Nonlinear Dynamic Modeling and Parametric Analysis of Oleo-Pneumatic Shock Absorbers with Contact-Separation Dynamics for Aircraft Landing on Uneven Runways

Purpose The dynamic response of aircraft during landing on uneven runways is critical to structural integrity and passenger safety, especially under conditions involving impact, nonlinear energy dissipation, and intermittent contact. Existing models commonly assume continuous tire-runway contact, limiting their ability to capture separation and impact-driven dynamics. This study develops a nonlinear two-degree-of-freedom model of an oleo-pneumatic shock absorber system to capture contact-separation transitions explicitly. Methods The proposed model incorporates polytropic gas compression, velocity-dependent hydraulic damping, nonlinear tire behavior, and frictional effects. A Lagrange multiplier formulation enforces piston-cylinder contact constraints, while a unilateral contact law represents tire-runway separation. The governing equations are solved in the time domain using an adaptive Runge-Kutta scheme with state-dependent contact activation. Parametric analyses evaluate the influence of initial gas pressure, damping level, polytropic exponent, and orifice discharge coefficient on system response. Results The results show that gas pressure dominates system stiffness, with low pressure leading to large stroke amplitudes, piston-wall impacts, and increased risk of tire lift-off. Hydraulic damping governs transient attenuation, reducing oscillations while increasing settling time. Under runway excitation, coupled piston impact and contact loss generate force spikes associated with velocity discontinuities. A regime classification framework identifies safe and unsafe operating conditions based on separation and impact criteria. Conclusions The model provides a physically consistent and computationally efficient approach for predicting impact-separation dynamics under non-ideal conditions. However, the study is limited to numerical verification and does not establish quantitative safety thresholds.