Dynamics of a cantilevered fluid-conveying straight pipe with centrosymmetric rib plates installed at its fixed end

Abstract

Rib plates are often used for improving load-bearing capacity, to study the influences of centrosymmetric rib plates installed at the fixed end on the dynamics of a cantilevered fluid-conveying straight pipe, the governing equation is deduced based on D’Alembert principle at first, during this process, the centrosymmetric rib plates are equivalently replaced by the combination of a series of linear and torsional springs whose stiffness coefficients are formulated according to thin plate bending theory. Then Galerkin method is used to discretize the above governing equation, where the shape functions are just the mode functions of cantilevered Euler-Bernoulli straight beam deduced by differential transformation method, the expressions of eigenfunction for flow-induced vibration and steady-state displacement response for forced vibration are obtained subsequently. Numerical experiments of a real water-supplying pipe are carried out, some conclusions never mentioned in published literatures are drawn. The same dynamic problems for other kinds of straight pipes and for curved pipes possessing one clamped end are also discussed. The investigation has reference meaning for optimal design of rib plates in aspects of geometric sizes and materials, also for optimal design of supporting formats of fluid-conveying pipes.