Surface wave interactions with submerged horizontal viscoelastic sheets

Abstract

In this study, the surface wave interactions with submerged horizontal viscoelastic sheets of varying rheological properties are investigated both experimentally and analytically. In the experiments, we adopt the novel development in preparing finite length viscoelastic sheets with different rheological properties using oil-doped polydimethylsiloxane (PDMS) materials reported earlier in Sree et al. (2017, 2018). The wave interactions with the submerged viscoelastic sheets are quantified using ultrasonic sensors at different locations in terms of the reflection and transmission behavior. The experimental results show that the wave-sheet interactions are complex. The wave pattern at the submerged sheet region significantly depends on its rheological properties. For larger submergence, a standing wave pattern with primarily lower order modes develops along the sheet with a significant reduction of transmitted wave energy past the sheet region for shorter period waves. An almost complete cutoff (up to 99% reduction in wave energy transmission) occurs with the flexible sheet held close to the mean water level (MWL), while 50-90% reduction in wave energy transmission is recorded with the stiffer sheets. An analytical study is also carried out under the assumption of small amplitude water wave theory. The sheet is modeled based on the viscoelastic representation of the Voigt model and the analytical problem is solved using the domain matching technique. The profiles of surface wave as well as sheet displacement are well predicted by the analysis compared to the experimental measurements. However, the displacement amplitude is underestimated due to the fixed end conditions assumed. The predicted dispersion relation for the surface waves also agrees well with the experimental results for the shorter period waves, however larger discrepancies are observed with longer wave periods. In addition, the experimental results are up to one order of magnitude higher with respect to wave reflection. Thus, further improvement is needed in the future for the analysis to better represent the surface wave interactions with submerged viscoelastic sheets.