Bifurcation behavior of nonlinear pipes conveying pulsating flow. (English) Zbl 0717.73058
Summary: The nonlinear behavior of supported pipes conveying pulsating fluid is examined in the vicinity of subharmonic and combination resonances. The method of averaging is used to yield a set of autonomous equations. The autonomous, averaged equations are then examined to determine the bifurcation behavior of the system. It is found that for subharmonic resonance, the averaged equation loses its stability through a simple or double zero bifurcation depending on the damping parameter; whereas, for combination resonance, the averaged system loses its stability through a Hopf bifurcation giving rise to a periodic solution. Explicit results for the stability boundaries and bifurcation paths are obtained. Numerical results are plotted for pinned-pinned pipes.
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74P10 | Optimization of other properties in solid mechanics |
| 74H55 | Stability of dynamical problems in solid mechanics |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C29 | Averaging method for ordinary differential equations |
| 37-XX | Dynamical systems and ergodic theory |
