Hopf Bifurcation of a Standing Cantilever Pipe Conveying Fluid with Time Delay

In this article, the dynamical behavior of a standing cantilever pipe conveying fluid is investigated with time − delay. By applying piezoelectric materials and considering delay voltage, motion equation built motion-limiting constraints elastic support. The discretized into ordinary differential equations by Galerkin method. A stability analysis equilibrium point three parameters obtained. system will lose at generate Hopf branches. central manifold theorem canonical type theory are used to study branching directions period solutions. Finally, numerical results validate theoretical analysis.