Nonlinear dynamics of viscoelastic fluid-conveying pipe installed within uniform external cross flow by pipe clamps

Nonlinear dynamic response of a viscoelastic fluid-conveying pipe excited by uniform external cross flow is investigated, which is installed by pipe clamps. A pipe clamp theoretical model is proposed for the actual pipe clamp instead of the commonly used simply supported or clamped boundary conditions. Based on the model, equivalent support stiffness and torsional stiffness are obtained from structure and material parameters of the pipe clamp. The vortex-induced lift force and the mean drag force are described by van der Pol oscillator model. The nonlinear equations of motion with the boundary conditions of different constraint stiffness are discretized by Differential Quadrature Method (DQM) and then solved by Runge-Kutta algorithm. The results are verified by Galerkin method for the pinned-pinned pipe, and by ANSYS for the pipe with two arbitrary constraint stiffnesses. The dependence of critical external fluid velocity upon constraint stiffness and pipe length is investigated. Moreover, the effects of support stiffness, torsional stiffness, internal fluid velocity, and viscoelastic coefficient on the amplitude response of the pipe are studied in detail. The influence of constraint stiffness on characteristics of lock-in region is elucidated. Consequently, pipe clamp spacing, material and structure parameters of the rubber mat can be designed to ensure the requirement of economy and safety, which are helpful to guide the layout and design of pipe clamps.