Vibration analysis of a beam on a layered transversely isotropic unsaturated subgrade subjected to a moving load - Ye, Zi; Ai, Zhi Yong; Chen, Yonghui; Chen, Long (Applied mathematical modelling, 2023)
•Governing equations of the beam are established by euler-bernoulli and dynamic unsaturated soil theories.•Equivalent stiffness of the subgrade is obtained in transformed domain based on compatibility conditions.•Solution of the beam-subgrade system is acquired by introducing the inverse fourier transform.•Performance of the beam on unsaturated subgrade due to moving load and the variation of saturation is evaluated. Performance evaluation of the beam subject to the variation of saturation change of the subgrade is of significance to the optimal design of the high speed railway (HSR). This study proposes a mathematical modelling to describe the dynamic interaction between a beam and a layered transversely isotropic unsaturated subgrade. Based on the Euler-Bernoulli theory and the dynamic unsaturated soil theory, governing equations of this mathematical model are established. With the aid of the precise integration method, Fourier transform and compatibility conditions, the equivalent stiffness of the subgrade is obtained in the transformed domain. Introducing the equivalent stiffness into the beam motion equation, the dynamic solution of the beam-subgrade system is acquired by further introducing the inverse Fourier transform. After verifying the correctness of this theory, a series of numerical examples are provided to discuss the parametric sensitivity.