Nonlinear Dynamics of Electrostatically Actuated Coupled MEMS Parallel Cantilever Resonators

Equations Of Motion ◽

Lagrange Equations ◽

Frequency Responses ◽

Beam System ◽

Ground Plate ◽

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.

Volume 7: Dynamic Systems and Control; Mechatronics and Intelligent Machines, Parts A and B ◽

Electrostatically Actuated Coupled MEMS Resonators

10.1115/imece2011-65462 ◽

2011 ◽

Author(s):

Dumitru I. Caruntu ◽

Kyle N. Taylor

Keyword(s):

Nonlinear Response ◽

Multiple Scales ◽

Equations Of Motion ◽

System Structure ◽

Lagrange Equations ◽

Beam System ◽

Mems Resonators ◽

The Mathematical Model ◽

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

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).

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.

Volume 7: 5th International Conference on Micro- and Nanosystems; 8th International Conference on Design and Design Education; 21st Reliability, Stress Analysis, and Failure Prevention Conference ◽

On Electrostatically Actuated CNT Bio-Sensors

10.1115/detc2011-48379 ◽

2011 ◽

Author(s):

Dumitru I. Caruntu ◽

Cone S. Salinas Trevino

Keyword(s):

Carbon Nanotubes ◽

Multiple Scales ◽

Van Der Waals ◽

Primary Resonance ◽

Mass Detection ◽

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.

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

Nonlinear tuning of microresonators for dynamic range enhancement

10.1098/rspa.2014.0969 ◽

2015 ◽

Vol 471 (2179) ◽

pp. 20140969 ◽

Cited By ~ 6

Author(s):

M. Saghafi ◽

H. Dankowicz ◽

W. Lacarbonara

Keyword(s):

Nonlinear Response ◽

Dynamic Range ◽

Multiple Scales ◽

Equations Of Motion ◽

Path Following ◽

Critical Amplitude ◽

Inertia Effects ◽

Response Characteristics ◽

The Galerkin Method

This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency

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

10.1115/imece2012-85966 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Kyle N. Taylor

Keyword(s):

Frequency Response ◽

Natural Frequency ◽

Multiple Scales ◽

Equations Of Motion ◽

Reduced Order Model ◽

Lagrange Equations ◽

Order Model ◽

Reduced Order ◽

Dc Voltage ◽

Ground Plate

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.

Nonlinear Vibrations of a Beam-Spring-Mass System

Journal of Vibration and Acoustics ◽

10.1115/1.2930446 ◽

1994 ◽

Vol 116 (4) ◽

pp. 433-439 ◽

Cited By ~ 38

Author(s):

M. Pakdemirli ◽

A. H. Nayfeh

Keyword(s):

Nonlinear Response ◽

Nonlinear Vibrations ◽

Multiple Scales ◽

Nonlinear Partial Differential Equations ◽

Primary Resonance ◽

Fast Time ◽

Lagrange Equations ◽

Response Curves ◽

Mass System

The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system.

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 ◽

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.

Volume 5: 6th International Conference on Micro- and Nanosystems; 17th Design for Manufacturing and the Life Cycle Conference ◽

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

10.1115/detc2012-70324 ◽

2012 ◽

Author(s):

Dumitru I. Caruntu ◽

Le Luo

Keyword(s):

Phase Behavior ◽

Multiple Scales ◽

Van Der Waals ◽

Mass Detection ◽

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.

Effect of Two-to-One Internal Resonances in a Nonlinearly Restrained Fluid Valve

Journal of Vibration and Acoustics ◽

10.1115/1.2893948 ◽

1999 ◽

Vol 121 (1) ◽

pp. 59-63 ◽

Cited By ~ 2

Author(s):

G. Anlas¸

Keyword(s):

Nonlinear Response ◽

Multiple Scales ◽

Primary Resonance ◽

Distributed Parameter ◽

Parameter System ◽

Response Curves ◽

Internal Resonances ◽

Relief Valve ◽

The effect of two-to-one internal resonances on the nonlinear response of a pressure relief valve is studied. The fluid valve is modeled as a distributed parameter system at one end and nonlinearly restrained at the other. The method of multiple scales is used to solve the system of partial differential equation and boundary conditions. Frequency-response curves are presented for the primary resonance of either mode in the presence of a two-to-one internal resonance. Stability of the steady-state solutions is investigated. Parameters of the system leading to two-to-one internal resonances are tabulated.