Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.
Abo-Raya, U., Ghaleb, A., Agag, Y. (2021). Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.. EKB Journal Management System, 25(2), 1-18. doi: 10.21608/bfemu.2021.157740
Usama Abo-Raya; Ahmed A. Ghaleb; Youssef I. Agag. "Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.". EKB Journal Management System, 25, 2, 2021, 1-18. doi: 10.21608/bfemu.2021.157740
Abo-Raya, U., Ghaleb, A., Agag, Y. (2021). 'Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.', EKB Journal Management System, 25(2), pp. 1-18. doi: 10.21608/bfemu.2021.157740
Abo-Raya, U., Ghaleb, A., Agag, Y. Free Vibrations of Cylindrical Shells by the Nodal Line Finite Difference Method-Part-I Theory.. EKB Journal Management System, 2021; 25(2): 1-18. doi: 10.21608/bfemu.2021.157740

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

MEJ- Mansoura Engineering Journal
Article 13, Volume 25, Issue 2, June 2000, Page 1-18  XML PDF (472.64 K)
Document Type: Research Studies
DOI: 10.21608/bfemu.2021.157740
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Authors
Usama Abo-Raya1; Ahmed A. Ghaleb email 2; Youssef I. Agag3
1Senior Engineer., Ministry of Irrigation., El-Mansoura Governorate., El-Mansoura, Egypt.
2Structural Engineering Department, El-Mansoura University., El-Mansoura., Egypt.
3Structural Engineering Department., El-Mansoura University., El-Mansoura., Egypt.
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. 
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