Mindlin cracked plates modelling and implementation in train-track coupled dynamics

Abstract

Nowadays, the widely constructed ballastless track in high-speed railways will inevitably suffer from localized damage cracks induced by complicate environmental effects, which would change its designed dynamic performance under train dynamic loads and further affect its service life and durability. To this end, a semi-analytical approach of the in-plane and the out of plane forced vibration for Mindlin plates with a side crack are derived, and is further implemented into the train-track coupled dynamic (TTCD) system which comprehensively considering nonlinear wheel-rail contact and 3D spatial flexibility of the cracked track slab. The dynamic partial differential equation of the cracked slab is derived by Hamilton principle and discretized by Galerkin method. Then the eigenvalues and forced vibrations of the cracked slabs for both in-plane and flexural vibrations are tackled utilizing a set of powerful trigonometric modified by special corner function, which can effectively explain the singularity of stress at the crack tip and the discontinuity of deformation on both sides of the crack. The eigenvalue analysis and mode shapes of the cracked plate mode in free boundary condition are compared with the finite element method to verify its accuracy. Meanwhile, the reliability of the proposed dynamics model is verified by comparing with the responses predicted by the co-simulation technology. Finally, the discrepancies of dynamic responses of the track slab with or without a side crack are analyzed, and the effects of various operation speeds and support stiffness on the dynamic behaviour of both slabs are revealed. Results indicates that the track slab with a side crack has significant distinctions on the slab dynamic signals in both time and frequency domains, and the amplitude amplification phenomenon occurs in some specific areas compared with the intact slab; The type-Ⅱ stress intensity factor (SIF) is more sensitive to train speeds, while the support stiffness is highly correlated to all types of SIFs. This work may contribute to the scientific maintenance and health monitoring of high-speed railway tracks.