AI Article Synopsis
- The study presents a new method to derive generalized Wiener-Hopf equations (GWHEs) for wave motion in elastic materials located in angular regions, addressing scenarios where sources are infinitely localized.
- The approach is inspired by techniques used in electromagnetism and aims to fully develop a theoretical framework for GWHEs specific to elasticity.
- A first-order vector differential equation with a matrix dependent on the medium is introduced, allowing for easy derivation of functional equations and their application to practical boundary condition problems, particularly in elastic scattering.
Article Abstract
In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener-Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8753162 | PMC |
| http://dx.doi.org/10.1098/rspa.2021.0624 | DOI Listing |
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