Scattering theory and cancellation of gravity-flexural waves of floating plates
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Preprint Posting Date2019-01-28
Permanent link to this recordhttp://hdl.handle.net/10754/660653
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AbstractWe 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.
CitationFarhat, M., Chen, P.-Y., Bagci, H., Salama, K. N., Alù, A., & Guenneau, S. (2020). Scattering theory and cancellation of gravity-flexural waves of floating plates. Physical Review B, 101(1). doi:10.1103/physrevb.101.014307
SponsorsThe authors thank anonymous referees for their useful comments that helped improve the presentation of this work. S.G. wishes to thank the Department of Mathematics at Imperial College London for a visiting position in the group of Prof. R.V. Craster in 2018-2019 (funded by EP-SRC grant EP/L024926/1).
PublisherAmerican Physical Society (APS)
JournalPhysical Review B