The Eigen Value Problem for Ice-Tongue Vibrations in 3-D and Thin-Plate Elastic Models
Y. V. Konovalov

Ice tongue forced vibration modeling is performed using a full 3D finite-difference elastic model, which also takes into account sub-ice seawater flow. The ocean flow in the cavity is described by the wave equation, therefore ice tongue flexures result from hydrostatic pressure perturbations in sub-ice seawater layer. Numerical experiments have been carried out for idealized rectangular and trapezoidal ice-shelf geometries. The ice-plate vibrations are modeled for harmonic in-going pressure perturbations and for high-frequency wave spectra of ocean swell. The spectra show distinct resonance peaks, which demonstrate the ability to model a resonant-like motion in the suitable conditions of forcing. The spectra and ice tongue deformations obtained by the developed full 3D model are compared with the spectra and the deformations modeled by the thin-plate Holds worth and Glynn model (1978). The main resonance peaks and ice tongue deformations in the corresponding modes, derived by the full 3D model, are in agreement with the peaks and deformations obtained by the Holds worth and Glynn model for relatively high aspect ratio (λ≥ 0.03). The relative deviation between the Eigen values (periodicities) in the two compared models is about 10%.

Full Text: PDF     DOI: 10.15640/jges.v4n2a5