THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY
This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wav...
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description | This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author) |
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Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author)</description><language>eng</language><subject>CONTINUUM MECHANICS ; MATHEMATICAL ANALYSIS ; MECHANICAL WAVES ; Mechanics ; PROPAGATION ; SHOCK WAVES ; VISCOELASTICITY</subject><creationdate>1965</creationdate><rights>APPROVED FOR PUBLIC RELEASE</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,776,881,27546,27547</link.rule.ids><linktorsrc>$$Uhttps://apps.dtic.mil/sti/citations/AD0626293$$EView_record_in_DTIC$$FView_record_in_$$GDTIC$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>FISHER,George M C</creatorcontrib><creatorcontrib>BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS</creatorcontrib><title>THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY</title><description>This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author)</description><subject>CONTINUUM MECHANICS</subject><subject>MATHEMATICAL ANALYSIS</subject><subject>MECHANICAL WAVES</subject><subject>Mechanics</subject><subject>PROPAGATION</subject><subject>SHOCK WAVES</subject><subject>VISCOELASTICITY</subject><fulltext>true</fulltext><rsrctype>report</rsrctype><creationdate>1965</creationdate><recordtype>report</recordtype><sourceid>1RU</sourceid><recordid>eNrjZHAI8XBVcHF1doxU8HdTCPBx9HNVCHcMcw1W8PRTAMn5ePq5OgaBmP5BYDVhnsHO_q4-jsEhns6eIZE8DKxpiTnFqbxQmptBxs01xNlDN6UkMzm-uCQzL7Uk3tHFwMzIzMjS2JiANADVGydt</recordid><startdate>196510</startdate><enddate>196510</enddate><creator>FISHER,George M C</creator><scope>1RU</scope><scope>BHM</scope></search><sort><creationdate>196510</creationdate><title>THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY</title><author>FISHER,George M C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-dtic_stinet_AD06262933</frbrgroupid><rsrctype>reports</rsrctype><prefilter>reports</prefilter><language>eng</language><creationdate>1965</creationdate><topic>CONTINUUM MECHANICS</topic><topic>MATHEMATICAL ANALYSIS</topic><topic>MECHANICAL WAVES</topic><topic>Mechanics</topic><topic>PROPAGATION</topic><topic>SHOCK WAVES</topic><topic>VISCOELASTICITY</topic><toplevel>online_resources</toplevel><creatorcontrib>FISHER,George M C</creatorcontrib><creatorcontrib>BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS</creatorcontrib><collection>DTIC Technical Reports</collection><collection>DTIC STINET</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>FISHER,George M C</au><aucorp>BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS</aucorp><format>book</format><genre>unknown</genre><ristype>RPRT</ristype><btitle>THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY</btitle><date>1965-10</date><risdate>1965</risdate><abstract>This paper is the sequel to AD-604 661 in which we have derived a necessary propagation condition governing the wavespeeds with which shocks and all higher order singular surfaces must propagate in a material subject to linear viscoelastic behavior. Of obvious interest is the manner in which the wave front varies with time. This subject, in the case of nonlinear, one-dimensional acceleration waves, has been treated by Coleman and Gurtin. Their work on general materials with memory includes onedimensional linear viscoelastic wave propagation as a special case. They show that when the stressstrain law is non-linear, the strength of an acceleration wave may either grow or decay; but it always decays in the linear theory providing the initial slope of the relaxation function is negative. These same results were established simultaneously by Varley for a slightly less general constitutive assumption (a constitutive equation of integral type), but for more general motions (plane, cylindrical, and spherical waves). Chen has also treated this problem. (Author)</abstract><oa>free_for_read</oa></addata></record> |
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subjects | CONTINUUM MECHANICS MATHEMATICAL ANALYSIS MECHANICAL WAVES Mechanics PROPAGATION SHOCK WAVES VISCOELASTICITY |
title | THE DECAY OF PLANE WAVES IN THE LINEAR THEORY OF VISCOELASTICITY |
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