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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Viscoelastic Plate Subjected to Low-Velocity Impact: a Nonlinear Impact Force Mechanism

Journal of Applied Nonlinear Dynamics 13(4) (2024) 781--793 | DOI:10.5890/JAND.2024.12.011

Ali Sadik Gafer Qanber$^1$, Omar Imad Shukri Windi$^{2}$

$^{1}$ Department of Biomedical Engineering, University of Babylon, College of Engineering, Babylon, Iraq

$^{2}$ Department of Mechanical Engineering, Al-Furat Al-Awsat Technical University, Babylon Technical Institute, Babylon 51015, Iraq

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Abstract

Based on the Hertz's nonlinear contact law, the purpose of this article is to analyze the theory of low-velocity impact (LVI) on a functionally graded (FG) viscoelastic plate. CNTs are used as a plate reinforcement and Poly (methyl methacrylate) is used as a matrix. Considering the size factor, CNTs are distributed along the thickness of the plate with different functions, including uniform (UD) and FG states. Considering the viscoelastic coefficient, the relationship between the stress and strain is rewritten. To obtain the motion equations of the forced vibrations caused by the impact, the first-order shear deformation theory (FSDT) of the plate and the kinetic and strain energies of the impactor and plate assembly are written. Finally, a set of mass, damping and stiffness matrices are provided. The effect of changes in the viscoelastic coefficient is investigated for the case that the distribution of CNTs includes states UD, FGV and FGX, and also the CNTs volume fraction includes values of 0.12, 0.17, and 0.28. For this purpose, the responses of impact force and plate center deflection are studied. The results show that the effect of changes in the viscoelastic coefficient is more focused on plate center deflection and the contact force did not change much. In other words, with the increase of viscoelastic coefficient, the maximum value of plate center deflection is decreased.

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