Global investigation of the nonlinear dynamics of carbon nanotubes

Handle URI:
http://hdl.handle.net/10754/622199
Title:
Global investigation of the nonlinear dynamics of carbon nanotubes
Authors:
Xu, Tiantian; Ruzziconi, Laura; Younis, Mohammad I. ( 0000-0002-9491-1838 )
Abstract:
Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Citation:
Xu T, Ruzziconi L, Younis MI (2016) Global investigation of the nonlinear dynamics of carbon nanotubes. Acta Mechanica. Available: http://dx.doi.org/10.1007/s00707-016-1740-0.
Publisher:
Springer Nature
Journal:
Acta Mechanica
Issue Date:
17-Nov-2016
DOI:
10.1007/s00707-016-1740-0
Type:
Article
ISSN:
0001-5970; 1619-6937
Sponsors:
The authors would like to thank the two anonymous reviewers for their valuable comments and constructive suggestions which contributed to improve our manuscript to a better scientific level. Laura Ruzziconi gratefully acknowledges financial support by the Italian Ministry of Education, Universities and Research (MIUR) by the PRIN funded program 2010/11, Grant N. 2010MBJK5B “Dynamics, Stability and Control of Flexible Structures.”
Additional Links:
http://dx.doi.org/10.1007/s00707-016-1740-0
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Tiantianen
dc.contributor.authorRuzziconi, Lauraen
dc.contributor.authorYounis, Mohammad I.en
dc.date.accessioned2017-01-02T08:42:37Z-
dc.date.available2017-01-02T08:42:37Z-
dc.date.issued2016-11-17en
dc.identifier.citationXu T, Ruzziconi L, Younis MI (2016) Global investigation of the nonlinear dynamics of carbon nanotubes. Acta Mechanica. Available: http://dx.doi.org/10.1007/s00707-016-1740-0.en
dc.identifier.issn0001-5970en
dc.identifier.issn1619-6937en
dc.identifier.doi10.1007/s00707-016-1740-0en
dc.identifier.urihttp://hdl.handle.net/10754/622199-
dc.description.abstractUnderstanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.en
dc.description.sponsorshipThe authors would like to thank the two anonymous reviewers for their valuable comments and constructive suggestions which contributed to improve our manuscript to a better scientific level. Laura Ruzziconi gratefully acknowledges financial support by the Italian Ministry of Education, Universities and Research (MIUR) by the PRIN funded program 2010/11, Grant N. 2010MBJK5B “Dynamics, Stability and Control of Flexible Structures.”en
dc.publisherSpringer Natureen
dc.relation.urlhttp://dx.doi.org/10.1007/s00707-016-1740-0en
dc.titleGlobal investigation of the nonlinear dynamics of carbon nanotubesen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalActa Mechanicaen
dc.contributor.institutionDepartment of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, USAen
dc.contributor.institutionFaculty of Engineering, eCampus University, via Isimbardi, 22060 Novedrate, Italyen
dc.contributor.institutionDepartment of Civil and Building Engineering and Architecture, Polytechnic University of Marche, via Brecce Bianche, 60131 Ancona, Italyen
kaust.authorYounis, Mohammad I.en
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