Publications

Mohapatra, S.C. and Guedes Soares, C. (2016), “Interaction of surface gravity wave motion with elastic bottom in three-dimensions”, Applied Ocean Research, Vol. 57, pp. 125-139

In the present paper, a three-dimensional hydroelastic model is developed to deal with the problems of surface gravity wave motion over an elastic bed in the presence of compressive force under linearized small amplitude water wave theory in finite water depth. The elastic bottom bed is modelled as a thin elastic plate which is based on the EulerBernoulli beam equation. The progressive wave characteristics in the presence of elastic bottom are analyzed in both the cases of deep and shallow water waves. Also, the long wave equation associated with surface gravity wave motion with elastic bottom under shallow water approximation is derived in a direct manner and the results derived based on the small amplitude wave theory in finite water depth are compared. Green’s function is derived in three-dimensions using the fundamental source potentials. Fourier-type expansion formula and corresponding orthogonal mode-coupling relations for the velocity potentials associated with surface gravity wave motion with elastic bottom are derived in three-dimensions. The application of the expansion formula is illustrated by demonstrating specific physical problems which will play significant role in the analysis of wave-structure interaction problems arising in ocean engineering. The effects of elastic bottom on surface gravity waves are analyzed by presenting several numerical results on reflection wave amplitudes in different cases. Further, the velocity potentials associated with free motions and free oscillations in a basin of closed and semi-infinite length with elastic bed in three-dimensions are discussed in specific cases.

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