Dynamic Response of an Elastic Tube-like Nanostructure Embedded in a Vibrating Medium and under the Action of Moving Nano-Objects

Abstract

In recent years, researchers have looked at how tube-like nanostructures respond to moving loads and masses. However, no one has explored the scenario of a nanostructure embedded in a vibrating medium used for moving nano-objects. In this study, the governing equations of the problem are methodically derived using the nonlocal elasticity of Eringen as well as the Rayleigh and Reddy–Bickford beam theories. Analytical and numerical solutions are developed for capturing the nonlocal dynamic deflection of the nanostructure based on the moving nanoforce approach (excluding the inertia effect) and the moving nanomass approach (including the inertia effect), respectively. The results predicted by the established models are successfully verified with those of other researchers in some special cases. The results reveal that for low velocities of the moving nano-object in the absence of the medium excitation, the midspan deflection of the simply supported nanotube exhibits an almost symmetric time-history curve; however, by increasing the nano-object velocity or the medium excitation amplitude, such symmetry is violated, mainly due to the lateral inertia of the moving nano-object, as displayed by the corresponding three-dimensional plots. The study addresses the effects of the mass and velocity of the moving nano-object, amplitude, and frequency of the medium excitation, and the lateral and rotational stiffness of the nearby medium in contact with the nanostructure on the maximum dynamic deflection. The achieved results underscore the significance of considering both the inertial effect of the moving nano-object and the shear effect of stocky nanotubes embedded in vibrating media. This research can serve as a strong basis for conducting further investigations into the vibrational properties of more intricate tube-shaped nanosystems that are embedded in a vibrating medium, with the aim of delivering nano-objects.