Interaction between Viscoelastic Composite Beams and Vehicles by a Decoupled Method and Its Application in Engineering

Asphalt mixture is a viscoelastic material composed of aggregates, asphalt mastics, and voids. Meanwhile, the dynamic interaction between vehicle and bridge makes asphalt deck pavement in a more complex stress state, leading to premature damage such as cracks and ruts during its operation service period. Therefore, the effects of the viscoelastic characteristics of asphalt mixtures and vehicle-bridge interactions on the dynamic behaviors of deck pavement cannot be ignored. However, it is difficult to directly couple the viscoelastic properties of mixtures and vehicle-bridge interactions using the finite element method. Thus, this paper presents a decoupled method named the separation reconstruction algorithm. To theoretically verify whether the separate construction (SR) algorithm is consistent with the direct coupling (DC) algorithm, two dynamic system models of a Bernoulli–Euler composite beam under a moving vehicle are established, which correspond to the two algorithms. The kinematic equations of the system are derived and dispersed by the classical Galerkin method. The nonlinear integral term is simplified by the parity of the function, periodicity of the trigonometric function, and derivation. Then, the coupled equation can be rewritten in an ordinary differential form and solved with the Runge–Kutta method. Finally, it is proven that the proposed SR algorithm is basically consistent with the DC algorithm, and the SR algorithm is extended to practical engineering to study the coupling dynamic responses of viscoelastic deck pavement more accurately. Some new insight is gained by exploring the stress status of viscoelastic deck pavement under coupled conditions, which is conducive to more accurate evaluations of surface tensile effects induced by vehicle-bridge interactions.