Volume 9, Issue 5
Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells

Adv. Appl. Math. Mech., 9 (2017), pp. 1145-1161.

Published online: 2018-05

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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 Fl ¨ugge 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 system as well as mode 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 waves, vectorial wave method, reflection matrices, circular cylindrical shell, Flügge theory, free vibration.

70J30, 74K25

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@Article{AAMM-9-1145, author = {}, title = {Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {5}, pages = {1145--1161}, 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 Fl ¨ugge 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 system as well as mode 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1195}, url = {http://global-sci.org/intro/article_detail/aamm/12194.html} }
TY - JOUR T1 - Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1145 EP - 1161 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1195 UR - https://global-sci.org/intro/article_detail/aamm/12194.html KW - Elasto-dynamic waves, vectorial wave method, reflection matrices, circular cylindrical shell, Flügge theory, free vibration. AB -

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 Fl ¨ugge 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 system as well as mode 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.

R. Poultangari & M. Nikkhah-Bahrami. (2020). Application of Vectorial Wave Method in Free Vibration Analysis of Cylindrical Shells. Advances in Applied Mathematics and Mechanics. 9 (5). 1145-1161. doi:10.4208/aamm.2015.m1195
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