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Global investigation of the nonlinear dynamics of carbon nanotubes

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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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY, 13902, USA

    Tiantian Xu & Mohammad I. Younis

  2. Faculty of Engineering, eCampus University, via Isimbardi, 22060, Novedrate, Italy

    Laura Ruzziconi

  3. Department of Civil and Building Engineering and Architecture, Polytechnic University of Marche, via Brecce Bianche, 60131, Ancona, Italy

    Laura Ruzziconi

  4. Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, Saudi Arabia

    Mohammad I. Younis

Authors
  1. Tiantian Xu
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  2. Laura Ruzziconi
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  3. Mohammad I. Younis
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Correspondence to Mohammad I. Younis.

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Xu, T., Ruzziconi, L. & Younis, M.I. Global investigation of the nonlinear dynamics of carbon nanotubes. Acta Mech 228, 1029–1043 (2017). https://doi.org/10.1007/s00707-016-1740-0

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  • DOI: https://doi.org/10.1007/s00707-016-1740-0

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