Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non‐linear micropolar medium
In this paper we consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: we consider...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2017-09, Vol.97 (9), p.1064-1071 |
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| creator | Erofeev, V. I. Leontieva, A. V. Malkhanov, A. O. |
| description | In this paper we consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: we consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves. The dependences of the amplitude on the wave number and the relative rotational angle of the stationary rotation wave has been obtained.
The authors consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: they consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves.… |
| doi_str_mv | 10.1002/zamm.201600146 |
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The authors consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: they consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves.…</description><identifier>ISSN: 0044-2267</identifier><identifier>EISSN: 1521-4001</identifier><identifier>DOI: 10.1002/zamm.201600146</identifier><language>eng</language><publisher>Weinheim: Wiley Subscription Services, Inc</publisher><subject>bending‐torsion tensor ; Cosserat continuum ; Damping ; elastic rotational wave ; evolution of a wave ; Heat transfer ; longitudinal thermoelastic wave ; Longitudinal waves ; Nonlinear differential equations ; Ordinary differential equations ; Riemann wave ; Riemann waves ; Sound waves ; the micropolar medium ; Thermal conductivity ; Wave propagation</subject><ispartof>Zeitschrift für angewandte Mathematik und Mechanik, 2017-09, Vol.97 (9), p.1064-1071</ispartof><rights>2017 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</rights><rights>Copyright © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2786-52b16ae33c6c32714fc72ffd5c0c0aac1ffefc81afc33c67cafd2f41c90fa4093</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fzamm.201600146$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fzamm.201600146$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Erofeev, V. I.</creatorcontrib><creatorcontrib>Leontieva, A. V.</creatorcontrib><creatorcontrib>Malkhanov, A. O.</creatorcontrib><title>Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non‐linear micropolar medium</title><title>Zeitschrift für angewandte Mathematik und Mechanik</title><description>In this paper we consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: we consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves. The dependences of the amplitude on the wave number and the relative rotational angle of the stationary rotation wave has been obtained.
The authors consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: they consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves.…</description><subject>bending‐torsion tensor</subject><subject>Cosserat continuum</subject><subject>Damping</subject><subject>elastic rotational wave</subject><subject>evolution of a wave</subject><subject>Heat transfer</subject><subject>longitudinal thermoelastic wave</subject><subject>Longitudinal waves</subject><subject>Nonlinear differential equations</subject><subject>Ordinary differential equations</subject><subject>Riemann wave</subject><subject>Riemann waves</subject><subject>Sound waves</subject><subject>the micropolar medium</subject><subject>Thermal conductivity</subject><subject>Wave propagation</subject><issn>0044-2267</issn><issn>1521-4001</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNo9kL1OwzAURi0EEqWwMltiTrl2HKcZq4o_qRUDsLBYxrHBVWIHx6EqE4_AM_IkJG3V6d7z6dOV7kHoksCEANDrb1nXEwqEAxDGj9CIZJQkrKdjNAJgLKGU56forG1X0KcFSUcoPkUZrXcybHDl3buNXWmdrHD80KH2upJttAqv5ZdusXTlkO_Jmy0Ev7uA46bR2Lpt6Lz7-_mtrNMy4Nqq4BtfDasubVefoxMjq1Zf7OcYvdzePM_vk8Xj3cN8tkgUzac8yegb4VKnqeIqpTlhRuXUmDJToEBKRYzRRk2JNGro5EqakhpGVAFGMijSMbra3W2C_-x0G8XKd6H_rhWkoDnjwPOsbxW71tpWeiOaYOvehiAgBq1i0CoOWsXrbLk8UPoP9pVy0A</recordid><startdate>201709</startdate><enddate>201709</enddate><creator>Erofeev, V. I.</creator><creator>Leontieva, A. V.</creator><creator>Malkhanov, A. O.</creator><general>Wiley Subscription Services, Inc</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201709</creationdate><title>Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non‐linear micropolar medium</title><author>Erofeev, V. I. ; Leontieva, A. V. ; Malkhanov, A. O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2786-52b16ae33c6c32714fc72ffd5c0c0aac1ffefc81afc33c67cafd2f41c90fa4093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>bending‐torsion tensor</topic><topic>Cosserat continuum</topic><topic>Damping</topic><topic>elastic rotational wave</topic><topic>evolution of a wave</topic><topic>Heat transfer</topic><topic>longitudinal thermoelastic wave</topic><topic>Longitudinal waves</topic><topic>Nonlinear differential equations</topic><topic>Ordinary differential equations</topic><topic>Riemann wave</topic><topic>Riemann waves</topic><topic>Sound waves</topic><topic>the micropolar medium</topic><topic>Thermal conductivity</topic><topic>Wave propagation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Erofeev, V. I.</creatorcontrib><creatorcontrib>Leontieva, A. V.</creatorcontrib><creatorcontrib>Malkhanov, A. O.</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Erofeev, V. I.</au><au>Leontieva, A. V.</au><au>Malkhanov, A. O.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non‐linear micropolar medium</atitle><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle><date>2017-09</date><risdate>2017</risdate><volume>97</volume><issue>9</issue><spage>1064</spage><epage>1071</epage><pages>1064-1071</pages><issn>0044-2267</issn><eissn>1521-4001</eissn><abstract>In this paper we consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: we consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves. The dependences of the amplitude on the wave number and the relative rotational angle of the stationary rotation wave has been obtained.
The authors consider the nonlinear thermoelastic plane longitudinal waves and plane nonlinear elastic rotational waves in the model of a geometrically nonlinear micropolar continuum (Cosserat medium). The equation for longitudinal thermoelastic waves is studied in two extreme cases: they consider the medium with low and high thermal conductivity. It has been shown that in these cases the equation for longitudinal thermoelastic waves reduces to the known equations describing the classical Riemann waves and Riemann waves with damping. The peculiarities of propagation of these waves have been analyzed. The equation for rotational waves in the absence of thermoelastic effects, is reduced to a nonlinear ordinary differential equation of the second order for stationary waves. It has been demonstrated that the equation has solutions in the supersonic case in the form of periodic waves.…</abstract><cop>Weinheim</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/zamm.201600146</doi><tpages>8</tpages></addata></record> |
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| subjects | bending‐torsion tensor Cosserat continuum Damping elastic rotational wave evolution of a wave Heat transfer longitudinal thermoelastic wave Longitudinal waves Nonlinear differential equations Ordinary differential equations Riemann wave Riemann waves Sound waves the micropolar medium Thermal conductivity Wave propagation |
| title | Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non‐linear micropolar medium |
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