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157740

Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.

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Last updated: 04 Jan 2025

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-

Tags

Civil Engineering

Abstract

In this paper, the nodal line finite difference method (NLFDM) is extended to the analysis of a thin circular cylindrical shell, as shown in Fig. 1, undergoing free vibrations [1]. The material of the circular cylindrical shell is assumed to be linear elastic isotropic. 
The complexity of a theoretical analysis of a vibration problem depends largely on the number of degrees of freedom of the structural system in question. Since a thin circular cylindrical shell is a continuous system it has an infinite number of degrees of freedom. The NLFDM [10] transforms this continuous system into a system having a finite number of degrees of freedom. While carrying out the dynamic (or static) analysis by the NLFDM, the number of degrees of freedom depends on the number of the used nodal lines. 
The natural frequencies and modes are treated in more detail because they are basic to understanding the dynamic response under any kind of excitation. It will be shown that the number of natural frequencies and that of normal modes, for axial wave number different from zero, are each equal to three times the number of nodal lines used. 
The orthogonality relationships of the normal modes obtained by the nodal line finite difference method are also included. It should be remarked that these relationships are slightly different from those obtained by the finite element method; in fact the overall matrix of coefficients replaces the stiffness matrix, and any two different modes are orthogonal with respect to the unit matrix instead of the mass matrix. 

DOI

10.21608/bfemu.2021.157740

Authors

First Name

Usama

Last Name

Abo-Raya

MiddleName

-

Affiliation

Senior Engineer., Ministry of Irrigation., El-Mansoura Governorate., El-Mansoura, Egypt.

Email

-

City

Mansoura

Orcid

-

First Name

Ahmed

Last Name

Ghaleb

MiddleName

A.

Affiliation

Structural Engineering Department, El-Mansoura University., El-Mansoura., Egypt.

Email

ag_edc@yahoo.com

City

Mansoura

Orcid

-

First Name

Youssef

Last Name

Agag

MiddleName

I.

Affiliation

Structural Engineering Department., El-Mansoura University., El-Mansoura., Egypt.

Email

yagag@mans.edu.eg

City

Mansoura

Orcid

-

Volume

25

Article Issue

2

Related Issue

21254

Issue Date

2000-06-01

Receive Date

2000-08-11

Publish Date

2021-03-18

Page Start

1

Page End

18

Print ISSN

1110-0923

Online ISSN

2735-4202

Article File

BFEMU_Volume 25_Issue 2_Pages 1-18.pdf

PDF . 484.0kB

Link

https://bfemu.journals.ekb.eg/article_157740.html

Detail API

https://bfemu.journals.ekb.eg/service?article_code=157740

Order

13

Type

Research Studies

Type Code

1,205

Publication Type

Journal

Publication Title

MEJ. Mansoura Engineering Journal

Publication Link

https://bfemu.journals.ekb.eg/

MainTitle

Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.

Details

Type

Article

Created At

22 Jan 2023