scholarly journals Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin A. Botello ◽  
Christian A. Reyes ◽  
Julio S. Beatriz
Keyword(s):  
Numerical Integration ◽  
Multiple Scales ◽  
Low Voltage ◽  
Second Order ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Bifurcation Points ◽  
Electrostatically Actuated ◽  
Modes Of Vibration

This paper investigates the voltage–amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage–amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.

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.

Bio-MEMS Circular Plate Sensors Under Electrostatic Hard Excitations: Frequency Response of Superharmonic Resonance of Fourth Order

2020 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Circular Plate ◽  
Fourth Order ◽  
Multiple Scales ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Elastic Circular Plate ◽  
Modes Of Vibration ◽  
The Difference

Abstract This paper investigates the frequency-amplitude response of electrostatically actuated Bio-MEMS clamped circular plates under superharmonic resonance of fourth order. The system consists of an elastic circular plate parallel to a ground plate. An AC voltage between the two plates will lead to vibrations of the elastic plate. Method of Multiple Scales, and Reduced Order Model with two modes of vibration are the two methods used in this work. The two methods show similar amplitude-frequency response, with an agreement in the low amplitudes. The difference between the two methods can be seen for larger amplitudes. The effects of voltage and damping on the amplitude-frequency response are reported. The steady-state amplitudes in the resonant zone increase with the increase of voltage and with the decrease of damping.

Frequency Response for MEMS Circular Plate Resonators Under Superharmonic Resonance of the Second Order

2018 ◽  
Author(s):  
Martin Botello ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Circular Plate ◽  
Software Package ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Micro Electro Mechanical System ◽  
Second Order ◽  
Mode Shapes ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Mems Resonator

A nonlinear dynamics investigation is conducted on the frequency-amplitude response of electrostatically actuated micro-electro-mechanical system (MEMS) clamped plate resonators. The Alternating Current (AC) voltage is operating in the realm of superharmonic resonance of second order. This is given by an AC frequency near one-fourth of the natural frequency of the resonator. The magnitude of the AC voltage is large enough to be considered as hard excitation. The external forces acting on the MEMS resonator are viscous air damping and electrostatic force. Two proven mathematical models are utilized to obtain a predicted frequency-amplitude response for the MEMS resonator. Method of Multiple Scales (MMS) allows the transformation of a partial differential equation of motion into zero-order and first-order problems. Hence, MMS can be directly applied to obtain the frequency-amplitude response. Reduced Order Model (ROM), based on the Galerkin procedure, uses mode shapes of vibration for undamped circular plate resonator as a basis of functions. ROM is numerically integrated using MATLAB software package to obtain time responses. Also, ROM is used to conduct a continuation and bifurcation analysis utilizing AUTO 07P software package in order to obtain the frequency-amplitude response. The time responses show the movement of the center of the MEMS circular plate as a function of time. The frequency-amplitude response allows one to observe bifurcation and pull-in instabilities within the nonlinear system over a range of frequencies. The influences of parameters (i.e. damping and voltage) are also included in this investigation.

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.

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.

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).

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 Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Micro Electro Mechanical System ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated ◽  
Sensing Applications

This paper investigates the voltage–amplitude response of soft alternating current (AC) electrostatically actuated micro-electro-mechanical system (MEMS) clamped circular plates for sensing applications. The case of soft AC voltage of frequency near half natural frequency of the plate is considered. Soft AC produces small to very small amplitudes away from resonance zones. Nearness to half natural frequency results in primary resonance of the system, which is investigated using the method of multiple scales (MMS) and numerical simulations using reduced order model (ROM) of seven terms (modes of vibration). The system is assumed to be weakly nonlinear. Pull-in instability of the voltage–amplitude response and the effects of detuning frequency and damping on the response are reported.

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

2020 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Benjamin Huerta
Keyword(s):  
Frequency Response ◽  
Circular Plate ◽  
Quantum Dynamics ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Primary Resonance ◽  
Second Order ◽  
Amplitude Response ◽  
Superharmonic Resonance

Abstract This work deals with the frequency-amplitude response of the superharmonic resonance of second order of electrostatically actuated clamped NEMS circular plate resonators. The NEMS system consists of a circular plate parallel to a ground plate. Hard excitations (large AC voltage) due to the electrostatic force of frequency near one fourth of the natural frequency of the plate resonator leads the plate into a superharmonic resonance of second order. Hard excitations are excitations significant enough to produce resonance although far from the primary resonance zone. There is no DC component in the voltage applied. For the partial differential equation of motion two reduced order models are developed. The first one uses one mode of vibration and it is solved using the Method of Multiple Scales (MMS), and the frequency-amplitude response is predicted. Hard excitations were modeled by keeping the first term of the Taylor polynomial of the electrostatic force as a large term. The second model uses two modes of vibration, and it is solved using numerical integration. This produces time responses of the resonator. In this work, the quantum dynamics effect such as Casimir effect is considered significant. The two branches, one unstable and one stable, with a saddle node bifurcation point are predicted. Both methods are in agreement for amplitudes up to 0.7 of the gap. The effect of damping and voltage on the frequency response are reported.

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