ◽  
Circular Plates ◽  
Order Model ◽  
Third Order ◽  
Micro Electro Mechanical Systems ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Unstable Branch

Abstract This paper uses the Reduced Order Model (ROM) as well as the Method of Multiple Scales (MMS) in order to investigate behavior of electrostatically actuated micro-electro-mechanical systems (MEMS) circular plates under superharmonic resonance of third order. ROM is solved using two methods, the first is a continuation and bifurcation approach by using software package called AUTO 07p in order to obtain the voltage response, and the second approach is a numerical integration using the Matlab built in function ode15s for obtaining time responses of the system. Overall MMS and ROM provide similar results, especially in the lower amplitudes. These methods seem to differ at higher amplitudes. The ROM shows a second unstable branch that MMS does not have. The time responses agree with the ROM voltage response. Furthermore, the influences of different parameters such as that of the detuning parameter, and damping are investigated.

Circular Plates Under Hard Excitations to Include Casimir Effect: Amplitude-Voltage Response of Superharmonic Resonance of Second Order

2020 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Jonathan Perez
Keyword(s):  
Circular Plate ◽  
Casimir Effect ◽  
Second Order ◽  
Peak Amplitude ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Circular Plates ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated

Abstract This paper deals with voltage-amplitude response of superharmonic resonance of second order of electrostatically actuated clamped MEMS circular plates. A flexible MEMS circular plate, parallel to a ground plate, and under AC voltage, constitute the structure under consideration. Hard excitations due to voltage large enough and AC frequency near one fourth of the natural frequency of the MEMS plate resonator lead the MEMS plate into superharmonic resonance of second order. These excitations produce resonance away from the primary resonance zone. No DC component is included in the voltage applied. The equation of motion of the MEMS plate is solved using two modes of vibration reduced order model (ROM), that is then solved through a continuation and bifurcation analysis using the software package AUTO 07P. This predicts the voltage-amplitude response of the electrostatically actuated MEMS plate. Also, a numerical integration of the system of differential equations using Matlab is used to produce time responses of the system. A typical MEMS silicon circular plate resonator is used to conduct numerical simulations. For this resonator the quantum dynamics effects such as Casimir effect are considered. Also, the Method of Multiple Scales (MMS) is used in this work. All methods show agreement for dimensionless voltage values less than 6. The amplitude increases with the increase of voltage, except around the dimensionless voltage value of 4, where the resonance shows two saddle-node bifurcations and a peak amplitude significantly larger than the amplitudes before and after the dimensionless voltage of 4. A light softening effect is present. The pull-in dimensionless voltage is found to be around 16. The effects of damping and frequency on the voltage response are reported. As the damping increases, the peak amplitude decreases. while the pull-in voltage is not affected. As the frequency increases, the peak amplitude is shifted to lower values and lower voltage values. However, the pull-in voltage and the behavior for large voltage values are not affected.

Voltage Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators: Comparison Between Boundary Value Problem Model and Reduced Order Model

2018 ◽  
Author(s):  
Julio Beatriz ◽  
Martin Botello ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value ◽  
Mode Shapes ◽  
Voltage Response ◽  
Order Model ◽  
Partial Differential ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

This paper deals with the voltage response of electrostatically actuated NEMS resonators at superharmonic resonance. In this work a comparison between Boundary Value Problem (BVP) model, and Reduced Order Model (ROM) is conducted for this type of resonance. BVP model is developed from the partial differential equation by replacing the time derivatives with finite differences. So, the partial differential equation is replaced by a sequence of boundary value problems, one for each step in time. Matlab’s function bvp4c is used to numerically integrate the BVPs. ROMs are based on Galerkin procedure and use the mode shapes of the resonator as a basis of functions. Therefore, the partial differential equation is replaced by a system of differential equations in time. The number of the equations in the system is equal to the number of mode shapes (or modes of vibration) used in the ROM. One mode of vibration ROM is solved using the method of multiple scales. Two modes of vibration ROM is numerically integrated using Matlab’s function ode15s in order to obtain time responses, and a continuation and bifurcation analysis is conducted using AUTO 07P. The effects of different nonlinearities in the system on the voltage response are reported. This work shows that BVP model is a valid method to predict the voltage response of a micro/nano cantilevers.

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.

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.

Reduced Order Model of Parametric Resonance of Electrostatically Actuated CNT Cantilever Resonators

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model (ROM) method. Forces acting on the CNT cantilever are electrostatic, van der Waals, and damping. 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 undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), and ROM are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of parametric resonance.

Reduced Order Model of CNT Cantilever Resonators Under AC Voltage Near Half Natural Frequency

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Damping Force ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model method. The system consists of a CNT parallel to a ground plate. An alternating current (AC) voltage is considered between the two. The CNT undergoes an oscillatory motion due to the electrostatic force generated by the voltage. Another two forces act on the CNT, namely a damping force, and a van der Waals force due to gaps less than 50 nm. The Method of Multiple Scales (MMS) and the Reduced Order Model (ROM) method (using AUTO solver) are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency response is found in the case of AC near half natural frequency.

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