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Area of Science:

  • Solid Mechanics
  • Wave Propagation
  • Materials Science

Background:

  • Structured plates with periodic elements exhibit unique wave phenomena.
  • Understanding wave localization is crucial for designing advanced materials and devices.

Purpose of the Study:

  • To investigate the localization and transmission of flexural waves in a plate with a semi-infinite array of rigid pins.
  • To analyze wave behavior at the interface between homogeneous and pinned regions.
  • To explore the connection between localized waves and flexural Bloch waves.

Main Methods:

  • Analysis of flexural wave propagation in a structured plate.
  • Identification and characterization of localized waves at the plate-pin interface.
  • Formal connection established with dispersion properties of flexural Bloch waves.

Main Results:

  • Localized flexural waves were identified and studied at the interface boundary.
  • A connection was made between localized waves and the dispersion properties of flexural Bloch waves.
  • Regimes of standing waves and Dirac-like points on dispersion surfaces were analyzed.
  • A novel half-grating problem yielded interesting wave solutions.

Conclusions:

  • The study provides new results on flexural wave localization and transmission in structured plates.
  • The findings contribute to the understanding of wave phenomena in phononic crystals and metamaterials.
  • The analysis of the half-grating problem opens new avenues for research in wave manipulation.