RETRACTED ARTICLE: A Study of Thermal Effects and Strain Gradient Elasticity in Wave Propagation Through Matrix-Embedded Wall Carbon Nanotubes

The study focuses on the vibrational characteristics of double-walled carbon nanotubes (DWCNTs) within a polymer matrix, using the theory of strain gradient elasticity.

The aim is to understand how the mechanical properties of DWCNTs and the polymer matrix change with temperature and how small-scale effects affect wave propagation in DWCNTs, especially in their free transverse vibration behavior.

The research derives governing equations for modeling the free transverse vibration of DWCNTs using the nonlocal Euler–Bernoulli beam model. This method takes into account temperature variations and the van der Waals forces between the inner and outer nanotubes.

The analysis provides insights into how temperature and inter-nanotube interactions impact the vibrational characteristics of DWCNTs embedded in polymer matrices. This comprehensive understanding is achieved through incorporating various factors into the study. The study underscores the importance of considering small-scale effects and inter-nanotube interactions in understanding the vibrational behavior of DWCNTs in polymer matrices, contributing to the broader field of nanomaterials research.