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.

On Nonlinear Response of Capacitive Sensors

2009 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht
Keyword(s):  
Nonlinear Response ◽  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Direct Approach ◽  
Electrostatically Actuated ◽  
Micro Sensor ◽  
Phase Amplitude

This paper investigates electrostatically actuated resonator micro-sensor response near natural frequency. The Casimir effect is included. Both the electrostatic force and the Casimir force introduce nonlinearities in the system. Hamilton’s principle is used to derive the partial-differential equation of motion for the general case of nonuniform sensors. The method of multiple scales is then used in a direct approach of the problem. Two approximation problems resulting from the direct approach are solved. The phase-amplitude relationship is obtained. Numerical results for uniform capacitive resonator micro-sensors are provided.

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.

Near Three Half Natural Frequency Resonance of Electrostatically Actuated MEMS Resonators

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

This paper investigates electrostatically actuated micro resonators response near three half natural frequency. Electrostatic force including fringe effect and Casimir force are included in the model. These forces 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 electrostatically actuated uniform micro resonator sensors are provided.

Response Near Twice the Natural Frequency of Electrostatically Actuated Microresonators

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

This paper deals with electrostatically actuated micro resonators response near twice natural frequency. Both the electrostatic force (including fringe effect) and the Casimir force 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. The phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors are provided.

On MEMS/NEMS Biosensor Sensitivity Near Half Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht
Keyword(s):  
Natural Frequency ◽  
Multiple Scales ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Direct Approach ◽  
Mass Detection ◽  
Additional Mass ◽  
Electrostatically Actuated ◽  
Virus Size ◽  
Phase Amplitude

This paper deals with sensitivity of electrostatically actuated Bio-MEMS/NEMS resonator sensors near half natural frequency for mass detection for applications in medicine and biology. 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. The phase-amplitude relationship is obtained. Numerical results for uniform electrostatically actuated micro resonator sensors are provided. An additional mass consisting of a film with a thickness of 100 nm (virus size), and a density of 0.43 of the density of the microsensor, has been added to the sensor. The additional mass shifted the amplitude-frequency curve of the sensor to lower frequencies.

Electrostatically Actuated MEMS Cantilevers of Linear Thickness Variation

2013 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Mostafa M. Fath El-Den
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Electrostatic Force ◽  
Constant Width ◽  
Thickness Variation ◽  
Electrostatically Actuated ◽  
Phase Amplitude ◽  
Mems Cantilevers ◽  
Relationship Of ◽  
Steady State Solutions

This paper deals with nonuniform linear thickness variation and constant width MEMS cantilever resonators electrostatically actuated through AC voltage near half natural frequency. The frequency response of the structure is investigated. Nonlinearities in the system arise from the electrostatic force. The electrostatic actuation introduces parametric coefficients in both linear and nonlinear parts of the governing equation. The method of multiple scales (MMS) is used to obtain the phase-amplitude relationship of the system, and the steady-state solutions. Parameters’ influences 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.

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.

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

2014 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Reynaldo Oyervides
Keyword(s):  
Casimir Force ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Voltage Response ◽  
Circular Plates ◽  
Amplitude Response ◽  
Weakly Nonlinear ◽  
Electrostatically Actuated

This paper investigates the voltage-amplitude response of soft AC electrostatically actuated M/NEMS clamped circular plates. AC frequency is near half natural frequency of the plate. This results in primary resonance. The system is analytically modeled using the Method of Multiple Scales (MMS). The system is assumed weakly nonlinear. The behavior of the system including pull-in instability as the AC voltage is swept up and down while the excitation frequency is constant is reported. The effects of detuning frequency, damping, Casimir force, and van der Waals force are reported as well.

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