In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide the maximum stability of a physical system. There is graduation distribution of constituent materials in functionally graded materials and is controlled by polynomial, exponential and trigonometric volume exponent fraction laws. In the present study a cylindrical shell is composed of three layers whereas the middle layer consists of functionally graded material and the extreme layer are of isotropic nature. Material composition of the FG layer is governed by polynomial, exponential and trigonometric volume fraction exponent laws. Impact of these laws is examined on shell vibration frequencies for different physical parameters. Love’s thin shell theory is adopted for shell motion equations. The vibration of cylindrical shells with FGM will be expressed by using the Raleigh-Ritz technique in this method. Three volume fraction laws are used to define the middle layer of tri-layer cylindrical shells. The Rayleigh-Ritz technique is applied to form the shell frequency equation which is solved by MATLAB software. The validity and accuracy of this method is investigated for a number of comparisons of numerical results.
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American Journal of Applied Mathematics (Volume 3, Issue 3-1)
This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015) |
| DOI | 10.11648/j.ajam.s.2015030301.16 |
| Page(s) | 32-40 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
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APA Style
Zermina Gull Bhutta, M. N. Naeem, M. Imran. (2015). On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer. American Journal of Applied Mathematics, 3(3-1), 32-40. https://doi.org/10.11648/j.ajam.s.2015030301.16
ACS Style
Zermina Gull Bhutta; M. N. Naeem; M. Imran. On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer. Am. J. Appl. Math. 2015, 3(3-1), 32-40. doi: 10.11648/j.ajam.s.2015030301.16
AMA Style
Zermina Gull Bhutta, M. N. Naeem, M. Imran. On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer. Am J Appl Math. 2015;3(3-1):32-40. doi: 10.11648/j.ajam.s.2015030301.16
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Download@article{10.11648/j.ajam.s.2015030301.16,
author = {Zermina Gull Bhutta and M. N. Naeem and M. Imran},
title = {On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {3-1},
pages = {32-40},
doi = {10.11648/j.ajam.s.2015030301.16},
url = {https://doi.org/10.11648/j.ajam.s.2015030301.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.16},
abstract = {In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide the maximum stability of a physical system. There is graduation distribution of constituent materials in functionally graded materials and is controlled by polynomial, exponential and trigonometric volume exponent fraction laws. In the present study a cylindrical shell is composed of three layers whereas the middle layer consists of functionally graded material and the extreme layer are of isotropic nature. Material composition of the FG layer is governed by polynomial, exponential and trigonometric volume fraction exponent laws. Impact of these laws is examined on shell vibration frequencies for different physical parameters. Love’s thin shell theory is adopted for shell motion equations. The vibration of cylindrical shells with FGM will be expressed by using the Raleigh-Ritz technique in this method. Three volume fraction laws are used to define the middle layer of tri-layer cylindrical shells. The Rayleigh-Ritz technique is applied to form the shell frequency equation which is solved by MATLAB software. The validity and accuracy of this method is investigated for a number of comparisons of numerical results.},
year = {2015}
}
TY - JOUR T1 - On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer AU - Zermina Gull Bhutta AU - M. N. Naeem AU - M. Imran Y1 - 2015/06/15 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.s.2015030301.16 DO - 10.11648/j.ajam.s.2015030301.16 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 32 EP - 40 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.s.2015030301.16 AB - In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide the maximum stability of a physical system. There is graduation distribution of constituent materials in functionally graded materials and is controlled by polynomial, exponential and trigonometric volume exponent fraction laws. In the present study a cylindrical shell is composed of three layers whereas the middle layer consists of functionally graded material and the extreme layer are of isotropic nature. Material composition of the FG layer is governed by polynomial, exponential and trigonometric volume fraction exponent laws. Impact of these laws is examined on shell vibration frequencies for different physical parameters. Love’s thin shell theory is adopted for shell motion equations. The vibration of cylindrical shells with FGM will be expressed by using the Raleigh-Ritz technique in this method. Three volume fraction laws are used to define the middle layer of tri-layer cylindrical shells. The Rayleigh-Ritz technique is applied to form the shell frequency equation which is solved by MATLAB software. The validity and accuracy of this method is investigated for a number of comparisons of numerical results. VL - 3 IS - 3-1 ER -
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