RETRACTED ARTICLE: Investigation of Thermal Impacts and Different Gradient Elasticity Theories on Wave Propagation through the Polymer Matrix Incorporated Carbon Nanotube Walls

This paper explores the vibrational properties of double-walled carbon nanotubes embedded in a polymer matrix within different gradient elasticity theories. The study considers how the mechanical behavior of double-walled carbon nanotubes and the polymer matrix changes with temperature. The research highlights the significance of scale effects on wave propagation in double-walled carbon nanotubes and shows that certain characteristics of transverse vibrations in double-walled carbon nanotubes are affected by temperature variations. In addition, the paper derives consistent governing equations for modeling free transverse vibrations of double-walled carbon nanotubes using the nonlocal Euler–Bernoulli beam model, considering the effects of temperature and Van der Waals forces between the inner and outer nanotubes.