Dynamic response of a floating flexible plate to a localised time-periodic and moving load

Abstract

Flexural-gravity waves generated by a time-periodic and moving external load on a floating flexible plate are studied. The floating flexible plate, similar to an ice sheet, is modelled using the Kelvin-Voigt model. The external load is represented as a localised pressure load. A complex dispersion relation involving the plate viscosity and in-plane compressive force is derived and analysed to obtain the criteria for the occurrence of wave blocking. The study reveals that no real roots of the dispersion relation exist in the presence of viscous damping, and no wave blocking occurs. However, the dispersion relation possesses multiple complex roots with very small imaginary parts for given values of frequency, load speed and compressive force. The viscoelastic plate response is derived using the Fourier transform method, yielding an integral with no singularities in the presence of plate viscosity. Two different mathematical approaches, the principal value theorem and the method of residues, are employed, followed by numerical techniques to analyse the viscoelastic plate response for different parameters. The study demonstrates a damped and non-uniform oscillatory plate response for a range of external load frequencies within the limit of blocking points. Additionally, a significantly higher amplitude in the plate response is observed for low-frequency loads when the load speed exceeds minimum phase velocity.