Size-dependent bifurcations of microtubes conveying fluid flow embedded in a nonlinear elastic medium

Abstract

The size-dependent bifurcation behaviour of a fluid-conveying microtube taking into account the effect of internal energy loss is studied in this paper. It is assumed that the viscoelastic microscale tube is externally excited by a transverse harmonic force. In addition, the viscoelastic microscale system is surrounded by a nonlinear spring bed. To take into account the influence of the internal energy loss on the size-dependent bifurcation behaviour, the Kelvin-Voigt scheme of viscoelasticity is employed. The modified couple stress theory (MCST), as a size-dependent theory, and the Hamilton principle, as an energy/work law, are utilised for deriving the governing coupled equations for the bifurcation response of the viscoelastic fluid-conveying microtube. The displacement along the transverse direction as well as the axial displacement are incorporated into the size-dependent continuum model, leading to an accurate coupled continuum-based model. The Galerkin weighted-residual scheme, as a decomposition approach, is then applied to the derived nonlinear differential equations. Clamped-clamped boundary conditions are taken into consideration for extracting numerical results. The sizedependent bifurcation behaviour of the fluid-conveying viscoelastic microtube is finally predicted by a numerical timeintegration technique.