The ground cross-modal impedance as a tool to analyse multiple plates coupled to the ground
Etude du couplage de plusieurs plaques avec le sol à l'aide de l’impédance intermodale vibratoire
Abstract
This study aims at presenting the ground-structure interaction for plates involved in the tramway railroad. This analytical modelling allows us to take into account the vibration of several finite plates lying on a stratified ground. The plates interact with each other via the ground. The ground behaviour, in response to the plate vibration, is described thanks to Navier equations, the one of the flexural plates with the Kirchhoff-Loves equation. The plate vibrations are decomposed in modal series of the flexural plate modes. The ground vibrational field is classically decomposed with the Helmholtz potentials and transformed in the Fourier domain. This leads to the calculation of ground cross-modal impedances representing the influence of the underlying ground on each plate mode. Moreover since several plates are considered, these impedances take into account the interaction between the plates due to the propagation in the underlying ground. This allows us to explain the vibrational plate behaviour of a single plate and its effects on the ground free surface at a characteristic distance and to compare with the case where a companion plate is lying parallel and close to the first. Moreover, this modelling allows us to calculate the stress field under both plates and especially below the second one representing building foundations. The calculation of the stress field under the plates can be useful for who wants to proceed to vibration calculation in buildings, using finit element modelling or SEA method (Statistical Energy Analysis), since mechanical injected powers can be easily deduced.