Forces in Mechanics (Sep 2021)
Coupled effects of magnetic field, number of walls, geometric imperfection, temperature change, and boundary conditions on nonlocal nonlinear vibration of carbon nanotubes resting on elastic foundations
Abstract
The present study focusses on the investigations of the combined effects of magnetic field, temperature, nonlocal parameter, number of walls, initial geometric imperfection and end supports on the nonlinear transverse vibrations of carbon nanotubes resting on linear and nonlinear elastic foundations. With the aids of Erigen's nonlocal elasticity, Euler-Bernoulli beam theories and van der Waal forces equation, systems of nonlinear partial differential equations governing the dynamics responses of slightly curved multi-walled carbon nanotubes resting on Winkler and Pasternak foundations in a thermal-magnetic environment are developed. The developed equations are decomposed into spatial and temporal equations using Galerkin separation approach. The time-dependent nonlinear differential equations are solved by homotopy perturbation method. Detailed studies are conducted to investigate the effects of the models parameters on the nonlinear vibrations of the structures. The parametric studies reveal that the frequency ratio decreases as the number of magnetic field strength, number of nanotube walls, temperature, spring constants and the ratio of the radius of curvature to the length of the slightly curved nanotubes increase. It is established that these trends are the same for all the boundary conditions considered. The study also reveals that the clamped-simple supported multi-walled nanotubes have the highest frequency ratio while the clamped-clamped supported multi-walled nanotubes have the lowest frequency ratio. Further investigations show that quadruple-walled carbon nanotubes can be taken as pure linear vibration even at any value of linear Winkler and Pasternak foundations constants. Such result can be used to control the nonlinear vibration of the carbon nanotubes and also restrains the chaos vibration in the objective structure. The findings in this work will help in the design of multi-walled carbon nanotubes for various structural, electrical, mechanical and biological applications in a thermal and magnetic environment.
