Analysis of torsional vibration in viscoelastic functionally graded nanotubes with viscoelastic constraints using doublet mechanics theory

Abstract

In this study, the torsional vibration behavior of functionally graded viscoelastic nanotubes under viscoelastic boundary conditions is investigated in detail within the framework of Doublet Mechanics Theory. A comprehensive solution method is presented that allows the combined consideration of nanoscale effects and viscoelastic behavior; the effects of fundamental parameters such as viscous damping parameter, scale parameter and power law exponent on the system dynamics are analytically revealed. Physical interpretations of both vibration frequencies and damping effects are made from the obtained complex frequency solutions, and the effects of these parameters on the frequency spectrum are analyzed in detail with the help of tables and graphs. The results clearly indicate that classical elastic models are inadequate for the torsional vibration behavior of viscoelastic nanotubes and damping effects at the nano level should not be ignored. Furthermore, it is displayed that there are clear mathematical relationships between the real and imaginary components of the complex frequencies obtained in the system under the direct influence of the viscoelastic model used. In this context, the study makes an important contribution not only theoretically but also in terms of practical applications for the design of nano-mechanical systems.