Stability of vertically and extensible cantilevered pipes conveying fluid under the effects of different slenderness ratio and gravity

Considering the influences of the rotational inertia and shear variables, the dynamical mathematical model for the vertically and extensible cantilevered pipes conveying fluid was established, and analyzed the stability of cantilevered pipes under different gravity and slenderness ratio. Based on the geometrically exact beam theory obtained the structural stiffness matrix of the cantilevered pipe, derived cantilevered pipes expression of the elastic potential energy. An extended Hamilton's principle was applied to establish a plane dynamic control equation for the cantilevered pipe, which includes the coupling between axial displacement, lateral displacement, and angular displacement. The weak form quadrature element method was used to discretize the dynamic control equation, then analyzed the variation under the different slender ratios and gravity by the numerical results.