Chongchong Liu, Xiaochuan Liu, Yan Xu
Conventional tire models for landing-gear shimmy analysis typically retain only one or two fixed lateral deformation modes, which limits their ability to capture the evolving nature of shimmy dynamics. To overcome this limitation, a coupled landing gear–tire shimmy model is developed to account for dynamic variations in tire lateral deformation modes. The proposed framework incorporates a delayed tire model to represent the spatial distribution of tire deformation and the nonlinear dynamics of the landing gear. By introducing a time delay to characterize the propagation of tire deformation waves, the governing partial differential equations are reduced to delay differential equations. The shimmy stability boundaries are then determined through Hopf bifurcation analysis. The model reproduces the key dynamic characteristics of a UAV landing-gear system and is validated against experimental results. In addition, comparative stiffness-coupling bifurcation analyses further reveal the limitations of conventional tire models. Parametric studies show that sufficient torsional stiffness is essential for stability, whereas maintaining the lateral bending frequency below the torsional frequency provides an effective and cost-effective strategy for shimmy suppression. This work extends the delayed tire model to aircraft landing-gear shimmy analysis and provides a new framework for improved dynamic design.