Dynamic Torsional Response of Viscoelastic Porous Nanorods with Viscoelastic Boundary Constraints

Abstract In this study, the torsional vibration behavior of a viscoelastic porous nanorod has been analyzed using a semi-analytical solution method under viscoelastic boundary conditions. The Kelvin–Voigt model has been employed to represent viscoelastic behavior, while the modified couple stress theory has been adopted to account for size effects. The equation of motion of the viscoelastic porous nanorod has been derived in accordance with Hamiltonian principle, and the problem has been solved using higher order derivatives obtained through Fourier series and Stokes’ transforms. Unlike previous studies in the literature, the proposed method has enabled the calculation of frequencies for various boundary conditions from a single eigenvalue problem. The accuracy of the results has been verified by comparison with existing studies and then analyses for the viscoelastic porous nanorod with viscoelastic boundary conditions presented in a series of tables and graphs. The analyses have revealed that the influence of the dimensionless damping parameter on frequency becomes more pronounced as the size parameter increases, while the porous parameter plays a significant role in the dynamic behavior of nanorods.