Nonlinear vibration of coupled nano- and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field

Abstract

Nonlinear vibration response of coupled viscoelastic carbon nanotubes (CNTs) conveying viscous fluid is investigated based on nonlocal and modified couple stress theories. The CNTs are placed in a uniform two-dimensional (2D) magnetic field and modeled by a Timoshenko beam. The effect of slip boundary condition is considered in the Navier–Stokes relations based on the Knudsen number correction factor. The higher-order governing equations of motion are derived based on the energy method and Hamilton’s principle where the differential quadrature (DQ) approach is applied to obtain the nonlinear frequency of coupled system. A detailed parametric study is conducted, focusing on the combined effects of 2D magnetic field, Visco-Pasternak foundation, Knudsen number, surface effect, velocity of conveying viscous fluid, and different theories. Also, the Galerkin method is applied to compare our linear results to those that are obtained by the DQ approach. The results of this article could be useful in designing and manufacturing of double nano-/micromechanical systems that are usually used in advanced biomechanics and optics.