科研之友
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摘要
The dynamical modeling, multi-pulse orbits and chaotic dynamics of cantilevered pipe conveying pulsating fluid with harmonic external force are studied using the energy-phase method for the first time. The nonlinear geometric deformation of the pipe and the Kelvin constitutive relation of the pipe material are considered. The nonlinear governing equation of motion for cantilevered pipe conveying pulsating fluid is determined using Hamilton principle. The four-dimensional averaged equation in the case of primary parametric resonance-1/2 subharmonic resonance and 1:2 internal resonance is obtained by directly using the method of multiple scales and the Galerkin approach to the partial differential governing equation of motion for cantilevered pipe conveying pulsating fluid. From the averaged equation, the normal form theory is used to find the explicit formulas of normal form. Based on normal form obtained here, the energy-phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics of cantilevered pipe conveying pulsating fluid. The analysis of global dynamics indicates that the multi-pulse jumping orbits exist in the perturbed phase space of the averaged equation. Based on the averaged equation, the chaotic motions and the multi-pulse orbits for the cantilevered pipe are found by using numerical simulations. The results described above indicate the existence of chaos in the Smale horseshoe sense for cantilevered pipe conveying pulsating fluid. It has been concluded that it is dangerous to induce the chaotic vibrations of the pipes conveying pulsating fluid because the amplitudes of the chaotic vibrations are larger than those of the periodic motions.
