Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment

Abstract

The size-dependent nonlinear free vibration and instability of fluid-conveying single-walled boron nitride nanotubes (SWBNNTs) embedded in thermal environment are studied in this paper. The fluid-conveying SWBNNT is modeled as a Timoshenko beam by which the effects of transverse shear deformation and rotary inertia is taken into consideration. The modified strain gradient theory is used to capture the size effect. To consider the nonlinear effect, the geometric nonlinearity, based on von Kármán׳s assumption is introduced to develop the nonlinear governing equations of motion. By employing Hamilton׳s principle, the governing equations and associated boundary conditions are derived. Thereafter, a numerical solution procedure based on the generalized differential quadrature (GDQ) is introduced, according to which the nonlinear governing equations and the corresponding boundary conditions are discretized via the operational matrix of differentiation. The discretized equations are then solved analytically through the harmonic balance approach. Effects of different parameters including material length scale parameter, spring and damping constants of surrounding viscoelastic medium, and flow velocity on the nonlinear free vibration and instability of SWBNNTs are examined.