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Theoretical development and closed-form solution of nonlinear vibrations of a directly excited nanotube-reinforced composite cantilevered beam

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Abstract

The nonlinear equations of motion of planar bending vibration of an inextensible viscoelastic carbon nanotube (CNT)-reinforced cantilevered beam are derived. The viscoelastic model in this analysis is taken to be the Kelvin–Voigt model. The Hamilton principle is employed to derive the nonlinear equations of motion of the cantilever beam vibrations. The nonlinear part of the equations of motion consists of cubic nonlinearity in inertia, damping, and stiffness terms. In order to study the response of the system, the method of multiple scales is applied to the nonlinear equations of motion. The solution of the equations of motion is derived for the case of primary resonance, considering that the beam is vibrating due to a direct excitation. Using the properties of a CNT-reinforced composite beam prototype, the results for the vibrations of the system are theoretically and experimentally obtained and compared.

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, Tarbiat Modarres University, P.O.Box 14115-177, Tehran, Iran

    S.N. Mahmoodi & S.E. Khadem

  2. Smart Structure and NanoElectroMechanical Systems Laboratory, Department of Mechanical Engineering, Clemson University, Clemson, SC, 29634-0921, USA

    N. Jalili

  3. Power and Water Institute of Technology, POB: 16765–1719, Tehran, Iran

    S.N. Mahmoodi

Authors
  1. S.N. Mahmoodi
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  2. S.E. Khadem
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  3. N. Jalili
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Correspondence to S.E. Khadem.

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Mahmoodi, S., Khadem, S. & Jalili, N. Theoretical development and closed-form solution of nonlinear vibrations of a directly excited nanotube-reinforced composite cantilevered beam. Arch Appl Mech 75, 153–163 (2006). https://doi.org/10.1007/s00419-005-0426-1

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  • DOI: https://doi.org/10.1007/s00419-005-0426-1

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