Nonlinear forced vibrations of supported pipe conveying fluid subjected to an axial base excitation

Abstract

The present work focuses on the nonlinear forced vibrations of a supported pipe conveying fluid under an axial base excitation, devoting to exploring the effects of internal flow velocity and axial base excitation on the nonlinear dynamical behaviors of the pipe. Based on Hamilton's principle, the nonlinear coupled governing equations of the pipe system are introduced and discretized into a set of coupled ordinary differential equations by the aid of a Galerkin method. The resulting equations are then solved by a fourth-order Runge-Kutta integration algorithm. Numerical results indicate that the excitation amplitude and internal flow velocity have a combined effect on the dynamic responses of the pipe. When the internal flow velocity is below the critical value for buckling instability, an axial base excitation with small, moderate or large amplitude can only induce oscillations of the pipe in the axial direction, while an axial excitation with very large amplitude, interestingly, could induce the oscillations of the pipe in both axial and transverse directions. When the internal flow velocity is beyond the critical value for buckling instability, however, an axial base excitation with small amplitude can make the pipe oscillate around a positive or a negative static/dynamic equilibrium position in a wide range of excitation frequencies. In addition, a strong axial base excitation with large amplitude can make the pipe conveying a supercritical fluid oscillate around both positive and negative equilibrium positions for relatively large excitation frequencies. Indeed, various dynamical behaviors including periodic, multi-periodic, quasi-periodic and chaotic oscillations can be observed in many cases.