Wave packets, signaling and resonances in a homogeneous waveguide
type: Item
instance of: scholarly article
title: Wave packets, signaling and resonances in a homogeneous waveguide
zbMATH Open document ID: 0922.73010
DOI: 10.1023/A:1007452811042
author: Leonid Brevdo
published in: Journal of Elasticity
publication date: 1999-10-18T00:00:00Z
review text: The author presents a fundamental study of a realistic dynamic model of the Earth crust. The Earth crust is assumed to be an infinite homogeneous thick plate whose upper surface is free whereas the lower one can be subjected to dynamic excitations. The associated mathematical problem is to find the displacement depending on \(z\) (directed towards the interior of the Earth), surface coordinate \(x\) and time \(t\). The initial perturbation is a displacement quasicompactly localized in space and in time. The author uses the Laplace and Fourier transforms and obtains asymptotic and approximate solutions. An essential feature of this study is the relevance of localized in space resonances due to multiple contributions of normal modes. It is worthy to say that the approach bases on the study of individual normal modes does not provide this phenomenon.
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74L05
Mathematics Subject Classification ID: 86A15
zbMATH DE Number: 1204384
zbMATH Keywords: Laplace transform
zbMATH Keywords: Fourier transform
zbMATH Keywords: dynamic model of Earth crust
zbMATH Keywords: infinite homogeneous thick plate
zbMATH Keywords: approximate solutions
zbMATH Keywords: localized in space resonances
zbMATH Keywords: multiple contributions of normal modes
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
full work available at URL: a:1007452811042
OpenAlex ID: W54274144
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description: scientific article; zbMATH DE number 1204384