Modified jeffreys viscoelastic model for axial vibration of nanorods with realistic boundary conditions

Abstract

In this study, the axial vibration behavior of viscoelastic nanorods has been investigated in detail by employing the modified Jeffreys viscoelastic model. This model is a series coupling of the Kelvin-Voigt model and a viscous damper and has the potential to simulate a wide range of material behavior, combining the advantages of both the Kelvin-Voigt and Maxwell viscoelastic models. The model used has been integrated with the theory of nonlocal elasticity, and the governing equations for axial vibrations of nano-rods have been derived, taking into account both damping and size effects. The problem has been solved by a semi-analytical method using Fourier series and Stokes transforms under more realistic viscoelastic boundary conditions. The obtained results have been presented in detail in tables and graphs, and it is believed that these results will contribute to a more accurate understanding of the dynamic behavior of nano-rods. In addition, it is predicted that it will pave the way for the development of more reliable and effective models in nanoscale engineering designs.