Global investigation of the nonlinear dynamics of carbon nanotubes

Tiantian Xu, Laura Ruzziconi, Mohammad I. Younis

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8 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)1029-1043
Number of pages15
JournalActa Mechanica
Issue number3
StatePublished - Nov 17 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.”


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