Parametric Resonance of MEMS Circular Plate Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Circular Plate ◽  
Parametric Resonance ◽  
Elastic Plate ◽  
Electrostatic Force ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate

This paper investigates parametric resonance of electrostatically actuated MEMS circular plates for resonator sensing applications. The system consists of a clamped circular elastic plate over a ground plate. Soft AC voltage of frequency near natural frequency of the plate gives the electrostatic force that leads the elastic plate into vibration, more specifically into parametric resonance which can be used afterwards for biosensing purposes. Frequency response and corresponding bifurcations are reported. The effects of damping and voltage are predicted.

Casimir and Van Der Waals Effects on Parametric Resonance of Bio-NEMS Circular Plate Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Frequency Response ◽  
Parametric Resonance ◽  
Elastic Plate ◽  
Electrostatic Force ◽  
Van Der Waals ◽  
Circular Plates ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Fixed Electrode ◽  
Electrode Plate

This paper deals with Casimir and van der Waals effects on the frequency response of parametric resonance of electrostatically actuated NEMS circular plates for bio-sensing applications. The bio-NEMS resonator consists of a clamped circular elastic plate over a fixed electrode plate. A soft AC voltage of frequency near natural frequency between the plates gives an electrostatic force that leads the elastic plate into vibration which leads to parametric resonance that can be used afterwards for biosensing purposes. Frequency response and the effects of Casimir, and van der Waals forces on the response are reported.

Casimir and Van der Waals Effects on Voltage Response of Electrostatically Actuated MEMS/NEMS Plates

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides ◽  
Valeria Garcia
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Electrostatic Force ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Voltage Response ◽  
Voltage Amplitude ◽  
Amplitude Response ◽  
Electrostatically Actuated ◽  
Ground Plate

This paper deals with electrostatically actuated MEMS plates. The model consists of a flexible MEMS plate above a parallel ground plate. An AC voltage of frequency near natural frequency of the plate provides the electrostatic force that actuates the flexible MEMS plate. This leads to parametric resonance. The effect of Casimir and/or van der Waals forces on the voltage-amplitude response of the plate is investigated.

ROM of Voltage Response of Parametric Resonance of Electrostatically Actuated MEMS Plates

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides ◽  
Valeria Garcia
Keyword(s):  
Natural Frequency ◽  
Circular Plate ◽  
Parametric Resonance ◽  
Electrostatic Force ◽  
Alternate Current ◽  
Voltage Response ◽  
Flexible Plate ◽  
Restoring Force ◽  
Electrostatically Actuated ◽  
Flexible Circular Plate

This paper deals with electrostatically actuated Micro-Electro-Mechanical Systems (MEMS) circular plates. The system consists of a flexible circular plate with the edge fixed above a parallel ground plate. The forces acting on the MEMS plate are the electrostatic, damping, and elastic restoring force. In this work Casimir and/or van der Waals forces are neglected, since they are significant for gaps less than one micron and/or 50 nanometers, respectively. The electrostatic force is given by a soft Alternate Current (AC) harmonic voltage between the two plates. The electrostatic force leads the flexible plate into vibration. The assumption of axisymmetrical vibrations is valid in this work. The AC frequency is near natural frequency of the flexible circular plate. Since the electrostatic force is proportional to the square of the voltage, this results in an electrostatic force of frequency twice the natural frequency. Therefore the system experiences a parametric resonance. The partial differential equation of motion is non-dimensionalized. Next the resulting lumped parameters are found from a typical MEMS circular plate resonator. Reduced Order Model (ROM) is the method of investigation used in this work, specifically two terms ROM. Numerical simulations are conducted to predict the voltage response of the system. The effects of frequency and damping on the response are predicted as well. MEMS circular plate systems are excellent candidates for resonator sensors, i.e. sensors functioning at resonance. They are capable of detecting cells, viruses, as well as any microparticles provided the plates are coated for such recognition.

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.

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.

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.

Parametric Resonance of Electrostatically Actuated MEMS Cantilever Resonators Using Method of Multiple Scales and Homotopy Perturbation Method

2017 ◽  
Author(s):  
Christopher Reyes ◽  
Dumitru I. Caruntu
Keyword(s):  
Perturbation Method ◽  
Parametric Resonance ◽  
Homotopy Perturbation Method ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Plate Electrode ◽  
Electrostatically Actuated ◽  
Homotopy Perturbation ◽  
Ground Plate

This paper investigates the dynamics governing the behavior of electrostatically actuated MEMS cantilever resonators. The cantilever is held parallel to a ground plate (electrode) with an AC voltage between the plate and the electrode causing the electrostatic actuation (excitation). For the purposes of this paper this is soft excitation. The frequency of the excitation is near the natural frequency of the cantilever leading to what is known as parametric resonance. The electrostatic force in the problem investigated throughout the paper is nonlinear in nature and includes the fringe effect. Two methods are used in investigating this problem: the method of multiple scales (MMS) and the homotopy perturbation method (HPM). The two methods work well for small non-linearities and small amplitudes. The influence of voltage, fringe, damping, Casimir, and Van der Waals parameters will be investigated in this paper using MMS and HPM as a means of verifying the results obtained.

Reduced Order Model on DC Bias Effect on the Frequency Response of Electrostatically Actuated Biosensor Microplates

2016 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Alternate Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Bias Effect ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Dc Bias

This paper investigates the frequency response of microplates under electrostatic actuation. The microplate is parallel to a fixed ground plate. The electrostatic force that actuates the system is given by both Alternate Current (AC) and Direct Current (DC) voltages. The AC frequency is set to be near half natural frequency of the structure. Damping influence is also investigated in this paper. The method of investigation is Reduced Order Model. The effects of various parameters on the response of the structure are reported.

Reduced Order Model of CNT Cantilever Resonators Under AC Voltage Near Half Natural Frequency

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Damping Force ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model method. The system consists of a CNT parallel to a ground plate. An alternating current (AC) voltage is considered between the two. The CNT undergoes an oscillatory motion due to the electrostatic force generated by the voltage. Another two forces act on the CNT, namely a damping force, and a van der Waals force due to gaps less than 50 nm. The Method of Multiple Scales (MMS) and the Reduced Order Model (ROM) method (using AUTO solver) are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency response is found in the case of AC near half natural frequency.

Influence of van der Waals Forces on Electrostatically Actuated MEMS/NEMS Circular Plates

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Iris Alvarado
Keyword(s):  
Circular Plate ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Circular Plates ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated ◽  
Ground Plate ◽  
Scale Surface ◽  
Two Bodies

This paper deals with electrostatically actuated micro and nano-electromechanical (MEMS/NEMS) circular plates. The system under investigation consists of two bodies, a deformable and conductive circular plate placed above a fixed, rigid and conductive ground plate. The deformable circular plate is electrostatically actuated by applying an AC voltage between the two plates. Nonlinear parametric resonance and pull-in occur at certain frequencies and relatively large AC voltage, respectively. Such phenomena are useful for applications such as sensors, actuators, switches, micro-pumps, micro-tweezers, chemical and mass sensing, and micro-mirrors. A mathematical model of clamped circular MEMS/NEMS electrostatically actuated plates has been developed. Since the model is in the micro- and nano-scale, surface forces, van der Waals and/or Casimir, acting on the plate are included. A perturbation method, the Method of Multiple Scales (MMS), is used for investigating the case of weakly nonlinear MEMS/NEMS circular plates. Two time scales, fast and slow, are considered in this work. The amplitude-frequency and phase-frequency response of the plate in the case of primary resonance are obtained and discussed.

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