Nonlocal Elastic Wave Propagation Dynamics in Nanostructured Rods and Carbon Nanotubes

ABSTRACT

Elastic waves provide improved dynamic properties and the ability to manipulate material behavior in micro and nano‐structured materials. This novel work deals with the vibrations and wave propagation in such a structure using the continuum theory. The characteristics of wave propagation and longitudinal vibrations of nanorods and carbon nanotubes (CNTs) in spatiotemporal nanostructures are studied using the Eringen stress and gradient elasticity theory. Systems of differential equations are derived to describe the proposed physical problem. These equations are solved using computational methods to investigate the physical properties of the nonlocal nanomaterials, considering the effect of utilizing nonlocal microscopic parameters and dispersion properties that characterize material behavior at the nanoscale. The model equations are solved using analytical methods to investigate the physical properties of the nonlocal nanomaterials and their effects on wave propagation. Additionally, it involves the examination of elastic curvature and displacement, which signify the nonlocal response influenced by various effects from adjacent points. The nonlocal parameters are determined based on values adopted from established literature, and the proposed model is validated through rigorous comparisons with previously published theoretical and numerical investigations. This approach ensures the accuracy and reliability of the analytical solutions in predicting the dynamic response of nanostructured materials. Furthermore, the phase‐plane and eigenvalue analyses demonstrate the coherence and mutual validation of Eringen's nonlocal stress theory and the strain‐gradient elasticity models within a unified dynamical framework.