Frequency-Amplitude Response of Subharmonic Resonance of One-Third Order of Electrostatically Actuated MEMS Circular Plates

2020 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Miguel Martinez
Keyword(s):  
Steady State ◽  
Circular Plate ◽  
Bifurcation Point ◽  
Multiple Scales ◽  
Subharmonic Resonance ◽  
Third Order ◽  
Amplitude Response ◽  
Saddle Node Bifurcation ◽  
Electrostatically Actuated ◽  
Saddle Node

Abstract This work deals with the subharmonic resonance of one-third order of electrostatically actuated clamped MEMS circular plate resonators. The system consists of flexible MEMS circular plate parallel to a ground plate actuated only by AC voltage. Hard excitations due to large enough AC voltage of frequency near three-halves of the natural frequency of the MEMS plate resonator lead it into a subharmonic resonance. The partial differential equation describing the motion of the resonator is nondimensionalized and two reduced order models are developed. The first one consists of a one mode of vibration model which is solved using the Method of Multiple Scales (MMS). The frequency-amplitude response (bifurcation diagram) is predicted. Hard excitations were modeled by keeping the first term of the Taylor polynomial of the electrostatic force as a large term and the rest of them as small terms. The second model uses two modes of vibration, and it is solved through numerical integration. This produces time responses of the resonator. Both methods show a zero-amplitude steady-state stable branch for the entire range of resonant frequencies. Also, two branches, one unstable and one stable, with a saddle node bifurcation point are predicted for non-zero steady state amplitudes. One can notice that non-zero steady state amplitudes can be reached only from large enough initial amplitudes. 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. As the damping increases, the saddle-node bifurcation point and consequently the non-zero steady-state branches are shifted to larger amplitudes. As the voltage increases, the saddle-node bifurcation point and the non-zero branches are shifted to lower amplitudes and lower frequency.

Subharmonic Resonance of Two Thirds Order of Electrostatically Actuated Bio-MEMS Circular Plates: Amplitude-Frequency Response

2021 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Marcos Alipi
Keyword(s):  
Steady State ◽  
Bifurcation Point ◽  
Multiple Scales ◽  
Subharmonic Resonance ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Flexible Circular Plate ◽  
Steady State Solutions ◽  
Steady State Amplitude ◽  
Lower Frequencies

Abstract This paper deals with subharmonic resonance of two thirds order or electrostatically activated BioMEMS circular plates. Specifically, this paper investigates the frequency amplitude response of this resonance. The system consists of a clamped flexible circular plate above a parallel electrode situated at a distance, and under an AC voltage of frequency near three fourths of the natural frequency of the plate. The method of multiple scales is used to model the hard excitations in the system, hard excitations that are necessary to produce this secondary resonance. This work predicts the response, as well as the effects of parameters such as voltage and damping on the response. This paper predicts that the subharmonic resonance of two thirds order consists of a near zero steady state amplitude, and higher values steady state amplitudes consisting of a stable branch and an unstable branch, and a saddle-node bifurcation point. The predictions regarding the effects of voltage and damping on the response of the BioMEMS plate shows that as the voltage increases, the bifurcation point is shifted to lower frequencies and lower amplitudes, while as the damping increases the bifurcation point is shifted to lower frequencies and high amplitudes. Therefore, the increase of damping leads to a case in which it is harder to reach higher amplitude steady-state solutions since it requires large initial amplitudes of the plate.

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.

Subharmonic Resonance of One Fourth Order of Electrostatically Actuated MEMS Circular Plates: Amplitude-Frequency Response

2021 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Julio Beatriz ◽  
Miguel Martinez
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Fourth Order ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Subharmonic Resonance ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Steady State Solutions

Abstract This work deals with the amplitude-frequency response subharmonic resonance of 1/4 order of electrostatically actuated circular plates. The method of multiple scales is used to model the hard excitations and to predict the response. This work predicts that the steady state solutions are zero amplitude solutions, and non-zero amplitude solutions which consist of stable and unstable branches. The effects of parameters such as voltage and damping on the response are predicted. As the voltage increases, the non-zero amplitude solutions are shifted to lower frequencies. As the damping increases, the non-zero steady-state amplitudes are shifted to higher amplitudes, so larger initial amplitudes for the MEMS plate to reach non-zero steady-state amplitudes.

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.

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.

Comparison of Frequency Response of Primary Resonance of DWCNT and CNT Resonators Under Electrostatic Actuation

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Electrostatic Actuation ◽  
Amplitude Response ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Abstract This paper deals with the frequency-amplitude response of primary resonance of electrostatically actuated Double-Walled Carbon Nanotubes (DWCNT) and Single-Walled Carbon Nanotubes (SWCNT) cantilever resonators. Their responses are compared. Both the DWCNT and SWCNT are modeled as Euler-Bernoulli cantilever beams. Electrostatic and damping forces are applied on both types of resonators. An AC voltage provides a soft electrostatic actuation. For the DWCNT, intertube van der Waals forces are present between the carbon nanotubes, coupling the deflections of the tubes and acting as a nonlinear spring between the two carbon nanotubes. Electrostatic (for SWCNT and DWCNT) and intertube van der Waals (for DWCNT) forces are nonlinear. Both resonators undergo nonlinear parametric excitation. The Method of Multiple Scales (MMS) is used to investigate the systems under soft excitations and weak nonlinearities. A 2-Term Reduced-Order-Model (ROM) is numerically solved for stability analysis using AUTO-07P, a continuation and bifurcation software. The coaxial vibrations of DWCNT are considered in this work, in order to draw comparisons between DWCNT and SWCNT. Effects of damping and voltage of the frequency-amplitude response are reported.

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.

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

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.

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