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Diffraction by a rigid strip in a plate modelled by Mindlin theory.

¹Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences

|December 28, 2020

Summary

This study analyzes flexural wave scattering by a rigid strip in a Mindlin plate. A novel quadrature method solves the resulting Wiener-Hopf equations, yielding diffraction coefficients and low-frequency approximations.

Keywords:

Mindlin plate diffraction flexural waves matrix Wiener–Hopf method

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Area of Science:

Solid Mechanics
Wave Propagation
Plate Theory

Background:

Mindlin plate theory accounts for shear deformation.
Plane flexural waves are fundamental in structural dynamics.
Rigid strip inclusions present complex scattering problems.

Purpose of the Study:

To analyze the scattering of plane flexural waves by a semi-infinite rigid strip in a Mindlin plate.
To develop and apply a method for solving the associated Wiener-Hopf equations.
To compute the far-field diffraction coefficient and investigate low-frequency behavior.

Main Methods:

Formulation of three Wiener-Hopf equations based on boundary conditions.
Decoupling of one equation, leaving a scalar and a 2x2 matrix problem.
Solution of the matrix problem using a quadrature-based method.

Main Results:

The far-field diffraction coefficient was calculated.
Numerical results for the scattering problem are presented.
The low-frequency limit was shown to reduce to the Kirchhoff model.

Conclusions:

A robust method for solving the Wiener-Hopf equations for this problem was demonstrated.
The study provides valuable insights into wave scattering in Mindlin plates.
The findings are relevant for understanding structural response to dynamic loads.