A Discrete Structural Model for Spinning Pipes Conveying Fluid: Hencky Bar-Chain Approach

A discrete structural model for the dynamic analysis of rotating pipes conveying fluid is presented based on the Hencky bar-chain discretization method. The continuous pipe structure is approximated as a chain of rigid segments interconnected by rotational springs and dampers that concentrate the bending flexibility at discrete joints. Two kinematic formulations are developed and compared. In the relative coordinate formulation, each segment orientation is measured with respect to the local frame of the adjacent segment, while in the absolute coordinate formulation all segments are referenced directly to the rotating base frame. The governing equations of motion are derived using Lagrangian mechanics, accounting for gyroscopic coupling, structural damping, and geometric nonlinearity. Convergence studies demonstrate that the discrete model systematically approaches the continuous solution as the number of segments increases. The absolute formulation exhibits superior computational efficiency, achieving excellent agreement with continuous finite-element-based Galerkin predictions using only fifteen segments. Linear stability analysis reveals critical parameter combinations in the rotational-speed–flow-velocity plane, while nonlinear bifurcation analysis captures post-critical equilibrium branches and dynamic instabilities. The proposed Hencky bar-chain framework provides an efficient alternative to continuum-based discretization schemes for predicting structural stability boundaries, natural frequencies, and nonlinear dynamic response of rotating tubular structures subjected to internal flow, with applications in turbomachinery, aerospace propulsion systems, and flexible piping networks.