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

2021 ◽  
Author(s):  
Dumitru Caruntu ◽  
Julio Beatriz
Keyword(s):  
Voltage Response ◽  
Circular Plates ◽  
Third Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated

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.

ROM of Superharmonic Resonance of Fourth Order of Electrostatically Actuated Clamped MEMS Circular Plates: Voltage Response

2020 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz
Keyword(s):  
Circular Plate ◽  
Fourth Order ◽  
Peak Amplitude ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Circular Plates ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Resonance Zone

Abstract This paper investigates the voltage-amplitude response of superharmonic resonance of fourth order of electrostatically actuated clamped MEMS circular plates. The system consists of flexible MEMS circular plate parallel to a ground plate. Hard excitations (voltage large enough) and AC voltage of frequency near one eight of the natural frequency of the MEMS plate resonator lead it into a superharmonic resonance. Hard excitations produce actuation forces large enough to produce resonance away from the primary resonance zone. There is no DC component in the voltage applied. The partial differential equation of motion describing the behavior of the system is solved using two modes of vibration reduced order model (ROM). This model is solved through a continuation and bifurcation analysis using the software package AUTO 07P which produces the voltage-amplitude response (bifurcation diagram of the system, and a numerical integration of the system of differential equations using Matlab that produces time responses of the system. Numerical simulations are conducted for a typical MEMS silicon circular plate resonator. For this resonator the quantum dynamics effects such as Casimir effect or Van der Waals effect are negligible. Both methods show agreement for the entire range of voltage values and amplitudes. The response consists of an increase of the amplitude with the increase of voltage, except around the value of 4 of the dimensionless voltage where the resonance shows two saddle-node bifurcations and a peak amplitude about ten times larger than the amplitudes before and after the dimensionless voltage of 4. The softening effect is present. The pull-in voltage is reached at large values of the dimensionless voltage, namely about 14. The effects of damping and frequency on the voltage response are reported. As the damping increases, the peak amplitude decreases for the resonance. However, the pull-in voltage is not affected. As the frequency increases, the resonance zone is shifted to lower voltage values and lower peak amplitudes. However, the pull-in voltage and the behavior for large voltage values are not affected.

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.

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Voltage Response ◽  
Circular Plates ◽  
Amplitude Response ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated

This paper investigates the voltage-amplitude response of soft AC electrostatically actuated M/NEMS clamped circular plates. AC frequency is near half natural frequency of the plate. This results in primary resonance. The system is analytically modeled using the Method of Multiple Scales (MMS). The system is assumed weakly nonlinear. The behavior of the system including pull-in instability as the AC voltage is swept up and down while the excitation frequency is constant is reported. The effects of detuning frequency, damping, Casimir force, and van der Waals force are reported as well.

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 Primary Resonance of Electrostatically Actuated MEMS/NEMS Plates

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Casimir Force ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Circular Plates ◽  
Order Model ◽  
Amplitude Response ◽  
Reduced Order ◽  
Electrostatically Actuated

This paper utilizes Reduced Order Model (ROM) method to investigate the voltage-amplitude response of electrostatically actuated M/NEMS clamped circular plates. Soft AC voltage at frequency near half natural frequency of the plate is used. This results in primary resonance of the system. The effects of nonlinearities of the system including pull-in instability on the voltage-amplitude response are investigated. Namely, the effects of detuning frequency, damping, Casimir force, and van der Waals force on the voltage response of clamped circular plates are reported. Casimir and van der Waals forces are found to have significant effects on the response of clamped circular plates and must be considered to accurately model and predict the behavior of the system.

Biosensing Mechanism Using Amplitude Voltage Response of Superharmonic Resonance of Fourth Order of Electrostatically Actuated MEMS Cantilever Resonators

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christopher Reyes
Keyword(s):  
Numerical Integration ◽  
Fourth Order ◽  
Bifurcation Point ◽  
Voltage Response ◽  
Excitation Voltage ◽  
Saddle Node Bifurcation ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Modes Of Vibration ◽  
Fringe Effect

Abstract This paper deals with the amplitude voltage response of electrostatically actuated MEMS cantilever resonators undergoing superharmonic resonance of fourth order. This can be used as sensing mechanism. The system consists of a MEMS cantilever beam held parallel to a ground plate with an applied voltage of alternating current (AC) causing the cantilever to vibrate. The driving frequency of the excitation voltage is near one eighth of the first natural frequency of the cantilever. This causes the cantilever to experience superharmonic resonance of order four. In order for this resonance to occur hard excitations are required wherein the magnitude of the excitation voltage must be large enough. This work models the electrostatic force to include fringe effect. The fringe effect is modeled using Palmer’s formula. Reduced order models (ROMs) are used in this work. The methods used to solve these models are 1) the method of multiple scales (MMS), 2) homotopy analysis method (HAM), and 3) numerical integration for ROM with 2 modes of vibration. The amplitude voltage response shows a softening. The response consists of three branches: two stable and one unstable. As the voltage is increased the system is stable until the first saddle-node bifurcation point is reached. Here the system experiences instability and it jumps to higher amplitude on the stable branch. As the voltage is swept down the system is stable until the second saddle-node bifurcation point in high amplitudes is reached and the system jumps down to lower amplitudes on the first stable branch. This is the biosensing mechanism proposed in this work. All three methods show excellent agreement with one another for detuning frequency values up to σ = −0.025. As the magnitude of the detuning frequency increases the MMS and HAM begin to disagree with the time responses obtained from the numerical integration of the ROM with 2 modes of vibration (or terms). This demonstrates the limitations of MMS and HAM to accurately predict the behavior for hard excitations where the voltage is very high.

Voltage Response of Parametric Resonance of MEMS Circular Plates Under Hard Excitations

2019 ◽  
Author(s):  
Julio S. Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Voltage Response ◽  
Circular Plates ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

Abstract This work deals with the voltage response of parametric resonance of electrostatically actuated microelectromechanical (MEMS) circular plates under hard excitations. Method of Multiple Scales (MMS) and Reduced Order Model (ROM) method using two modes of vibration are used to predict the voltage-amplitude response of the MEMS circular plates. ROM is solved using AUTO 07p, a software package for continuation and bifurcation. MMS used in this paper has one term in the electrostatic force being considered significant. This is the way MMS is used to model hard excitations. MMS shows results similar to those of ROM at lower amplitudes and lower voltages. The differences between the two methods, MMS and ROM, are significant in high amplitudes for all voltages, and the differences are significant in all amplitudes for larger voltages. Significant differences can be noted in the effect of different parameters such as the detuning frequency and damping on the voltage response. ROM AUTO 07p is calibrated using ROM time responses in which the ROM is solved using the solver ode15s in Matlab.

Sign in / Sign up

Export Citation Format

Share Document