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ns1:datePublished "2014-09" ;
ns1:datePublishedReg "2014-09-01" ;
ns1:description "The differential equation of damped string vibrations was obtained with the finite speed of extension and strain propagation in the Hooke’s law formula taken into account. In contrast to the well-known equations, the obtained equation contains the first and third time derivatives of the displacement and the mixed derivative with respect to the space and time variables. Separation of variables was used to obtain its exact closed-form solution, whose analysis showed that, for large values of the relaxation coefficient, the string return to the initial state after its escape from equilibrium is accompanied by high-frequency low-amplitude damped vibrations, which occur on the initial time interval only in the region of positive displacements. And in the limit, for some large values of the relaxation coefficient, the string return to the initial state occurs practically without any oscillatory process." ;
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ns1:inLanguage "en" ;
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ns1:volumeNumber "49" ],
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ns1:issueNumber "5" ],
;
ns1:keywords "Hooke’s law formula",
"account",
"analysis",
"closed-form solution",
"coefficient",
"contrast",
"derivatives",
"differential equations",
"displacement",
"equations",
"equilibrium",
"escape",
"exact closed-form solution",
"extension",
"finite speed",
"formula",
"hyperbolic equations",
"initial state",
"initial time interval",
"intervals",
"large values",
"law formula",
"limit",
"material relaxation properties",
"mixed derivatives",
"oscillatory processes",
"positive displacement",
"process",
"propagation",
"properties",
"region",
"relaxation coefficient",
"relaxation properties",
"respect",
"return",
"separation",
"separation of variables",
"solution",
"space",
"speed",
"state",
"string return",
"string vibration",
"third time derivative",
"time derivative",
"time interval",
"time variable",
"values",
"variables",
"vibration" ;
ns1:name "Exact closed-form solution of the hyperbolic equation of string vibrations with material relaxation properties taken into account" ;
ns1:pagination "531-542" ;
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ns1:value "10.3103/s0025654414050057" ],
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ns1:value "pub.1070973402" ] ;
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ns1:sdDatePublished "2022-01-01T18:34" ;
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ns1:name "Springer Nature - SN SciGraph project" ] ;
ns1:url "https://doi.org/10.3103/s0025654414050057" ;
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ns1:name "Mathematical Sciences" .
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ns1:name "Pure Mathematics" .
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ns1:issn "0025-6544",
"1934-7936" ;
ns1:name "Mechanics of Solids" ;
ns1:publisher "Allerton Press" .
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ns1:affiliation ;
ns1:familyName "Kudinov" ;
ns1:givenName "I. V." ;
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ns1:familyName "Kudinov" ;
ns1:givenName "V. A." ;
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ns1:alternateName "Samara State Architecture and Civil Engineering University, ul. Molodogvardeyskaya 194, 443001, Samara, Russia" ;
ns1:name "Samara State Architecture and Civil Engineering University, ul. Molodogvardeyskaya 194, 443001, Samara, Russia" .
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ns1:alternateName "Samara State Technical University, ul. Molodogvardeyskaya 244, 443100, Samara, Russia" ;
ns1:name "Samara State Technical University, ul. Molodogvardeyskaya 244, 443100, Samara, Russia" .