Vibration Analysis of Nonuniform Single-Walled Carbon Nanotube Resting on Winkler Elastic Foundation Using DQM

Abstract

This study present frequency parameters and mode shapes of nonuniform Single-Walled Carbon Nanotube (SWCNT) placed on Winkler elastic foundation. Eringen’s nonlocal theory is implemented in the Euler–Bernoulli beam to inquire size-dependent behavior of single-walled carbon nanotube. Here flexural stiffness is assumed to vary exponentially which is responsible for making it nonuniform since many nanoelectromechanical systems acquire geometrically nonuniform model. Differential Quadrature Method (DQM) is adopted and MATLAB code has been developed to explore the tabular and graphical results for different scaling parameters. All the standard boundary condition, viz, S-S, C-S, C-C, and C-F are taken into consideration, and obtained results are compared with the well-known results available in the literature showing excellent agreement. Also, the effects of various scaling parameters like nonuniform parameter, the nonlocal parameter, aspect ratio, and Winkler modulus parameter on frequency parameters are demonstrated using numerical as well as graphical results.