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Materials (Basel). 2016 Sep 21;9(9). pii: E786. doi: 10.3390/ma9090786.

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory.

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School of Mechanical Engineering, University of Tehran, Tehran 1193653471, Iran.
Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah 6715685438, Iran.
Laboratory of Bio-Inspired & Graphene Nanomechanics, Department of Civil, Environmental and Mechanical Engineering, Università di Trento, via Mesiano, 77, Trento 38123, Italy.
Center for Materials and Microsystems, Fondazione Bruno Kessler-via Sommarive 18, Povo, Trento 38123, Italy.
School of Engineering & Materials Science, Queen Mary University of London-Mile End Road, London E1 4NS, UK.


Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.


curved SWCNT; differential quadrature method (DQ); imperfection; nonlinear vibration; nonlocal theory

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