Nonlocal Timoshenko beam model for dynamic stability of double-walled boron nitride nanotubes conveying nanoflow

Abstract

Based on nonlocal piezoelasticity theory, dynamic stability of double-walled boron nitride nanotube conveying viscous fluid is investigated using Timoshenko beam theory. Double-walled boron nitride nanotube is surrounded in visco-Pasternak medium and conducts the internal fluid. Modified Navier–Stokes relation is used to evaluate fluid–double-walled boron nitride nanotube interaction considering the effects of bulk viscosity and slip boundary condition. Mechanical harmonic excitation and thermal loadings are exerted on double-walled boron nitride nanotube with zero electrical boundary condition. Nonlinear van der Waals forces between the inner and outer layers of double-walled boron nitride nanotube are taken into account. Hamilton’s principle is utilized to derive governing equations with regard to von Kármán geometric nonlinearity. Charge equation is used to consider the coupling of electric potential and mechanical displacement. Space and time domains are discretized using Galerkin and incremental harmonic balance approaches. Finally the eigenvalue equations are solved based on the iterative method to derive dynamic instability regions. The detailed parametric study is conducted, focusing on the combined effects of aspect ratio, nonlocal parameter, fluid velocity, Knudsen number, thermal changes, van der Waals forces and surrounding medium on dynamic instability regions of double-walled boron nitride nanotube.

Keywords

Double-walled boron nitride nanotube dynamic stability visco-Pasternak piezoelasticity viscous fluid

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