Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Andrey Bochkarev, Aleksandr Zemlyanukhin, Vladimir Erofeev, Aleksandr Ratushny
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	cylindrical shells analytically solvable models exact solutions physically realizable solutions Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1791308897b54d1187a95ebcda3e9337
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:1791308897b54d1187a95ebcda3e9337
record_format	dspace
spelling	oai:doaj.org-article:1791308897b54d1187a95ebcda3e93372021-11-25T19:07:48ZAnalytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells10.3390/sym131122272073-8994https://doaj.org/article/1791308897b54d1187a95ebcda3e93372021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2227https://doaj.org/toc/2073-8994The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity.Andrey BochkarevAleksandr ZemlyanukhinVladimir ErofeevAleksandr RatushnyMDPI AGarticlecylindrical shellsanalytically solvable modelsexact solutionsphysically realizable solutionsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2227, p 2227 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	cylindrical shells analytically solvable models exact solutions physically realizable solutions Mathematics QA1-939
spellingShingle	cylindrical shells analytically solvable models exact solutions physically realizable solutions Mathematics QA1-939 Andrey Bochkarev Aleksandr Zemlyanukhin Vladimir Erofeev Aleksandr Ratushny Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
description	The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity.
format	article
author	Andrey Bochkarev Aleksandr Zemlyanukhin Vladimir Erofeev Aleksandr Ratushny
author_facet	Andrey Bochkarev Aleksandr Zemlyanukhin Vladimir Erofeev Aleksandr Ratushny
author_sort	Andrey Bochkarev
title	Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
title_short	Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
title_full	Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
title_fullStr	Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
title_full_unstemmed	Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells
title_sort	analytically solvable models and physically realizable solutions to some problems in nonlinear wave dynamics of cylindrical shells
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1791308897b54d1187a95ebcda3e9337
work_keys_str_mv	AT andreybochkarev analyticallysolvablemodelsandphysicallyrealizablesolutionstosomeproblemsinnonlinearwavedynamicsofcylindricalshells AT aleksandrzemlyanukhin analyticallysolvablemodelsandphysicallyrealizablesolutionstosomeproblemsinnonlinearwavedynamicsofcylindricalshells AT vladimirerofeev analyticallysolvablemodelsandphysicallyrealizablesolutionstosomeproblemsinnonlinearwavedynamicsofcylindricalshells AT aleksandrratushny analyticallysolvablemodelsandphysicallyrealizablesolutionstosomeproblemsinnonlinearwavedynamicsofcylindricalshells
_version_	1718410262541762560

Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

Ejemplares similares