The determination of elastic parameters of a half-space using a monochromatic vibration field at the surface
type: Item
instance of: scholarly article
title: The determination of elastic parameters of a half-space using a monochromatic vibration field at the surface
zbMATH Open document ID: 0599.73024
DOI: 10.1016/0165-2125(87)90038-2
author: V. M. Markushevich
published in: Wave Motion
publication date: 1987-01-01T00:00:00Z
review text: The paper presents a method to determine Lamé parameters \(\lambda\), \(\mu\) and density \(\rho\) in a layered half-space, using monochromatic vibrations of its surface, excited by a harmonic source which is assumed to be known. The equations governing the vibrations are reduced to the Sturm-Liouville problem in scalar form for Love-type displacements, and in matrix form for the Rayleigh type. The scalar and matrix potentials of the Sturm-Liouville equations can be recovered from the corresponding impedance. Explicit formulas are given to construct the potentials by amplitudes and wavenumbers of normal (progressive) modes and attenuated standing waves. The potentials then are used to determine the elastic parameters and the density. The method can also be used for the acoustic equation.
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 74J15
zbMATH DE Number: 3968001
zbMATH Keywords: Lamé parameters
zbMATH Keywords: density
zbMATH Keywords: layered half-space
zbMATH Keywords: monochromatic vibrations of its surface
zbMATH Keywords: harmonic source
zbMATH Keywords: reduced to the Sturm-Liouville problem in scalar form for Love-type displacements
zbMATH Keywords: matrix form for the Rayleigh type
MaRDI profile type: Publication
full work available at URL: 0165-2125(87)90038-2
OpenAlex ID: W1999422992
cites work: Q3662696
cites work: Q3732061
cites work: Q3993487
description: scientific article; zbMATH DE number 3968001