# Dynamic Response Analysis of Asphalt Pavement under Pavement-Unevenness Excitation
## 1 Introduction  
Pavement unevenness acts as a medium between the vehicle and the pavement, and the vehicle generates random loads under its excitation, which increases the mechanical response within the pavement and accelerates the deterioration of the pavement serviceability. Therefore, the response of pavement under the excitation of pavement unevenness is a concern of road engineers. In the study of this kind of problem, scholars use the linear filtering white-noise method, the harmonic superposition method (or trigonometric series method), AR and ARMA methods, and the Poisson method to establish a pavement-unevenness model. Vehicles are simplified into quarter-vehicle models, half-vehicle models, and whole-vehicle models, and the road surface is assumed to be a beam or plate model on an elastic foundation [1, 2, 3, 4, 5]. Initially, scholars regarded the vehicle-road interaction as a weakly coupled problem which could be solved by sequential decoupling. Because the vertical deformation of the road surface is usually much smaller than the displacement of vehicle suspension and tire, and the vehicle-road coupling has little influence on vehicle vibration, scholars usually assume the road surface as a rigid body to solve the vehicle random load and then apply the random load to the road-surface model to solve the mechanical response of the road surface [6]. [PERSON] et al. [7] used the quarter-vehicle model to study the impactof heavy vehicles on the road surface and optimized the suspension of heavy vehicles based on the road-surface results. [PERSON] et al. [8] used the triple Fourier transform and mode superposition method to study the dynamic problem of infinite plates on the Winkler foundation under the action of vehicle dynamic load, and the results showed that the increase of pavement unevenness and vehicle wheelbase would lead to the increase of maximum deflection and stress. [PERSON] et al. [9] conducted an in-depth study on the dynamic response of Eulaberly beams on the Pasternak foundation under the influence of moving loads. [PERSON] et al. [10] conducted an in-depth study on the dynamic response of Winkler foundation thin plate under the influence of moving load and observed that the foundation stiffness, vehicle speed, and frequency would all affect the dynamic response of pavement. [PERSON] et al. [11] considered the vehicle load caused by pavement unevenness. The road surface was regarded as a Kirchhoff sheet, and the roadbed was made of elastic material with saturated holes. [PERSON] et al. [12] explored the finite integral transform approach for analytical thermal buckling solutions of composite thin plates with all edges rotationally restrained. [PERSON] et al. [13,14] simplified the vehicle as a four-degree-of-freedom, half-vehicle model and the asphalt pavement as an infinite double-layer Kirchhoff sheet on the Kelvin foundation. They solved the analytical solution of the dynamic response of the pavement through Fourier integral transformation. The effects of pavement unevenness, vehicle load, suspension stiffness, suspension damping, tire stiffness, and tire damping on the road's dynamic response were also discussed. In recent years, scholars have begun to think that vehicle-road interaction is a coupled system, and it is necessary to establish a coupling model to solve it. [PERSON] et al. [15] proposed a vehicle-road coupling model based on a quarter-vehicle model and pavement unevenness. [PERSON] et al. [16] used the Eulbernoulli beam pavement model to study a quarter-vehicle model and found that the coupling effect had more impact on the road-surface deflection than on the wheel displacement. [PERSON] et al. [17] studied the vibration problem of a vehicle-pavement coupled system of Timoshenko beams on a nonlinear foundation. [PERSON] et al. [18] discussed the dynamic response of vehicle-pavement systems based on the Eulabenouli beam model on elastic foundations, taking into account the viscoelastic properties of asphalt materials. [PERSON] et al. [19] and [PERSON] et al.