Axisymmetric resonant disturbances in a homogeneous wave guide
type: Item
instance of: scholarly article
title: Axisymmetric resonant disturbances in a homogeneous wave guide
zbMATH Open document ID: 0941.74023
DOI: 10.1016/S0997-7538(98)90505-8
author: Leonid Brevdo
published in: European Journal of Mechanics. A. Solids
publication date: 2000-08-07T00:00:00Z
review text: The author investigates the initial boundary-value stability problem for small localized axisymmetric disturbances in a homogeneous elastic wave guide, with free upper surface and the lower surface being rigidly attached to a half-space. The problem is formally solved by Laplace transform in time and by Hankel transforms of zero- and first-order in space. The author considers small three-dimensional localized perturbations in a linearly elastic isotropic layer of finite thickness and infinite horizontal extension. The analysis shows that axisymmetric resonant responses, with the growth of at least \(\sqrt t\), are present in a rather wide set of physically relevant wave guides, although all axisymmetric normal modes in any homogeneous wave guide are neutrally stable. The temporally resonant frequencies with the response of \(\sqrt t\) coincide with high-order temporally resonant frequencies with the response of \(t^{3/4}\) found in two-dimensional case. The abundance of temporally resonant frequencies in every homogeneous wave guide in the two-dimensional case is the basis for hypothesis put in the paper, i.e., that certain earthquakes can be triggered by a chain of events at the origin of which was a resonant response of a plate in the earth crust to a localized oscillation with a temporally resonant frequency. Since vibrations of low amplitude are always present in regions of seismic activity, the above hypothetical mechanism of triggering of earthquakes throught resonant growth can be of practical importance.
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 86A17
zbMATH DE Number: 1300271
zbMATH Keywords: stability
zbMATH Keywords: algebraically growing response
zbMATH Keywords: Hankel transform
zbMATH Keywords: initial boundary-value problem
zbMATH Keywords: small axisymmetric disturbances
zbMATH Keywords: homogeneous elastic wave guide
zbMATH Keywords: Laplace transform
zbMATH Keywords: temporally resonant frequencies
reviewed by: Vasile Marinca
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1300271