Response Near Twice the Natural Frequency of Electrostatically Actuated Microresonators

Electrostatic Force ◽

Equation Of Motion ◽

Direct Approach ◽

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.

Near Three Half Natural Frequency Resonance of Electrostatically Actuated MEMS Resonators

Volume 8: Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2010-38004 ◽

2010 ◽

Author(s):

Dumitru I. Caruntu ◽

Martin W. Knecht

Keyword(s):

Natural Frequency ◽

Casimir Force ◽

Multiple Scales ◽

Electrostatic Force ◽

Direct Approach ◽

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.

Sensitivity of MEMS/NEMS Biosensors Near Twice Natural Frequency

Volume 8: Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2010-38007 ◽

2010 ◽

Author(s):

Dumitru I. Caruntu ◽

Martin W. Knecht

Keyword(s):

Natural Frequency ◽

Multiple Scales ◽

Casimir Effect ◽

Electrostatic Force ◽

Equation Of Motion ◽

Direct Approach ◽

Mass Detection ◽

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.

Volume 6: ASME Power Transmission and Gearing Conference; 3rd International Conference on Micro- and Nanosystems; 11th International Conference on Advanced Vehicle and Tire Technologies ◽

On Nonlinear Response of Capacitive Sensors

10.1115/detc2009-86144 ◽

2009 ◽

Cited By ~ 1

Author(s):

Dumitru I. Caruntu ◽

Martin Knecht

Keyword(s):

Nonlinear Response ◽

Casimir Force ◽

Multiple Scales ◽

Casimir Effect ◽

Electrostatic Force ◽

Direct Approach ◽

Micro Sensor ◽

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.

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

Casimir Effect Influence on NEMS Cantilever Resonators

10.1115/dscc2011-5966 ◽

2011 ◽

Author(s):

Dumitru I. Caruntu ◽

Martin Knecht ◽

Roberto J. Zapata

Keyword(s):

Casimir Force ◽

Multiple Scales ◽

Casimir Effect ◽

Electrostatic Force ◽

Direct Approach ◽

Sensing Applications ◽

Approximation Problems ◽

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.

Volume 4: 12th International Conference on Advanced Vehicle and Tire Technologies; 4th International Conference on Micro- and Nanosystems ◽

On MEMS/NEMS Biosensor Sensitivity Near Half Natural Frequency

10.1115/detc2010-28612 ◽

2010 ◽

Author(s):

Dumitru I. Caruntu ◽

Martin Knecht

Keyword(s):

Natural Frequency ◽

Multiple Scales ◽

Casimir Effect ◽

Electrostatic Force ◽

Direct Approach ◽

Mass Detection ◽

Additional Mass ◽

Virus Size ◽

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.

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

Volume 4: Dynamics, Control and Uncertainty, Parts A and B ◽

10.1115/imece2012-85963 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Israel Martinez

Keyword(s):

Natural Frequency ◽

Nonlinear Response ◽

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).

Electrostatically Actuated MEMS Cantilevers of Linear Thickness Variation

Volume 4A: Dynamics, Vibration and Control ◽

10.1115/imece2013-64067 ◽

2013 ◽

Author(s):

Dumitru I. Caruntu ◽

Mostafa M. Fath El-Den

Keyword(s):

Multiple Scales ◽

Electrostatic Force ◽

Constant Width ◽

Thickness Variation ◽

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.

Response of Electrostatically Actuated Sensors Near Half of the Natural Frequency

Volume 10: Mechanical Systems and Control, Parts A and B ◽

10.1115/imece2009-10663 ◽

2009 ◽

Author(s):

Dumitru I. Caruntu ◽

Martin W. Knecht

Keyword(s):

Natural Frequency ◽

Governing Equation ◽

Multiple Scales ◽

Equation Of Motion ◽

Casimir Forces ◽

Order Model ◽

Reduced Order ◽

Micro Sensor ◽

A cantilever micro-resonator electrostatically actuated near half of the natural frequency is investigated. Hamilton’s principle is used to derive the partial-differential equation of motion for a general non-uniform sensor. Nonlinearities arise due to the electrostatic and Casimir forces. The electrostatic actuation introduces parametric coefficients in both linear and nonlinear parts of the governing equation. A direct approach is taken using the method of multiple scales resulting in a phase-amplitude relationship for the system. Numerical results for a uniform capacitive resonator micro-sensor are provided and tested numerically using a reduced-order model of the governing equation of motion.

ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY ACTUATED MICRORESONATORS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455411004282 ◽

2011 ◽

Vol 11 (04) ◽

pp. 641-672 ◽

Cited By ~ 20

Author(s):

DUMITRU I. CARUNTU ◽

MARTIN KNECHT

Keyword(s):

Natural Frequency ◽

Nonlinear Response ◽

Multiple Scales ◽

Casimir Effect ◽

Electrostatic Force ◽

Order Model ◽

Reduced Order ◽

First Order ◽

Fringe Effect

This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A first-order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The influences of damping, actuation, and fringe effect on the resonator response are found.

Volume 3: Vibration in Mechanical Systems; Modeling and Validation; Dynamic Systems and Control Education; Vibrations and Control of Systems; Modeling and Estimation for Vehicle Safety and Integrity; Modeling and Control of IC Engines and Aftertreatment Systems; Unmanned Aerial Vehicles (UAVs) and Their Applications; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Control of Smart Buildings and Microgrids; Energy Systems ◽

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

10.1115/dscc2017-5124 ◽

2017 ◽

Author(s):

Christopher Reyes ◽

Dumitru I. Caruntu

Keyword(s):

Perturbation Method ◽

Parametric Resonance ◽

Homotopy Perturbation Method ◽

Multiple Scales ◽

Electrostatic Force ◽

Plate Electrode ◽

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.