An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

Handle URI:
http://hdl.handle.net/10754/593270
Title:
An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes
Authors:
Xu, Tiantian; Younis, Mohammad I. ( 0000-0002-9491-1838 )
Abstract:
Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Publisher:
ASME International
Journal:
Volume 4: 19th Design for Manufacturing and the Life Cycle Conference; 8th International Conference on Micro- and Nanosystems
Conference/Event name:
ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Issue Date:
17-Aug-2014
DOI:
10.1115/DETC2014-35626
Type:
Conference Paper
Additional Links:
http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?doi=10.1115/DETC2014-35626
Appears in Collections:
Conference Papers; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Tiantianen
dc.contributor.authorYounis, Mohammad I.en
dc.date.accessioned2016-01-11T13:16:06Zen
dc.date.available2016-01-11T13:16:06Zen
dc.date.issued2014-08-17en
dc.identifier.doi10.1115/DETC2014-35626en
dc.identifier.urihttp://hdl.handle.net/10754/593270en
dc.description.abstractBecause of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.en
dc.publisherASME Internationalen
dc.relation.urlhttp://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?doi=10.1115/DETC2014-35626en
dc.titleAn Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubesen
dc.typeConference Paperen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalVolume 4: 19th Design for Manufacturing and the Life Cycle Conference; 8th International Conference on Micro- and Nanosystemsen
dc.conference.dateAugust 17–20, 2014en
dc.conference.nameASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conferenceen
dc.conference.locationBuffalo, New York, USAen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionState University of New York, Binghamton, NYen
kaust.authorYounis, Mohammad I.en
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