Analysis of Nonlocality, Surface Energy, and Initial Stress on the Dynamic Behaviour of Carbon Nanotubes Conveying Fluid Resting on Elastic Foundations in a Thermo-Magnetic Environment using Variation of Parameter Method

Abstract

Gbeminiyi M Sobamowo, Olorunfemi O Isaac, Suraju A Oladosu, Rafiu O Kuku

This work analyzes the simultaneous impacts of surface elasticity, initial stress, residual surface tension and nonlocality on the nonlinear vibration of single-walled carbon conveying nanotube resting on linear and nonlinear elastic foundation and operating in a thermo-magnetic environment. Equation of motion govern- ing the vibration of the nanotube was derived using Erigen’s theory, Euler-Bernoulli’s theory and Hamilton’s principle. The partial differential equation was converted to ordinary differential equation using Galerkin’s decomposition method and the ordinary differential equation was solved with the aid of variation of parameter method. Through the parametric studies, it was revealed that the ratio of the nonlinear to linear frequencies increases with the negative value of the surface stress while it decreases with the positive value of the surface stress. At any given value of nonlocal parameters, the surface effect reduces for increasing in the length of the nanotube. ratio of the frequencies decreases with increase in the strength of the magnetic field, nonlocal parameter and the length of the nanotube. The natural frequency of the nanotube gradually approaches the nonlinear Euler–Bernoulli beam limit at high values of nonlocal parameter and nanotube length. nonlocal parameter reduces the surface effects on the ratio of the frequencies. Increase in temperature change at high temperature causes decrease in the frequency ratio. However, at room or low temperature, the frequency ratio of the hybrid nanostructure increases as the temperature change increases. Also, the ratio of the frequencies at low temperatures is lower than at high temperatures. The present work will assist in the control and design of carbon nanotubes operating in thermo-magnetic environment and resting on elastic foundations.

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