Nonlinear Instability of Coupled CNTs Conveying Viscous Fluid

In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are derived. The differential quadrature (DQ) method is applied to obtain the nonlocal frequency of coupled visco-CNTs system. The effects of various parameters such as the longitudinal magnetic field, visco-Pasternak foundation, Knudsen number, surface effect, aspect ratio and velocity of conveying viscous are specified. It is shown that the longitudinal magnetic field is responsible for an up shift in the frequency and an improvement of the instability of coupled system. Results also reveal that the surface effect and internal conveying fluid plays an important role in the instability of nano coupled system. Also, it is found that trend of figures have good agreement with previous researches. It is hoped that the nonlinear results of this work could be used in design and manufacturing of nano/micro mechanical system in advanced nanomechanics applications where in this study the magnetic field is a controller parameter.