Flutter and vibration of elastically restrained nanowires under a nonconservative force

This paper investigates vibration and flutter behavior of a cantilevered nanowire under the action of a subtangential follower force. Taking the surface effects into account, we apply Hamilton principle to derive a governing equation for an elastically restrained nanobeam. A characteristic equation is obtained. Force-frequency interaction curves are displayed to show the influence of the surface elasticity, surface stress, restraint stiffness on divergence and flutter force. Natural frequencies and divergence loads are calculated for conservative forces at the free end. For a generalized follower force with various tangency coefficients, dynamic instability of nanocantilevers is presented and flutter loads are calculated for subtangential, supertangential and tangential follower forces. Flutter loads are sensitive to translational and rotational spring stiffness and surface elasticity. Some special cases with some vanishing parameters reduce to the well-known results.