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Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells

Part of: Linear vibration theory Thin bodies, structures

Published online by Cambridge University Press:  11 July 2017

R. Poultangari  and
M. Nikkhah-Bahrami
R. Poultangari
Affiliation:
Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful 64616-45165, Iran
M. Nikkhah-Bahrami*
Affiliation:
Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran 14515-775, Iran
*
*Corresponding author. Email:mbahrami@ut.ac.ir (M. N. Bahrami)
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Abstract

The vectorial form of the Wave Propagation Method (VWM), regarding the dispersion of harmonic plain (elasto-dynamic) waves within certain wave-guides, is developed for the vibration analysis of circular cylindrical shells. To obtain this goal, all plain waves are divided into positive-negative going wave vectors along with the shell axis. Based on the Flügge thin shell theory, the shell continuity as well as boundary conditions are well satisfied by introducing the propagation and reflection matrices. Furthermore, all elements of the reflection matrix are derived for certain classical supports. As an example, for demonstrating the feasibility of VWM in the shell vibration analysis, a circular cylindrical shell with two ended flexible support is adopted. The natural frequencies of the systemaswell asmode shapes are obtained using VWM. The aquired results are compared with those of the previous works and found in excellent agreement. It is also found that VWM could mathematically provide a reduced dimensional matrix (dominant matrix) to calculate the natural frequencies of the system. Accordingly, the proposed method can provide high computational efficiency and remarkable accuracy, simultaneously.

Keywords

Elasto-dynamic wavesvectorial wave methodreflection matricescircular cylindrical shellFlügge theoryfree vibration

MSC classification

Secondary: 70J30: Free motions 74K25: Shells
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1145 - 1161
Copyright
Copyright © Global-Science Press 2017 

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