Aircraft-runway dynamic interaction has been studied in three separate strands: coupled aircraft-pavement models that linearize the aircraft, stochastic pavement-response models that equivalent-linearize the strongly nonlinear landing gear and tire, and nonlinear oleo-pneumatic landing-gear models that treat the runway as a prescribed roughness input rather than a coupled structure. No existing work combines all three ingredients. The open problem is to formulate and solve a fully coupled nonlinear stochastic aircraft-pavement model in which genuinely nonlinear landing-gear dynamics interact two-way with the pavement structure while runway roughness and aircraft parameters (weight, gear, tire characteristics) are random, and to determine how this interaction governs pavement dynamic load coefficients, deflection and strain, and fatigue life or allowable load cycles relative to linearized and uncoupled treatments.

Background

When an aircraft lands and taxies, pavement surface roughness excites vertical vibration of the aircraft, and the aircraft in turn applies dynamic loads to the pavement. Two communities model this interaction with different simplifications. Pavement engineers abstract the aircraft to a small rigid-mass system: Li and Guo (2022) coupled a two-degree-of-freedom (2-DOF) aircraft model — a suspension mass and a non-suspension mass — to a rigid pavement represented as a finite-length Euler-Bernoulli beam (the standard slender-beam bending model) resting on a Pasternak foundation (a soil model in which the pavement is supported by a dense array of springs plus a shear layer transmitting shear between adjacent points). They showed the coupling significantly changes the dynamic load coefficient (DLC, the ratio of the fluctuating to the mean wheel load) and the pavement vertical displacement compared with treating the pavement as a fixed support. A related line adds randomness: Liu et al. (2022) analyzed a coupled 2-DOF aircraft/asphalt-runway system under roughness modeled as a random process, using the pseudo excitation method (a frequency-domain technique that converts a random-excitation problem into deterministic harmonic analyses), and Liu et al. (2025) extended the coupled aircraft-runway model (6-DOF aircraft on a double-layer thin-plate runway) to random structural parameters via the probability density evolution method (PDEM, which evolves the probability density of the response directly, an order of magnitude cheaper than Monte Carlo simulation). Hou et al. (2026) made the aircraft parameters themselves random — aircraft weight, landing-gear, and tire characteristics — in a coupled aircraft-rigid-pavement stochastic model with measured roughness from three runways, finding that parameter randomness can flip pilot-station acceleration (PSA, the vibration acceptability metric at the cockpit) from acceptable to unacceptable and change the allowable number of pavement load cycles by up to 235%. Crucially, this stochastic line handles the landing gear and tire, which are strongly nonlinear, by equivalent (statistical) linearization — replacing nonlinear elements by linear ones matched in mean-square response, as stated explicitly in the group's earlier paper (Hou et al. 2023). Aircraft-dynamics researchers, by contrast, model the gear faithfully but drop the pavement structure: Sivakumar et al. (2021) simulated landing on random runways with a nine-degree-of-freedom (9-DOF) nonlinear model including heave, pitch, and roll of the airframe and the vertical and longitudinal motions of the gears, with nonlinear air-spring stiffness of the oleo-pneumatic shock absorber (a strut whose stiffness comes from compressed gas), orifice (velocity-dependent) oleo damping, and nonlinear tire stiffness and damping — but the runway enters only as a prescribed random roughness profile (a nonstationary random process during touchdown), not as a vibrating structure. Similar nonlinear-stochastic gear studies without pavement coupling include Zhang, Nie, and Zhu (2010) and Lyu et al. (2026), and deterministic coupled finite-element aircraft-runway models (Wani and Nallasivam 2025; Huo et al. 2025 on snow runways) remain linear. Thus three ingredients — genuine time-domain gear nonlinearity, two-way structural coupling, and joint randomness in roughness and aircraft parameters — have never been combined, and their interaction's effect on the pavement-side quantities that matter for runway design (DLC, deflection and strain, fatigue life expressed as allowable load cycles, governed by accumulated damage under repeated dynamic loads) is unknown.

Problem Statement

Formulate and analyze a fully coupled nonlinear stochastic aircraft-pavement interaction model in which: (i) the landing gears are represented in the time domain with their genuine nonlinear elements — oleo-pneumatic air-spring stiffness, velocity-dependent orifice damping, and nonlinear tire stiffness and damping — for the landing and taxiing phases; (ii) the pavement is a deformable structure (e.g., a plate or beam on an elastic or two-parameter foundation) two-way coupled to the gears through tire-pavement contact on a randomly rough profile, not a prescribed kinematic input; and (iii) runway roughness and the aircraft parameters (weight, landing-gear, and tire characteristics) are modeled as random. The problem is to determine how this fully nonlinear, fully coupled, stochastic interaction governs the pavement-side quantities used in runway design and evaluation — dynamic load coefficients, pavement deflection and strain, and fatigue life or allowable load cycles — and to quantify how much the linearized coupled treatments (equivalent-linearized gear on a coupled structure) and the uncoupled nonlinear gear treatments (nonlinear gear on a fixed roughness input) misestimate these quantities.

References

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