An edge moving load on an orthotropic plate resting on a Winkler foundation

Abstract

Steady-state motion of a bending moment along the edge of a semi-infinite orthotropic Kirchhoff plate supported by a Winkler foundation is considered. The analysis of the dispersion relation reveals a local minimum of the phase velocity, coinciding with the value of the group velocity, corresponding to the critical speed of the moving load. In contrast to a free plate, the bending edge wave on an elastically supported plate possesses a cut-off frequency, arising due to the stiffening effect of the foundation. It is shown that the steady-state solution of a moving load problem corresponds to a beam-like edge behaviour. This feature is then confirmed from the specialised parabolic-elliptic formulation, which is oriented to extracting the contribution of the bending edge wave to the overall dynamic response.