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.

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.

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.

Voltage Response of Parametric Resonance of MEMS Circular Plates Under Hard Excitations

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

Abstract This work deals with the voltage response of parametric resonance of electrostatically actuated microelectromechanical (MEMS) circular plates under hard excitations. Method of Multiple Scales (MMS) and Reduced Order Model (ROM) method using two modes of vibration are used to predict the voltage-amplitude response of the MEMS circular plates. ROM is solved using AUTO 07p, a software package for continuation and bifurcation. MMS used in this paper has one term in the electrostatic force being considered significant. This is the way MMS is used to model hard excitations. MMS shows results similar to those of ROM at lower amplitudes and lower voltages. The differences between the two methods, MMS and ROM, are significant in high amplitudes for all voltages, and the differences are significant in all amplitudes for larger voltages. Significant differences can be noted in the effect of different parameters such as the detuning frequency and damping on the voltage response. ROM AUTO 07p is calibrated using ROM time responses in which the ROM is solved using the solver ode15s in Matlab.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for uniform microresonators with mass deposition and without are reported.

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.

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.

Reduced Order Model for MEMS Cantilever Resonators Under Soft AC Voltage Near Natural Frequency

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator is investigated. The AC voltage is of frequency near resonator’s natural frequency. A first order fringe correction of the electrostatic force and viscous damping are included in the model. The dynamics of the resonator is investigated using the Reduced Order Model (ROM) method, based on Galerkin procedure. Steady-state motions are found. Numerical results for the uniform microresonator are compared with those obtained via the Method of Multiple Scales (MMS).

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.

Nonlinear Parametric Resonance for NEMS and MEMS Biosensor Applications

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Parametric Resonance ◽  
Nonlinear Behavior ◽  
Electrostatic Actuation ◽  
Mass Detection ◽  
Actuation Frequency ◽  
Electrostatically Actuated ◽  
Biosensor Applications

This paper deals with electrostatically actuated resonator micro- and nano-sensor for mass detection for applications in medicine and biology. Nonlinear parametric resonance of the sensor when the electrostatic actuation frequency is near natural frequency of the system is investigated. Mass deposition is included and its effect on the nonlinear behavior of the resonator is predicted.

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.

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