# Vibration Response Law of Aircraft Taxing under Random Roughness Excitation
## 1 Introduction  
The airport runway functions as a crucial support platform for aircraft during taxiing, takeoff, and landing. Owing to a combination of factors such as construction variability, external environment, aircraft loading, and other uncertainties, the pavement exhibits random roughness. Pavement roughness is the vertical deviation of the pavement surface relative to the ideal plane. When subjected to random roughness excitation, high-speed taxiing aircraft experience random vibrations, which can negatively impact passenger comfort, accelerate fatigue damage to aircraft components, cause dynamic damage to runway structures, and even compromise flight safety [1]. As a result, comprehending the vibration response patterns of aircraft under random roughness excitation is vital for optimizing aircraft structural design, ensuring runway structure safety, and maintaining operational safety standards. Numerous studies have demonstrated that road surface or pavement roughness can be characterized as an ergodic, steady Gaussian stochastic process with zero mean, and its statistical properties can be represented by power spectral density (PSD) [2]. In the field of road research, various roughness models have been developed using PSD through the analysis of measured road roughness data [3; 4; 5; 6; 7]. However, runway roughness studies are limited by the available data samples, resulting in few investigations into the power spectrum of runway roughness. For instance, [PERSON] proposed a PSD expression for airport pavement roughness based on measuring the relative elevation data of longitudinal sections at only two runways, which lacks representativeness [8]. Most researchers have directly adopted road surface roughness models when studying runway roughness [9; 10; 11; 12]. Nevertheless, this approach can introduce significant deviations in the analysis of runway roughness due to the considerable differences between runways and roads concerning structural forms and service object characteristics [13]. In aircraft vibration response research, the majority of scholars utilize measured or simulated pavement roughness samples for time-domain simulations. For instance, [PERSON] and [PERSON] calculated aircraft acceleration under measured roughness excitation using ProFAA and evaluated pavement roughness accordingly [14]. [PERSON] et al. simulated the pavement roughness curve with the harmonic superposition method and calculated the taxiing dynamic load of a four-degrees-of-freedom aircraft using the Full method [15]. [PERSON] et al. and [PERSON] et al. employed the filtered white noise method or harmonic superposition method to generate pavement roughness, and determined the dynamic load coefficient of the six-degrees-of-freedom (6-DOF) model at different speeds using Simulink [16; 17]. [PERSON] et al. used the cosine function as the roughness input and analyzed the superposition effect of aircraft vibration with automatic dynamic analysis of mechanical systems (ADAMS) [18]. [PERSON] et al. applied PSD to reconstruct runway roughness and investigated the aircraft taxiing dynamic load using ADAMS [19]. However, measured or simulated single roughness curves only represent pavement roughness excitation at a certain probability level during the runway's long-term service. Single deterministic time history analysis based on this does not adequately reflect the random vibration characteristics of the aircraft. To address this limitation, several researchers have conducted frequency domain analyses based on random vibration theory, establishing a direct correlation between the power spectrum input of pavement roughness and the power spectrum output of aircraft vibration response. For instance, [PERSON] and [PERSON] used the PSD method to analyze the vibration response of a simplified multiple-degrees-of-freedom aircraft under stationary random excitation [20]. [PERSON] solved the single-degree-of-freedom vibration problem of the aircraft using random vibration theory [21].