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.

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.

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 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.

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).

Reduced Order Model of Frequency Response of Superharmonic Resonance of Electrostatically Actuated MEMS Resonators

2015 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christian Reyes
Keyword(s):  
Frequency Response ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Mems Resonators ◽  
Ground Plate

This paper deals with superharmonic resonance of electrostatically actuated MEMS resonator sensors. The system consists of a MEMS cantilever on top of a parallel ground plate. An AC voltage of frequency near one fourth the natural frequency of the resonator provides the electrostatic force of actuation. The frequency response of the superharmonic resonance of the structure is investigated using two term Reduced Order Model (ROM) method.

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.

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

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christopher Reyes
Keyword(s):  
Frequency Response ◽  
Cantilever Beam ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Beam Theory ◽  
Driving Frequency ◽  
Third Order ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Amplitude Frequency Response

Abstract This work deals with amplitude frequency response of MEMS cantilever resonators undergoing superharmonic resonance of third order. The cantilever resonator is parallel to a ground plate and under alternating current (AC) voltage that excites the cantilever into vibrations. The driving frequency of the AC voltage is near one sixth of the first natural frequency of the cantilever beam resulting into superharmonic resonance of third order. The cantilever beam is modeled using Euler-Bernoulli beam theory. The electrostatic force is modeled using Palmer’s formula to include the fringe effect. In order to investigate the amplitude frequency behavior of the system reduced order models (ROMs) are developed. Three methods are used to solve these ROMs they are 1) the method of multiple scales (MMS) for ROM with one mode of vibration, 2) homotopy analysis method (HAM) for ROM with one mode of vibration, and 3) direct numerical integration for 2 modes of vibration Reduced Order Model (2T ROM) producing time responses of the tip of the cantilever resonator. In this work the limitations of MMS and HAM are highlighted when considering large voltage values i.e hard excitations. For large voltage values MMS and HAM cannot accurately predict the amplitude frequency response; the results from 2T ROM time responses disagree significantly with the MMS and HAM solutions. The effect of voltage on the frequency response is investigated. As the voltage values in the system increase the responses shift to lower frequencies and larger amplitudes.

Casimir Effect on Frequency Response of Superharmonic Resonance of NEMS Resonators

2017 ◽  
Author(s):  
Martin Botello ◽  
Christian Reyes ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Frequency Response ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Nonlinear Partial Differential Equation ◽  
Equation Of Motion ◽  
Casimir Forces ◽  
Superharmonic Resonance ◽  
Reference Length

This paper investigates the frequency response of superharmonic resonance of the second order of electrostatically actuated nano-electro-mechanical system (NEMS) resonator sensor. The structure of the MEMS device is a resonator cantilever over a ground plate under Alternating Current (AC) voltage. Superharmonic resonance insinuates that the AC voltage is operating in a frequency near one-fourth the natural frequency of the resonator. The forces acting on the system are electrostatic, damping and Casimir force. For the electrostatic force, the AC voltage is in the category of hard excitation in order to induce a bifurcation phenomenon. For Casimir forces to affect the system, the gap distance between the cantilever resonator and base plate is in the range of 20 nm to 1 μm. 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) is 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. The influences of parameters (i.e. Casimir, damping, second voltage and fringe) were also 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.

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