Multi-frequency blocking effects by multiple vertical cylinders designed using combination grating theories

A novel waveguide type breakwater has been developed based on wave space modulation and grating control technologies. The waveguide to the distribution of wave field is analyzed with the boundary integral equation to study the blocking effects by multiple vertical cylinders designed based on the combination grating theories. For the bottom mounted multiple vertical cylinders scattering problems, the Helmholtz equations with Neumann boundary conditions are solved using boundary integer equation (BIE) method. The proposed model has been successfully validated through a comparison with Thompson et al.‘s results. Three cases consisted of 57 vertical cylinders with same radius: [a] linear topology with same spacing using multi-slit gratings conditions, [b] sinusoidal topology with same longitudinal projection spacing designed by multi-slit grating and sinusoidal grating conditions and [c] linear topology with unstructured spacing. Numerical results illustrate that case [b] has better blocking effect than the others not only for short period waves but also for medium or long period waves using combination grating theories. To the best of authors' knowledge, this is the first work devoted to presenting thorough combination grating theories using the topology control in multiple cylinders. This paper opens up a new field of mathematical analysis on wave barrier designs.