A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.