Combined Effects of Surface Energy, Initial Stress and Nonlocality on Vibration of Carbon Nanotubes Conveying Fluid Resting on Elastic Foundations in a Thermo-Magnetic Environment

Abstract

This paper scrutinizes the simultaneous impacts of surface elasticity, initial stress, residual surface stress and nonlocality on the nonlinear vibration of carbon nanotube conveying fluid resting while resting on linear and nonlinear elastic foundations and operating in a thermo-magnetic environment. The derived partial differential equation is decomposed into spatial and temporal equations using Galerkin method of decomposition. Thereafter, the temporal differential equation is solved with the aid of method of homotopy perturbation. Studies of the significance of the model parameters reveal that the negative value of the surface stress enhances the frequency ratio while the positive value of the surface stress abates the ratio. At any given value of nonlocal parameters, the surface effect is lessened for enhancing value of the length of the nanotube. The frequency ratio is abated as strength of the magnetic field, nonlocal parameter and the length of the nanotube are increased. The nonlocality lessens the surface effects and ratio of the frequencies. At high values of nonlocal parameter and nanotube length, the natural frequency of the structure gradually approaches nonlinear Euler–Bernoulli beam limit. The ratio of the frequencies is heightened when the temperature change is reduced at high temperature while at room/low temperature, such ratio is enhanced as the temperature change is augmented. Also, the frequency ratio at low temperatures is lower than at high temperatures. The present work will be very useful in the design and control of carbon nanotubes in thermo-magnetic environment while resting on elastic foundations.