Parametric resonance of a cantilevered pipe conveying fluid subjected to distributed motion constraints

Pipes conveying fluid have been widely used in the fields of aerospace, mechanics, marine, hydraulic and nuclear engineering. The stability analysis, dynamic response and safety assessment of fluid-conveying pipes subjected to nonlinear constraints are particularly important for both engineering applications and scientific researches. Although the dynamical behaviors of fluid-conveying pipes subjected to single-point loose constraints have been discussed for four decades, the literature on the dynamics of fluid-conveying pipes subjected to distributed motion constraints is very limited. To obtain a better understanding of the dynamics of a cantilevered pipe conveying fluid subjected to distributed motion constraints, both cubic and modified trilinear spring models are employed in this study to describe the restraining force between the pipe and the motion constraints. This study is also concerned with the parametric resonance when the pipe is excited by an internal pulsating fluid. Firstly, the modified nonlinear equation of the pipe system was discretized via Galerkin's approach and solved using a fourth-order Runge-Kutta method. Via the Floquet theory, the nonlinear equation of motion was simplified to a linear one to calculate the parametric resonance regions versus the pulsating amplitude and frequency. Two representative values of mean flow velocity were employed to calculate the parametric resonance regions. Both the two values of mean flow velocity are assumed to be lower than the critical velocity for the cantilevered pipe system. Then, considering the geometric nonlinearity, the nonlinear dynamic responses focusing on the effect of external nonlinear restraining forces generated by the distributed motion constraints are discussed in detail. Results show that the stability regions of the nonlinear system agree well with that predicted by analyzing the linearized system. It is found that the distributed motion constraints would mainly affect the displacement amplitudes. Various oscillation types may arise when the pulsating frequency of the flow velocity is varied. Several bifurcation diagrams show that, however, a significant difference can be observed between the routes to chaos for the two constraint models, i. e., the pipe with a trilinear spring model can exhibit chaotic oscillations more easily than that with a cubic spring model. © 2019, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.