Viscoelastic Plate Subjected to Low-Velocity Impact: a Nonlinear Impact Force Mechanism - Qanber, Ali Sadik Gafer; Windi, Omar Imad Shukri (Journal of Applied Nonlinear Dynamics, 2026)
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.