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Scattering theory and cancellation of gravity-flexural waves of floating plates

Abstract : We combine theories of scattering for linearized water waves and flexural waves in thin elastic plates to characterize and achieve control of water wave scattering using floating plates. This requires manipulating a sixth-order partial differential equation with appropriate boundary conditions of the velocity potential. Making use of multipole expansions, we reduce the scattering problem to a linear algebraic system. The response of a floating plate in the quasistatic limit simplifies, considering a distinct behavior for water and flexural waves. Unlike for similar studies in electromagnetics and acoustics, scattering of gravity-flexural waves results in a nonvanishing scattering cross-section in the zero-frequency limit, dominated by its zeroth-order multipole. Potential applications lie in floating structures manipulating ocean water waves.
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https://hal-amu.archives-ouvertes.fr/hal-03139952
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Submitted on : Friday, February 12, 2021 - 1:56:47 PM
Last modification on : Wednesday, November 3, 2021 - 5:54:59 AM
Long-term archiving on: : Friday, May 14, 2021 - 9:32:31 AM

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PhysRevB.101.014307.pdf
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M. Farhat, P.-y. Chen, H. Bagci, K. N Salama, A. Alù, et al.. Scattering theory and cancellation of gravity-flexural waves of floating plates. Physical Review B, American Physical Society, 2020, 101 (1), ⟨10.1103/PhysRevB.101.014307⟩. ⟨hal-03139952⟩

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