Bifurcation behavior and chaotic self-sustained vibrations of cantilevered nanotube conveying fluid

Abstract

A beam model of geometrical nonlinear longitudinal-flexural self-sustained vibrations of nanotubes conveying fluid is obtained with account of nonlocal elasticity. The system of two nonlinear partial differential equations is derived to describe the nanotube’s self-sustained vibrations. The Galerkin method is applied to obtain the system of nonlinear ordinary differential equations. The harmonic balanced method is used to analyze the monoharmonic vibrations. The infinite sequence of the period-doubling bifurcations of the longitudinal-flexural self-sustained vibrations is observed numerically. The chaotic motions occur after these bifurcations. The multiharmonic self-sustained vibrations of the nanotube are analyzed. Significant longitudinal self-sustained vibrations of the nanotube are observed in this case. Such motions are not observed with macro-beams.