Size-dependent longitudinal–transverse mode interaction of fluid-conveying nanotubes under base excitation

Nonlinear coupled modal interaction at nanoscale has attracted much attention in designing the nanoelectromechanical systems for wider functionalities which are unable to be achieved through conventional linear theories. The longitudinal–transverse coupled auto-parametric resonance of flow-conveying nanotubes under base excitation is studied. The size dependency at nanoscale including non-local stress, strain gradient, surface effect and slip flow is fully examined. In addition, a size-dependent "stretchable" tube model is developed to characterize the nonlinear longitudinal–transverse coupling relationship. The computation model of the Galerkin truncation–incremental harmonic balance method is devised to characterize the stability boundary, amplitude–frequency bifurcation curves, and amplitude–amplitude bifurcation curves. The calculation accuracy is confirmed through numerical validation. Typical stability boundary and bifurcation topologies under coupling conditions are presented to reveal the modal interaction and energy exchange mechanism between modes. The degree of significance from structural damping, flow velocity, and boundary mass on both modes are analyzed for exploring the tunability of unstable regions and bifurcation responses. Further, the influences of size effects on modal interaction are also revealed. Results show saturation and permeation phenomena between the two modes. By tuning the boundary mass, flow velocity, and damping coefficient, mode coupling resonance can occur in the desired frequency band. Also, among the size effects, surface energy has the greatest significance, not only changing the resonance band, amplitude, but also changing the bifurcation topology.