Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Reduced Order Model ◽  
Plane Boundary ◽  
Beam Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range

This work presents an investigation of the nonlinear dynamics of carbon nanotubes (CNTs) when actuated by a dc load superimposed to an ac harmonic load. Cantilevered and clamped-clamped CNTs are studied. The carbon nanotube is described by an Euler–Bernoulli beam model that accounts for the geometric nonlinearity and the nonlinear electrostatic force. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the carbon nanotube. The free-vibration problem is solved using both the reduced-order model and by solving directly the coupled in-plane and out-of-plane boundary-value problems governing the motion of the nanotube. Comparison of the results generated by these two methods to published data of a more complicated molecular dynamics model shows good agreement. Dynamic analysis is conducted to explore the nonlinear oscillation of the carbon nanotube near its fundamental natural frequency (primary-resonance) and near one-half, twice, and three times its natural frequency (secondary-resonances). The nonlinear analysis is carried out using a shooting technique to capture periodic orbits combined with the Floquet theory to analyze their stability. The nonlinear resonance frequency of the CNTs is calculated as a function of the ac load. Subharmonic-resonances are found to be activated over a wide range of frequencies, which is a unique property of CNTs. The results show that these resonances can lead to complex nonlinear dynamics phenomena, such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequency bands with an inevitable escape from a potential well.

Nonlinear Dynamics of Electrically-Actuated Carbon Nanotube Resonator

2008 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotube ◽  
Natural Frequency ◽  
Primary Resonance ◽  
Beam Model ◽  
Harmonic Load ◽  
Shooting Technique ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

This paper presents an investigation into the nonlinear dynamics of a carbon nanotube (CNT) actuated electrically by a DC force and an AC harmonic load. The CNT is described by an Euler Bernoulli beam model that accounts for the system nonlinearities due to mid-plane stretching and electrostatic forcing. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic response of the CNT. The static deflection of the CNT and its pull-in voltage are calculated and validated by comparing them to published results. It was found that mid-plane stretching has a major impact on the pull-in prediction of CNT. Dynamic analysis is conducted to explore the nonlinear oscillation of the CNT near its fundamental natural frequency (primary resonance) and near one half, twice, and three times its natural frequency (secondary resonances). The nonlinear analysis is carried out using a shooting technique combined with the Floquet theory to capture periodic orbits and analyze their stability. The results show that these resonances can lead to complex nonlinear dynamics phenomena such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequencies bands with an inevitable escape from a potential well.

Forced Vibrations of Slacked Carbon Nanotube Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Beam Model ◽  
Harmonic Load ◽  
Arch Model ◽  
Order Model ◽  
Reduced Order ◽  
Model Equations

In this paper, we present an investigation of the dynamics of electrically actuated carbon nanotubes (CNTs) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear arch model is used to simulate the motion of the slacked CNT. A reduced-order model using a multimode Galerkin procedure based on the mode shapes of the straight un-actuated CNTs is derived. The reduced-order model equations are integrated numerically with time to reveal the steady-state response of the CNT when actuated by a DC load superimposed to an AC harmonic load. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNT. Results of the perturbation method are verified with those obtained by numerically integrating the reduced-order model equations. The effective nonlinearity of the CNT is calculated as function of the slack and the DC load while using a beam model for the CNTs showing a softening dominant behavior.

Statistics of Extreme Events in Fluid Flows and Waves

2021 ◽  
Vol 53 (1) ◽  
pp. 85-111 ◽  
Author(s):  
Themistoklis P. Sapsis
Keyword(s):  
Nonlinear Dynamics ◽  
Natural Disasters ◽  
Extreme Events ◽  
Fluid Flows ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range ◽  
Expensive Model ◽  
Statistics Of Extreme Events

Extreme events in fluid flows, waves, or structures interacting with them are critical for a wide range of areas, including reliability and design in engineering, as well as modeling risk of natural disasters. Such events are characterized by the coexistence of high intrinsic dimensionality, complex nonlinear dynamics, and stochasticity. These properties severely restrict the application of standard mathematical approaches, which have been successful in other areas. This review focuses on methods specifically formulated to deal with these properties and it is structured around two cases: ( a) problems where an accurate but expensive model exists and ( b) problems where a small amount of data and possibly an imperfect reduced-order model that encodes some physics about the extremes can be employed.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Reduced Order Model of MEMS Sensors Near Natural Frequency

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Jose C. Solis Silva
Keyword(s):  
Natural Frequency ◽  
Nonlinear Response ◽  
Casimir Effect ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Mass Detection ◽  
Order Model ◽  
Reduced Order ◽  
First Order ◽  
Electrostatically Actuated

The nonlinear response of an electrostatically actuated cantilever beam microresonator sensor for mass detection is investigated. The excitation is near the natural frequency. A first order fringe correction of the electrostatic force, viscous damping, and Casimir effect 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 uniform microresonators with mass deposition and without are reported.

