Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section

In this work, the longitudinal wave propagation in stressed rock with variable cross-section is investigated analytically. Considered the stress-sensibility of dynamic elastic modulus and the viscosity of rock, a modified viscoelastic stress-strain relationship is established. Based on the continuit...

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Main Authors: Wei Yuan, Jiefang Jin, Zhongqun Guo, Yue Wu
Format: Article
Language:English
Published: Frontiers Media S.A. 2019-10-01
Series:Frontiers in Earth Science
Subjects:
Online Access:https://www.frontiersin.org/article/10.3389/feart.2019.00270/full
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spelling doaj-451f0969beb64f839cab957dd5e451eb2020-11-24T21:11:05ZengFrontiers Media S.A.Frontiers in Earth Science2296-64632019-10-01710.3389/feart.2019.00270495397Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-SectionWei Yuan0Jiefang Jin1Zhongqun Guo2Yue Wu3School of Architecture and Surveying Engineering, Jiangxi University of Science and Technology, Ganzhou, ChinaSchool of Architecture and Surveying Engineering, Jiangxi University of Science and Technology, Ganzhou, ChinaSchool of Architecture and Surveying Engineering, Jiangxi University of Science and Technology, Ganzhou, ChinaFaculty of Resource and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou, ChinaIn this work, the longitudinal wave propagation in stressed rock with variable cross-section is investigated analytically. Considered the stress-sensibility of dynamic elastic modulus and the viscosity of rock, a modified viscoelastic stress-strain relationship is established. Based on the continuity equation, motion equation and stress-strain relation equations, the wave propagation equation for a stressed rock with variable cross-section is obtained. The harmonic wave propagation is discussed in detail by calculating the attenuation coefficient in amplitude. The combined effects of static stress and geometry on the wave attenuation are analyzed. The results show that due to the variable static stress along the propagation path, the wave attenuation is space-dependent, and the distribution of attenuation coefficients may be remarkably different under different levels of static stress. The wave attenuation in a stressed rock with variable cross-section is also frequency-dependent, and the influence of static stress on the lower-frequency wave components is more obvious compared with that on the higher-frequency wave components. Comparing the wave attenuation among rocks with three different geometries, we conclude that the wave attenuation depends on actual normal static stress, the cross-sectional areas and the changing rates of cross-sectional area.https://www.frontiersin.org/article/10.3389/feart.2019.00270/fullwave propagationstressed rockvariable cross-sectionwave equationattenuation coefficient
collection DOAJ
language English
format Article
sources DOAJ
author Wei Yuan
Jiefang Jin
Zhongqun Guo
Yue Wu
spellingShingle Wei Yuan
Jiefang Jin
Zhongqun Guo
Yue Wu
Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
Frontiers in Earth Science
wave propagation
stressed rock
variable cross-section
wave equation
attenuation coefficient
author_facet Wei Yuan
Jiefang Jin
Zhongqun Guo
Yue Wu
author_sort Wei Yuan
title Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
title_short Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
title_full Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
title_fullStr Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
title_full_unstemmed Theoretical Analysis of Longitudinal Wave Attenuation in a Stressed Rock With Variable Cross-Section
title_sort theoretical analysis of longitudinal wave attenuation in a stressed rock with variable cross-section
publisher Frontiers Media S.A.
series Frontiers in Earth Science
issn 2296-6463
publishDate 2019-10-01
description In this work, the longitudinal wave propagation in stressed rock with variable cross-section is investigated analytically. Considered the stress-sensibility of dynamic elastic modulus and the viscosity of rock, a modified viscoelastic stress-strain relationship is established. Based on the continuity equation, motion equation and stress-strain relation equations, the wave propagation equation for a stressed rock with variable cross-section is obtained. The harmonic wave propagation is discussed in detail by calculating the attenuation coefficient in amplitude. The combined effects of static stress and geometry on the wave attenuation are analyzed. The results show that due to the variable static stress along the propagation path, the wave attenuation is space-dependent, and the distribution of attenuation coefficients may be remarkably different under different levels of static stress. The wave attenuation in a stressed rock with variable cross-section is also frequency-dependent, and the influence of static stress on the lower-frequency wave components is more obvious compared with that on the higher-frequency wave components. Comparing the wave attenuation among rocks with three different geometries, we conclude that the wave attenuation depends on actual normal static stress, the cross-sectional areas and the changing rates of cross-sectional area.
topic wave propagation
stressed rock
variable cross-section
wave equation
attenuation coefficient
url https://www.frontiersin.org/article/10.3389/feart.2019.00270/full
work_keys_str_mv AT weiyuan theoreticalanalysisoflongitudinalwaveattenuationinastressedrockwithvariablecrosssection
AT jiefangjin theoreticalanalysisoflongitudinalwaveattenuationinastressedrockwithvariablecrosssection
AT zhongqunguo theoreticalanalysisoflongitudinalwaveattenuationinastressedrockwithvariablecrosssection
AT yuewu theoreticalanalysisoflongitudinalwaveattenuationinastressedrockwithvariablecrosssection
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