Fractional derivative modeling for dynamic response of layered viscoelastic media under moving time-harmonic loads

Abstract

The dynamic response of layered viscoelastic media under moving time-harmonic loads is an important issue in transportation geotechnics. However, the existing research often has limitations in terms of the constant creep rate or time-independent relaxation modulus. To fill this gap, this study introduces a fractional Zener model to simulate the viscoelastic properties of media. First, the governing equations of the elastic medium are converted into ordinary differential equations using an integral transform. Subsequently, by introducing the fractional viscoelastic model and extended precise integration method, a solution to the dynamic response of layered viscoelastic media under moving time-harmonic loads is obtained. After comparing the results with those in existing literature, the reliability and accuracy of the proposed solution were verified. Finally, a parametric analysis was performed to further explore the influence of load velocity and fractional order on the dynamic response of the viscoelastic media.