ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Diffraction by a rigid strip in a plate modelled by Mindlin theory | JoVE Visualize

Home
Research Domains
Mathematical Sciences

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

Ian Thompson¹

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

Proceedings. Mathematical, Physical, and Engineering Sciences|December 28, 2020

Related Experiment Videos

View abstract on PubMed

Summary

This study analyzes flexural wave scattering by a rigid strip in a Mindlin plate, presenting a method to solve the resulting Wiener-Hopf equations and calculate diffraction coefficients. Results align with the Kirchhoff model at low frequencies.

Area of Science:

Solid Mechanics
Wave Propagation
Plate Theory

Background:

Investigates plane flexural wave interaction with semi-infinite rigid strips in Mindlin plates.
Addresses complex boundary conditions leading to multiple Wiener-Hopf equations.

Purpose of the Study:

To solve the Wiener-Hopf equations governing wave scattering.
To calculate the far-field diffraction coefficient.
To analyze low-frequency behavior and its relation to the Kirchhoff model.

Main Methods:

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

Main Results:

The far-field diffraction coefficient is calculated.
Numerical results are presented for the scattering problem.
Demonstration of the reduction to the Kirchhoff model in the low-frequency limit.

Conclusions:

A method for solving the complex wave scattering problem is established.
The study provides insights into the behavior of flexural waves interacting with rigid inclusions.
The connection between Mindlin plate theory and the Kirchhoff model is clarified for low frequencies.

Keywords:

Related Concept Videos

Pure Mathematics

Partial Differential Equations

Diffraction By A Rigid Strip In A Plate Modelled By Mindlin Theory

matrix Wiener–Hopf method

Related Experiment Videos