Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell a...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Rui Nie, Tianyun Li, Xiang Zhu, Cheng Zhang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	free surface cylindrical shell image method Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ef6ac322ce5f4c4e8d72390fe0d45b90
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:ef6ac322ce5f4c4e8d72390fe0d45b90
record_format	dspace
spelling	oai:doaj.org-article:ef6ac322ce5f4c4e8d72390fe0d45b902021-11-25T19:07:15ZAnalysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle10.3390/sym131121622073-8994https://doaj.org/article/ef6ac322ce5f4c4e8d72390fe0d45b902021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2162https://doaj.org/toc/2073-8994Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.Rui NieTianyun LiXiang ZhuCheng ZhangMDPI AGarticlefree surfacecylindrical shellimage methodMathematicsQA1-939ENSymmetry, Vol 13, Iss 2162, p 2162 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	free surface cylindrical shell image method Mathematics QA1-939
spellingShingle	free surface cylindrical shell image method Mathematics QA1-939 Rui Nie Tianyun Li Xiang Zhu Cheng Zhang Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
description	Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.
format	article
author	Rui Nie Tianyun Li Xiang Zhu Cheng Zhang
author_facet	Rui Nie Tianyun Li Xiang Zhu Cheng Zhang
author_sort	Rui Nie
title	Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
title_short	Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
title_full	Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
title_fullStr	Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
title_full_unstemmed	Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle
title_sort	analysis of free vibration characteristics of cylindrical shells with finite submerged depth based on energy variational principle
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ef6ac322ce5f4c4e8d72390fe0d45b90
work_keys_str_mv	AT ruinie analysisoffreevibrationcharacteristicsofcylindricalshellswithfinitesubmergeddepthbasedonenergyvariationalprinciple AT tianyunli analysisoffreevibrationcharacteristicsofcylindricalshellswithfinitesubmergeddepthbasedonenergyvariationalprinciple AT xiangzhu analysisoffreevibrationcharacteristicsofcylindricalshellswithfinitesubmergeddepthbasedonenergyvariationalprinciple AT chengzhang analysisoffreevibrationcharacteristicsofcylindricalshellswithfinitesubmergeddepthbasedonenergyvariationalprinciple
_version_	1718410315275698176

Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

Ejemplares similares