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

2021 ◽  
Author(s):  
Dumitru Caruntu ◽  
Julio Beatriz ◽  
Jonathan Perez
Keyword(s):  
Casimir Effect ◽  
Second Order ◽  
Voltage Response ◽  
Circular Plates ◽  
Superharmonic Resonance

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 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.

Casimir Effect on Voltage Response of Superharmonic Resonance of NEMS Resonators

2017 ◽  
Author(s):  
Martin Botello ◽  
Christian Reyes ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Equation Of Motion ◽  
Second Order ◽  
Mode Shapes ◽  
Voltage Response ◽  
Casimir Forces ◽  
Superharmonic Resonance ◽  
Reference Length

This paper investigates the voltage response of superharmonic resonance of the second order of electrostatically actuated nano-electro-mechanical system (NEMS) resonator sensor. The structure of the NEMS device is a resonator cantilever over a ground plate under Alternating Current (AC) voltage. Superharmonic resonance of second order occurs when the AC voltage is operating in a frequency near-quarter the natural frequency of the resonator. The forces acting on the system are electrostatic, damping and Casimir. To induce a bifurcation phenomenon in superharmonic resonance, the AC voltage is in the category of hard excitation. The gap distance between the cantilever resonator and base plate is in the range of 20 nm to 1 μm for Casimir forces to be present. The differential equation of motion is converted to dimensionless by choosing the gap as reference length for deflections, the length of the resonator for the axial coordinate, and reference time based on the characteristics of the structure. The Method of Multiple Scales (MMS) and Reduced Order Model (ROM) are used to model the characteristic of the system. MMS transforms the nonlinear partial differential equation of motion into two simpler problems, namely zero-order and first-order. ROM, based on the Galerkin procedure, uses the undamped linear mode shapes of the undamped cantilever beam as the basis functions. The influences of parameters (i.e. Casimir, damping, fringe, and detuning parameter) were also investigated.

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.

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).

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.

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.

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.

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