Dynamic Stability and Vibration Analysis of Spinning Rockets Modeled as Free–Free Thin-Walled Composite Beams

This study investigates the vibration and dynamic stability characteristics of flexible spinning rockets subjected to thrust during powered flight. The rocket is modeled as a free–free thin-walled composite beam subjected to a constant follower force, accounting for spin-induced gyroscopic coupling and material anisotropy. The governing equations of motion are derived based on thin-walled composite beam theory, and the Galerkin method is employed to solve the resulting eigenvalue problem. A Circumferential Uniform Stiffness laminate configuration is adopted to capture the coupled vertical–lateral bending behavior, and stability boundaries for divergence and flutter are established through parametric analyses involving ply angle orientation, rotary inertia, aspect ratio, and thickness ratio. The results reveal that ply angle is the dominant factor governing stability, with higher orientations markedly increasing the critical flutter load and corresponding spin speeds. Rotary inertia introduces strong gyroscopic coupling that reduces flutter loads but does not affect divergence thresholds, while geometric parameters such as aspect and thickness ratios exhibit secondary yet notable effects. Overall, the inclusion of rotary inertia and ply angle variation is shown to be essential for accurate and conservative prediction of flutter boundaries.