Dynamic instability mechanism of post-buckled FG nanotubes transporting pulsatile flow: size-dependence and local/global dynamics

Abstract

For bistable structures such as post-bucked nanotubes, the size-dependence may have influences on both local and global dynamics. A local/global dynamic instability study of post-buckled nanotubes transporting pulsatile flow is conducted for the first time. To model the size-dependence of both the solid and fluid, the nonlocal strain gradient beam model coupled with surface elasticity is established, and the slip-flow model is introduced. The governing equations are derived based on Zhang-Fu's refined beam theory and von Kármán type geometric relationship. A new computation mode is developed that combines the two-step perturbation- Galerkin truncation, incremental harmonic balance method (IHBM), and Runge-Kutta method to obtain the stability boundary and amplitude-frequency bifurcation diagram. Also, the dynamic characteristics in different parameter regions are presented through displacement-time history diagram, phase diagram, Poincaré map and spectrum diagram. The complex motions of local attractor- two-well chaos- global snap-through, and hysteresis are observed. Subsequently, the nonlinear dynamic instability mechanism and the physical significance of stability boundary are revealed. It is revealed that the structural size-dependence have dual effects and may change the bifurcation topology, such as the change of motion from local attractor to global attractor, and from periodic motion to chaotic motion.