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

Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes. To this end, the nanoscale pipe is modeled as a Timoshenko nanobeam. The equations of motion of the nanoscale pipe are obtained based on Hamilton's principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect. Afterwards, the generalized differential quadrature method is employed to discretize the governing 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 frequency of nanoscale pipes and the critical velocity of fluid is discussed.