Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Abstract

Presented in this paper is a precise investigation of the effect of surface stress on the vibration character- istics and instability of fluid-conveying nanoscale pipes. To this end, the nanoscale pipe is modeled as a Timo- shenko nanobeam. The equations of motion of the nanoscale pipe are obtained based on Hamilton's principle and the Gurtin-Murdoch continuum elasticity incorporating the sur- face stress effect. Afterwards, the generalized differential quadrature method is employed to discretize the govern- ing equations and associated boundary conditions. To what extent important parameters such as the thickness, material and surface stress modulus, residual surface stress, surface density, and boundary conditions influence the natural fre- quency of nanoscale pipes and the critical velocity of fluid is discussed.