CNT Cantilevers Under Soft AC Actuation of Frequency Near Half Natural Frequency for Bio-Sensing Applications

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Phase Behavior ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Frequency Phase

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers for bio-sensing applications. Four forces act on the CNT cantilever, namely electrostatic, elastostatic, van der Waals, and damping. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The method of multiple scales (MMS) is used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behavior are reported. The CNT bio-sensor is to be used for mass detection applications.

On Electrostatically Actuated CNT Bio-Sensors

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Cone S. Salinas Trevino
Keyword(s):  
Carbon Nanotubes ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Ground Plate ◽  
Frequency Phase

This paper deals with electrostatically actuated Carbon NanoTubes (CNT) cantilevers for bio-sensing applications. There are three kinds of forces acting on the CNT cantilever: electrostatic, elastostatic, and van der Waals. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT dynamics is nonlinear parametric. The method of multiple scales is used to investigate the system under soft excitations and/or weakly nonlinearities. The frequency-amplitude and frequency-phase behavior are found in the case of primary resonance. The CNT bio-sensor is to be used for mass detection applications.

Reduced Order Model of Electrostatically Actuated Carbon Nanotube Cantilever Biosensors for Primary Resonance

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Multiple Scales ◽  
Van Der Waals ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate

This paper investigates electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers biosensors using the Reduced Order Model (ROM) method. Forces acting on the CNT are electrostatic, damping, and van der Waals. The electrostatic actuation is given by soft AC voltage. Van der Waals forces are significant for gaps between the CNT and a ground plate lower than 100 nm. Both forces electrostatic and van der Waals are nonlinear. CNT undergoes nonlinear parametric dynamics. ROM is used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude response is found in the case of primary resonance and compared to the Method of Multiple Scales (MMS). The CNT biosensor is to be used for mass detection applications.

Reduced Order Model of Parametric Resonance of Electrostatically Actuated CNT Cantilever Resonators

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Parametric Resonance ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model (ROM) method. Forces acting on the CNT cantilever are electrostatic, van der Waals, and damping. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), and ROM are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of parametric resonance.

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

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Le Luo
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Van Der Waals ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Carbon Nano Tubes ◽  
Ground Plate ◽  
Phase Behaviors

This paper deals with electrostatically actuated Carbon Nano-Tubes (CNT) cantilevers using Reduced Order Model method. There are three kinds of forces acting on the CNT cantilever: electrostatic, elastostatic, and van der Waals. The van der Waals forces are significant for values of 50 nm or lower of the gap between the CNT and the ground plate. As both forceselectrostatic and van der Waals are nonlinear, and the CNT electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The Method of Multiple Scales (MMS), Reduced Order Model (ROM) and AUTO are used to investigate the system under soft excitations and/or weak nonlinearities. The frequency-amplitude and frequency-phase behaviors are found in the case of resonance near half natural frequency.

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.

Sensitivity of MEMS/NEMS Biosensors Near Twice Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Equation Of Motion ◽  
Direct Approach ◽  
Mass Detection ◽  
Electrostatically Actuated ◽  
Phase Amplitude

Bio-MEMS/NEMS resonator sensors near twice natural frequency for mass detection are investigated. Electrostatic force along with fringe correction and Casimir effect are included in the model. They introduce parametric nonlinear terms in the system. The partial-differential equation of motion of the system is solved by using the method of multiple scales. A direct approach of the problem is then used. Two approximation problems resulting from the direct approach are solved. Phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors 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.

Nonlinear Dynamics of Electrostatically Actuated Coupled MEMS Parallel Cantilever Resonators

2012 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Frequency Responses ◽  
Beam System ◽  
Ground Plate ◽  
Steady State Solutions

This paper deals with the nonlinear response of a coupled cantilever system composed of two micro beams electrostatically actuated. The AC frequency of actuation is near natural frequency of the cantilevers. The two cantilevers are identical. Lagrange equations are used to develop a mathematical model of the system. These equations of motion are nondimensionalized and subjected to the method of multiple scales in order to find steady state solutions. Alternating Current (AC) and Direct Current (DC) actuation voltages are applied between the first cantilever and ground plate with DC voltage applied between the first and second cantilevers. Amplitude-frequency and phase-frequency responses of the system are provided for typical micro beam system structures.

Casimir Effect Influence on NEMS Cantilever Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht ◽  
Roberto J. Zapata
Keyword(s):  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Direct Approach ◽  
Electrostatically Actuated ◽  
Sensing Applications ◽  
Approximation Problems ◽  
Phase Amplitude

This paper investigates electrostatically actuated nanoelectromechanical (NEMS), to include Casimir effect, resonator response near natural frequency. Both electrostatic force and Casimir force are nonlinear. The method of multiple scales is used in a direct approach of the problem in the case of small actuation, damping, and Casimir effect. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform NEMS cantilever resonators for possible sensing applications are provided.

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