A Reduced-Order Model for the Preliminary Design of Small-Scale Radial Inflow Turbines

2021 ◽  
Author(s):  
Marco Manfredi ◽  
Marco Alberio ◽  
Marco Astolfi ◽  
Andrea Spinelli
Keyword(s):  
Heat Recovery ◽  
Internal Combustion Engines ◽  
Reduced Order Model ◽  
Pollutant Emissions ◽  
Small Scale ◽  
Preliminary Design ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range ◽  
Loss Models

Abstract Power production from waste heat recovery represents an attractive and viable solution to contribute to the reduction of pollutant emissions generated by industrial plants and automotive sector. For transport applications, a promising technology can be identified in bottoming mini-organic Rankine cycles (ORCs), devoted to heat recovery from internal combustion engines (ICE). While commercial ORCs exploiting turbo-expanders in the power range of hundreds kW to several MW are a mature technology, well-established design guidelines are not yet available for turbines targeting small power outputs (below 50 kW). The present work develops a reduced-order model for the preliminary design of mini-ORC radial inflow turbines (RITs) for high-pressure ratio applications, suitable to be integrated in a comprehensive cycle optimization. An exhaustive review of existing loss models, whose development pattern is retraced up to the original approaches, is proposed. This investigation is finalized in a loss models effectiveness analysis performed by testing several correlations over six existing geometries. These test case turbines, operating with different fluids and covering a wide range of target expansion ratio, size, and gross power output, are then employed to carry out the validation procedure, whose results prove the robustness and prediction capability of the proposed reduced-order model.

A Reduced Order Model of Unsteady Flows in Turbomachinery

1994 ◽  
Author(s):  
Kenneth C. Hall ◽  
Răzvan Florea ◽  
Paul J. Lanzkron
Keyword(s):  
Fluid Motion ◽  
Unsteady Flows ◽  
Reduced Order Model ◽  
Lanczos Algorithm ◽  
Order Model ◽  
Reduced Order ◽  
Unsteady Aerodynamic ◽  
Natural Modes ◽  
Wide Range ◽  
Modes Of Vibration

A novel technique for computing unsteady flows about turbomachinery cascades is presented. Starting with a frequency domain CFD description of unsteady aerodynamic flows, we form a large, sparse, generalized, non-Hermitian eigenvalue problem which describes the natural modes and frequencies of fluid motion about the cascade. We compute the dominant left and right eigenmodes and corresponding eigenfrequencies using a Lanczos algorithm. Then, using just a few of the resulting eigenmodes, we construct a reduced order model of the unsteady flow field. With this model, one can rapidly and accurately predict the unsteady aerodynamic loads acting on the cascade over a wide range of reduced frequencies and arbitrary modes of vibration. Moreover, the eigenmode information provides insights into the physics of unsteady flows. Finally we note that the form of the reduced order model is well suited for use in active control of aeroelastic and aeroacoustic phenomena.

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).

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Israel Martinez ◽  
Martin W. Knecht
Keyword(s):  
Natural Frequency ◽  
Microelectromechanical Systems ◽  
Multiple Scales ◽  
Alternating Current ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Mems Resonator ◽  
Fringe Effect

This paper uses the reduced order model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions.

scholarly journals A reduced order model of the spine to study pediatric scoliosis

2020 ◽  
Author(s):  
Sunder Neelakantan ◽  
Prashant K. Purohit ◽  
Saba Pasha
Keyword(s):  
Idiopathic Scoliosis ◽  
Inflection Point ◽  
Reduced Order Model ◽  
The Other ◽  
Sagittal Profile ◽  
Deformation Pattern ◽  
Elastic Rod ◽  
Order Model ◽  
Reduced Order ◽  
Wide Range

AbstractThe S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work we proposed a reduced order model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern showing that for rods deforming in a loop 1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the loop 2 shape the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves - Lenke 1 and Lenke 5. Our elastic rod model predicts deformations that are similar to those of a pediatric spine and it can differentiate between the clinically observed deformation patterns. This provides validation to the hypothesis that changes in the sagittal profile of the spine can be a mechanical factor in parthenogenesis of pediatric idiopathic scoliosis.

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