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

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    Type
    Article
    Authors
    Farhat, Mohamed
    Chen, P. Y.
    Bagci, Hakan cc
    Salama, Khaled N. cc
    Alù, A.
    Guenneau, S.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2020-01-28
    Preprint Posting Date
    2019-01-28
    Submitted Date
    2019-05-01
    Permanent link to this record
    http://hdl.handle.net/10754/660653
    
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    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.
    Citation
    Farhat, 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
    Sponsors
    The 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).
    Publisher
    American Physical Society (APS)
    Journal
    Physical Review B
    DOI
    10.1103/PhysRevB.101.014307
    arXiv
    1901.09733
    Additional Links
    https://link.aps.org/doi/10.1103/PhysRevB.101.014307
    ae974a485f413a2113503eed53cd6c53
    10.1103/PhysRevB.101.014307
    Scopus Count
    Collections
    Preprints; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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