Dual-Boundary Mechanism of Shimmy over the Full Speed Range in Nose Landing Gear and Inerter-Based Shimmy Suppression Design

To overcome the limitation of conventional nose landing gear shimmy damper design, which is mainly based on the critical damping for torsional shimmy while neglecting the high-damping-side instability boundary, this study establishes a nonlinear shimmy dynamic model of a nose landing gear equipped with a hydraulic damper and an inerter-based suppression system. Hopf bifurcation analysis, numerical continuation, and energy-evolution analysis are employed to investigate the effects of damper, structural, and inerter parameters on the zero-shimmy region over the full speed range. The results show that the zero-shimmy damping interval is not governed by a single torsional critical damping value but is jointly bounded by the tire-induced torsional shimmy boundary on the low-damping side and the lateral or structural torsional shimmy boundary on the high-damping side. Thus, increasing damper damping is not always beneficial. Among the structural parameters, trail determines the existence of the zero-shimmy region, strut torsional stiffness mainly regulates the high-damping-side boundary, and rake angle provides local correction. With proper inertance and tuning-stiffness matching, the inerter-based system raises the upper critical damping by about 210% and improves low-speed shimmy suppression by transferring vibration energy to the damping branch through inertial coupling.