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Scattering of oblique waves by a semi-infinite floating elastic plate within the framework of wave blocking

Abstract

Scattering of obliquely incident surface gravity wave by a semi-infinite floating elastic plate in the presence of lateral compressive force is studied within the framework of blocking dynamics in time-space. In the presence of lateral compressive force, primary and secondary wave blocking occur for two different values of time-period where the group velocity vanishes, whilst the phase velocity remains positive. Moreover, for each time-period within the limits of blocking points, three propagating wave modes exist in the plate-covered region, out of which two are related with positive group velocities and another one is associated with the negative group velocity. Further, all the three wave modes coalesce at the saddle point for a particular value of the compressive force. The energy identity for the scattering problem in the case of multiple propagating modes depends on the amplitude of the reflected and transmitted waves as well as the ratio of the energy transfer rate. In the case of obliquely incident waves, full-wave reflection occurs beyond a critical angle for a certain time-period whilst the same phenomenon occurs for certain incident angles before a critical time-period. Moreover, the scattering coefficients are having removable singularities at the blocking as well as saddle points. Besides, irregular pattern in plate deflection occurs due to the superposition of multiple propagating wave modes for a certain time-period within the blocking limits. The normal strain in the floating plate sheet has a certain oscillatory pattern for the time-period lying within the limits of blocking points. Surface plots for the scattering coefficients as well as plate deflection are demonstrated for various values of incident angle as well as compressive force. A comparison of various results in the case of small amplitude wave theory and shallow water approximation reveals the accuracy of the analysis in different cases.

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Acknowledgements

PN acknowledges the financial support received from the Department of Science and Technology, Government of India through award No: DST/CCP/CoE/79/2017(G). SB acknowledges the financial support received from the Council of Scientific and Industrial Research, New Delhi, India through the senior research fellowship vide file no: 09/081(1345)/2019-EMR-I.

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Correspondence to T. Sahoo.

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Negi, P., Boral, S. & Sahoo, T. Scattering of oblique waves by a semi-infinite floating elastic plate within the framework of wave blocking. J Eng Math 135, 1 (2022). https://doi.org/10.1007/s10665-022-10230-x

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  • DOI: https://doi.org/10.1007/s10665-022-10230-x

Keywords

  • Compressive force
  • Critical time-period
  • Critical wave angle
  • Flexural gravity waves
  • Incident wave angle
  • Wave blocking
  • Wave scattering