Gravity wave interaction with an articulate d submerge d plate resting on a Winkler foundation

Surface gravity wave interaction with an articulated flexible submerged plate in the pres-ence of lateral compressive force is investigated within the framework of blocking dynam-ics, assuming that the submerged plate is resting on a uniform Winkler foundation. The problem is studied considering small-amplitude plate response and linearised water wave theory in finite water depth. The loci of the dispersion relation reveal the occurrence of wave blocking in the submerged plate mode for a range of wave frequency and compres-sive force when the submerged plate is resting on a Winker foundation. However, in the absence of the Winkler foundation, no wave blocking occurs in the plate mode irrespec-tive of the values of compressive force, and plane wave propagation in plate mode does not happen for particular values of compressive force. Four propagating wavenumbers ex-ist within the blocking frequencies, of which one is in the surface mode, and others are in the submerged plate mode. Thus, to account for the four propagating wave modes, the existing solution approach for a pair of propagating wave modes is modified in an appro-priate manner within the limit of blocking frequencies. Consequently, the energy relation is obtained using Green's identity, in which the reflection and transmission coefficients are a combination of the amplitudes of different reflected and transmitted wave modes and the associated energy transfer rates. The reflection coefficient in the submerged plate mode jumps from one to zero for very small values of frequency due to the introduction of the Winkler foundation in the presence of compressive force. In addition, zero wave reflection occurs for a higher frequency range with an increase in the values of the Win-kler constant. Removable discontinuities are observed at the blocking and saddle points, whilst jump discontinuities occur in the reflection and transmission coefficients due to the change of incident wave mode within the blocking frequencies. Linear time-dependent displacements in surface and submerged plate modes are presented prior to the blocking limit. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The interaction between surface gravity waves and an articulated flexible submerged plate under lateral compressive force is studied. The study considers small-amplitude plate response and linearized water wave theory in finite water depth. It is found that wave blocking occurs in the submerged plate mode when the plate is resting on a Winkler foundation, but not in the absence of the foundation. Four propagating wavenumbers exist within the blocking frequencies, with one in the surface mode and the others in the submerged plate mode.