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Nonlinear forced vibrations of three-phase nanocomposite shells considering matrix rheological behavior and nano-fiber waviness

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Abstract

The present study investigates the nonlinear vibrations in thin-walled shells consisting of three-phase polymer nanocomposites with regard to the viscoelastic properties of polymer and curved shape of carbon nanotubes (CNTs). To this end, a hierarchical micromechanical framework is introduced to study the effective properties of multi-scale hybrid (MSH) nanocomposite. Next, the von Kármán-type nonlinearity is considered together with the displacement field of the classical shell theory to derive the governing equations in the context of Hamilton’s principle. In addition, the impacts of both axial compression and transverse harmonic stimulation on the dynamic response of the system are taken into consideration. Afterward, the method of harmonic balance is implemented to find the frequency–response relation of the structure. The transient response is also achieved with the aid of fourth-order Runge–Kutta method. The results of this work reveal that resonance estimation in such hybrid nanomaterial structures will be inaccurate if the softening effect of waviness phenomenon on the modulus is ignored. On one hand, it is demonstrated that the amplitude of the dynamic deflection of the shell will be reduced with time (i.e., due to the viscoelastic properties of the polymer). On the other hand, it is depicted that rising the content of glass fibers (GFs) in the MSH nanocomposite shell results in softer oscillations. The reason for this trend is the reducing impact of this change on the content of the CNTs in the composition of the polymer nanocomposite.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave., 15875-4413, Tehran, Iran

    R. Nopour & M. M. Aghdam

  2. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Noroozian Blvd, 34148-96818, Qazvin, Iran

    F. Ebrahimi

  3. School of Mechanical Engineering, College of Engineering, University of Tehran, North Kargar St, 11155-4563, Tehran, Iran

    A. Dabbagh

Authors
  1. R. Nopour
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  2. F. Ebrahimi
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  3. A. Dabbagh
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  4. M. M. Aghdam
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Corresponding author

Correspondence to F. Ebrahimi.

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Nopour, R., Ebrahimi, F., Dabbagh, A. et al. Nonlinear forced vibrations of three-phase nanocomposite shells considering matrix rheological behavior and nano-fiber waviness. Engineering with Computers 39, 557–574 (2023). https://doi.org/10.1007/s00366-022-01608-7

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  • DOI: https://doi.org/10.1007/s00366-022-01608-7

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