TY - GEN
T1 - The vertical mode method in a problem of hydroelastic waves generated by an external load
AU - Sibiryakova, Tatyana
AU - Shishmarev, Konstantin
AU - Zavyalova, Kristina
AU - Korobkin, Alexander
N1 - Funding Information:
This work was carried out according to project MK-204.2020.1 "Initial-boundary value problems for equations of fluid motion in poroelastic media and their application in the dynamics of snow-ice cover" with the support of a grant from the President of the Russian Federation.
Publisher Copyright:
© 2021 Author(s).
PY - 2021/12/6
Y1 - 2021/12/6
N2 - Two-dimensional problem of the response of an ice cover to an applied external load is considered. The ice cover is modeled as a thin elastic plate. The fluid under the plate is incompressible, inviscid and is of finite depth. The external load has a given shape and does not move. Amplitude of the load oscillates at a given frequency. The deflections of the ice have the form of standing waves far away from the load. The problem is solved using the Green's function and the method of vertical modes. The eigenvalues of the vertical modes are the roots of the dispersion relation for hydroelastic waves propagating along the plate. The contribution of each type of roots to the formation of the ice deflections is studied. It is shown that the ice deflections for an elastic plate approximate the ice deflections for a porous plate with low porosity.
AB - Two-dimensional problem of the response of an ice cover to an applied external load is considered. The ice cover is modeled as a thin elastic plate. The fluid under the plate is incompressible, inviscid and is of finite depth. The external load has a given shape and does not move. Amplitude of the load oscillates at a given frequency. The deflections of the ice have the form of standing waves far away from the load. The problem is solved using the Green's function and the method of vertical modes. The eigenvalues of the vertical modes are the roots of the dispersion relation for hydroelastic waves propagating along the plate. The contribution of each type of roots to the formation of the ice deflections is studied. It is shown that the ice deflections for an elastic plate approximate the ice deflections for a porous plate with low porosity.
UR - http://www.scopus.com/inward/record.url?scp=85122162899&partnerID=8YFLogxK
U2 - 10.1063/5.0073826
DO - 10.1063/5.0073826
M3 - Conference contribution
AN - SCOPUS:85122162899
T3 - AIP Conference Proceedings
BT - Numerical Methods for Solving Problems in the Theory of Elasticity and Plasticity, EPPS 2021
A2 - Fomin, Vasily
A2 - Buzyurkin, Andrey
PB - American Institute of Physics Inc.
T2 - 27th Conference on Numerical Methods for Solving Problems in the Theory of Elasticity and Plasticity, EPPS 2021
Y2 - 5 July 2021 through 9 July 2021
ER -