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.

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.

Frequency Response of Parametric Resonance of Electrostatically Actuated Circular Plates Under Hard Excitations

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

Abstract In this paper, the Method of Multiple Scales, and the Reduced Order Model method of two modes of vibration are used to investigate the amplitude-frequency response of parametric resonance of electrostatically actuated circular plates under hard excitations. Results show that the Method of Multiple Scales is accurate for low voltages. However, it starts to separate from the Reduced Order Model results as the voltage values are larger. The Method of Multiple Scales is good for low amplitudes and weak non-linearities. Furthermore the Reduced Order Model running with AUTO 07p is validated and calibrated using the 2 Term ROM time responses.

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.

Reduced Order Model of Electrostatically Actuated MEMS Resonators Resonance Near Half Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Mems Resonators

This paper uses the Reduced Order Model (ROM) method to investigate the influence of nonlinearities from parametric electrostatic excitation due to soft AC voltage of frequency near half natural frequency of the MEMS cantilever resonator on its frequency response. Most of the analysis in literature investigates pull-in phenomenon, stability, amplitude–frequency relations, or finds time responses of such systems. In this work it is showed that the bifurcation points in the amplitude-frequency response occur at lower frequencies and amplitudes than predicted by the Method of Multiple Scales (MMS), a perturbation method. This result is extremely important for predicting pull-in phenomena. Also the ROM predicts pull-in instability for large initial amplitudes and AC frequencies less than half natural frequency of the resonator. MMS fails to predict this behavior. Increasing the damping and/or decreasing the voltage increases the frequency at which the system undergoes into a pull-in phenomenon.

Amplitude-Frequency Response for Superharmonic Resonance of Fourth Order of Electrostatically Actuated MEMS Cantilever Resonators

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christopher Reyes
Keyword(s):  
Frequency Response ◽  
Fourth Order ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Damping Force ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Homotopy Analysis ◽  
Ground Plate

Abstract This paper deals with the frequency response of superharmonic resonance of order four of electrostatically actuated MicroElectroMechanical Systems (MEMS) cantilever resonators. The MEMS structure in this work consists of a microcantilever parallel to an electrode ground plate. The MEMS resonator is elelctrostatically actuated through an AC voltage between the cantilever and the ground plate. The voltage is in the category of hard excitation. The AC frequency is near one eight 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 fourth 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 Homotopy Analysis Method (HAM), and third, the Reduced Order Model (ROM) method using two modes of vibration are also utilized to investigate the resonance. ROM is solved through numerical integration using Matlab in order to simulate time responses of the structure. All methods are in agreement for moderate nonlinearities and small to moderate amplitudes. This work shows that adequate MMS and HAM provide good predictions of the resonance.

On Nonlinear Dynamics of Nanotweezers

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Bin Liu
Keyword(s):  
Nonlinear Dynamics ◽  
Frequency Response ◽  
Parametric Resonance ◽  
Taylor Series ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
The Other ◽  
Amplitude Frequency Response

This paper deals with amplitude-frequency response of electrostatic nanotube nanotweezer device system. Soft alternating current (AC) of frequency near natural frequency actuates the nanotubes. This leads the system into parametric resonance. The Method of Multiple Scales (MMS) in which the nonlinear electrostatic and van der Waals forces are expanded in Taylor series is used to compare two expansions, one up to third power and the other up to fifth power. The frequency response of the system is reported and the effects of van der Waals forces, electrostatic forces, and damping forces on the frequency response are investigated.

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.

Electrostatically Actuated MEMS Cantilevers of Linear Thickness Variation

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Mostafa M. Fath El-Den
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Constant Width ◽  
Thickness Variation ◽  
Electrostatically Actuated ◽  
Phase Amplitude ◽  
Mems Cantilevers ◽  
Relationship Of ◽  
Steady State Solutions

This paper deals with nonuniform linear thickness variation and constant width MEMS cantilever resonators electrostatically actuated through AC voltage near half natural frequency. The frequency response of the structure is investigated. Nonlinearities in the system arise from the electrostatic force. The electrostatic actuation introduces parametric coefficients in both linear and nonlinear parts of the governing equation. The method of multiple scales (MMS) is used to obtain the phase-amplitude relationship of the system, and the steady-state solutions. Parameters’ influences are reported.

Frequency Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation for Noncoaxial Vibration

2017 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ezequiel Juarez
Keyword(s):  
Carbon Nanotube ◽  
Frequency Response ◽  
Multiple Scales ◽  
Van Der Waals ◽  
First Order ◽  
Electrostatically Actuated ◽  
The Stability ◽  
Euler Bernoulli Beam ◽  
Steady State Solutions ◽  
High Length

In this paper, the Method of Multiple Scales is used to investigate the influences of dimensionless damping and voltage parameters on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube. The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping forces are assumed. Herein, the noncoaxial case is investigated at near-zero amplitude conditions in the free vibration, which eliminates the influence of the cubic van der Waals in the first-order solution. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order MMS solution. The importance of the results in this paper are the effect of damping and detuning frequency on the stability of the DWCNT vibration.

Boundary Value Problem Method to Investigate Superharmonic Resonance of MEMS Resonators

2017 ◽  
Author(s):  
Julio Beatriz ◽  
Martin Botello ◽  
Christian Reyes ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equation Of Motion ◽  
The Other ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Problem Method ◽  
Mems Resonators

This paper deals with two different methods to analyze the amplitude frequency response of an electrostatically actuated micro resonator. The methods used in this paper are the method of multiple scales, which is an analytical method with one mode of vibration. The other method is based on system of odes which is derived using the partial differential equation of motion, as well as the boundary conditions. This system is then solved using a built in matlab function known as BVP4C. Results are then shown comparing the two methods, under a variety of parameters, including the influence of damping, voltage, and fringe.

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