Scattering theory and cancellation of gravity-flexural waves of floating plates
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2020-01-28Preprint Posting Date
2019-01-28Submitted Date
2019-05-01Permanent link to this record
http://hdl.handle.net/10754/660653
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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.101.014307Sponsors
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 BarXiv
1901.09733Additional Links
https://link.aps.org/doi/10.1103/PhysRevB.101.014307ae974a485f413a2113503eed53cd6c53
10.1103/PhysRevB.101.014307