Longitudinal Forced Vibration Analysis of a Single-Walled Carbon Nanotube Embedded in an Elastic Medium

Purpose: Single walled carbon nanotubes (SWCNT) are materials described as nanoscale cylindrically shaped allotropes of carbon possessing high surface area and aspect ratio (length to diameter ratio) which makes them to be modelled as one-dimensional tubes. SWCNTs have superior mechanical properties, which makes them a primary filler in the polymer matrix to enhance its mechanical characteristics. This study aims to examine the longitudinal forced vibration of SWCNT embedded in elastic medium subjected to different types of axial loads such as uniform, linearly varying and sinusoidal. Methods: Formulation is considered based on Hamilton’s principle and Eringen’s nonlocal elasticity theory. Analytical solution is obtained based on variation of parameters to get modal frequencies, shapes and dynamic displacements within the nanotube. Results: Obtained frequency results are compared with those available in the literature and a high level of accuracy is achieved. Parametric analyses are carried out to examine the influences of elastic medium stiffness, nonlocal parameter and aspect ratio on mode shapes and dynamic displacements. Conclusion: Increase in the elastic medium stiffness leads to increase in the modal frequencies and this increase is greater for nanotubes with clamped-free (C-F) boundary conditions. Dynamic displacement value of the midpoint decreases as stiffness is increased at the same non-dimensional frequency. Change in modal frequency due to the increase in stiffness remains the same for different aspect ratios. The influence of nonlocal parameter on modal frequencies is the highest at smaller aspect ratios, which implies the necessity of the use of nonlocal elasticity theory at nano-scale vibration analysis.