Abstract
Surface gravity wave interaction with a semi-infinite floating elastic plate in the presence of multiple undulations has been studied under the assumption of linearized water wave theory and small amplitude structural response. The elastic plate is modeled using the Euler-Bernoulli beam equation, whilst the multiple undulations are categorized as an array of submerged trenches or breakwaters. The numerical solution obtained in finite water depth using the boundary element method is validated with the semi-analytic solution obtained under shallow water approximation. Bragg resonance occurs due to the scattering of surface waves by an array of trenches or breakwaters irrespective of the presence of the floating semi-infinite plate. The zero-minima in wave reflection occur when the width of the trench and breakwater is an integer multiple of 0.6 and 0.35 times wavelength, respectively, as the number of trenches or breakwaters increases. In contrast to trenches and breakwaters in isolation, non-zero minima in wave reflection occur in the presence of a semi-infinite plate. Moreover, the number of complete cycles in trenches is less than the number of complete cycles in breakwaters, irrespective of the presence of the floating structure. The frequency of occurrence of zero minimum in wave reflection is reduced in the presence of the semi-infinite plate, and wave reflection increases with an increase in rigidity of the floating plate. Time-dependent simulation of free surface displacement and plate deflection due to multiple undulations of seabed in the presence of the semi-infinite floating plate is demonstrated in different cases.
Highlights
One of the challenges due to global warming is the rise in sea level contributing to coastal flooding and erosion
Bragg scattering by multiple submerged trenches/breakwaters in isolation has been studied in the presence of a semi-infinite plate under the assumption of linear small amplitude water wave theory, as well as structural response in finite water depth, using boundary element method (BEM)
The closed-form analytical solution is obtained under the premise of linear long wave theory by matching the continuity of pressure and mass flux at the interface boundaries
Summary
One of the challenges due to global warming is the rise in sea level contributing to coastal flooding and erosion. Studied the scattering of surface gravity waves by a semi-infinite floating elastic plate and analyzed the role of different types of edge conditions on the vibration of the floating structure. Kar et al [18] studied the scattering of long gravity waves due to an array of submerged trenches and breakwaters in the presence of an array of floating flexible plates. Bragg scattering of surface gravity waves by an array of submerged trenches and breakwaters is analyzed in the presence of a semi-infinite floating flexible plate. Energy identity is derived and used to check the accuracy of the results Various physical quantities, such as reflection coefficients, plate deflection, and free surface elevations, are computed for analyzing the effects of different physical parameters associated with wave motion, trenches, breakwaters, and floating semi-infinite plate. The wave packets interacting with an array of trenches or breakwaters are demonstrated in the presence/absence of the semi-infinite plate
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