Torsional Vibration Analysis of Double‐Walled Carbon Nanotubes Incorporating Viscoelasticity and Nonlocal Elasticity Under Deformable Boundary Conditions

ABSTRACT

This study investigates the torsional vibration characteristics of double‐walled carbon nanotubes (DWCNTs) considering viscoelastic effects and nonlocal elasticity theory. The equations of motion are formulated based on the nonlocal constitutive relations and viscoelastic material behavior to accurately capture the small‐scale and time‐dependent responses of the nanotube system. The interlayer interaction between the inner and outer tubes is modeled using van der Waals forces. Boundary conditions are modelled using torsional springs, where clamped and free cases are recovered as limiting cases. A semi‐analytical solution procedure is developed by applying the Fourier series expansion in conjunction with the Stokes' transform. This approach enables the derivation of an eigenvalue problem that includes the effects of boundary deformability, nonlocal elasticity, and viscoelastic damping. A comprehensive analysis is conducted to examine how the nonlocal parameter, viscous damping parameter, geometric ratios, and boundary flexibility influence the torsional vibration frequencies of DWCNTs. The proposed model offers a versatile and efficient framework for analyzing the dynamic behavior of nanotubes with complex boundary and material characteristics.