Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects

This paper is aimed to examine the geometrically nonlinear vibration and stability of nanoscale pipe conveying fluid incorporating surface stress effect. To approach this, the von-Karman hypothesis and Timoshenko beam theory are used to model the nanoscale pipe as a nonlinear Timoshenko nanobeam. Then, Hamilton's principle and the Gurtin-Murdoch continuum elasticity are used to derive the governing equations of motion and associated boundary conditions incorporating the surface stress effect. Afterward, by the generalized differential quadrature method and harmonic balance method, the obtained nonlinear differential equations are discretized and simplified, before solving numerically through the Newton-Raphson method. The effects of the surface stress parameters on the stability and imaginary and real parts of frequency of nanopipes are discussed. Results are performed for nanopipes with different end supports made of silicon (Si) and aluminum (Al).