"531-542" .
_:N30b1c81426184d39ba8465b813f26716 .
"solution" .
_:N0d84a1ce66cf45f1906f3c46dc042208 .
.
"Samara State Technical University, ul. Molodogvardeyskaya 244, 443100, Samara, Russia" .
_:N4ba7f92051614c5b86365395058fc26c .
_:N55e004b576014cd88a808d4168cc6517 .
"false"^^ .
.
"material relaxation properties" .
"speed" .
.
"initial time interval" .
"Hooke\u2019s law formula" .
"Allerton Press" .
"analysis" .
_:N9ed3b8bc34744f4f8199b15d2b43ca89 .
"Samara State Architecture and Civil Engineering University, ul. Molodogvardeyskaya 194, 443001, Samara, Russia" .
"large values" .
"equations" .
"oscillatory processes" .
_:Ncc77ae1191414bcd92f883fa727132ea .
"2014-09" .
"intervals" .
"V. A." .
"space" .
"0025-6544" .
"displacement" .
.
.
"https://scigraph.springernature.com/explorer/license/" .
.
"finite speed" .
"contrast" .
"derivatives" .
_:N67a70307e17d4b7b9d044ebe0a89726a "doi" .
.
"variables" .
.
"string return" .
_:N9ed3b8bc34744f4f8199b15d2b43ca89 .
"The differential equation of damped string vibrations was obtained with the finite speed of extension and strain propagation in the Hooke\u2019s 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." .
"2014-09-01" .
_:N0d84a1ce66cf45f1906f3c46dc042208 "dimensions_id" .
"law formula" .
.
.
.
.
.
_:N30b1c81426184d39ba8465b813f26716 .
"articles" .
"initial state" .
_:N30b1c81426184d39ba8465b813f26716 _:N4ba7f92051614c5b86365395058fc26c .
.
"time interval" .
"limit" .
.
"en" .
.
"return" .
"state" .
_:N0d84a1ce66cf45f1906f3c46dc042208 "pub.1070973402" .
"relaxation coefficient" .
"Mathematical Sciences" .
"separation" .
"Kudinov" .
"escape" .
"2022-01-01T18:34" .
_:Ncc77ae1191414bcd92f883fa727132ea .
.
.
"extension" .
_:N67a70307e17d4b7b9d044ebe0a89726a .
.
"account" .
"1934-7936" .
"mixed derivatives" .
"positive displacement" .
"coefficient" .
"values" .
"respect" .
.
"closed-form solution" .
.
_:N0d84a1ce66cf45f1906f3c46dc042208 .
"differential equations" .
_:Ncc77ae1191414bcd92f883fa727132ea "Springer Nature - SN SciGraph project" .
"separation of variables" .
"string vibration" .
"exact closed-form solution" .
.
_:N67a70307e17d4b7b9d044ebe0a89726a "10.3103/s0025654414050057" .
.
.
"Pure Mathematics" .
"equilibrium" .
_:N55e004b576014cd88a808d4168cc6517 .
"Mechanics of Solids" .
_:N67a70307e17d4b7b9d044ebe0a89726a .
"time variable" .
"relaxation properties" .
"properties" .
_:N55e004b576014cd88a808d4168cc6517 "5" .
.
"Samara State Technical University, ul. Molodogvardeyskaya 244, 443100, Samara, Russia" .
"I. V." .
"Exact closed-form solution of the hyperbolic equation of string vibrations with material relaxation properties taken into account" .
.
"vibration" .
"propagation" .
"https://doi.org/10.3103/s0025654414050057" .
"region" .
_:N4ba7f92051614c5b86365395058fc26c .
"third time derivative" .
"time derivative" .