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Smart Structures and Systems Volume 27, Number 5, May 2021 , pages 729-743 DOI: https://doi.org/10.12989/sss.2021.27.5.729 |
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Vibration analysis of FG cylindrical shell: Evaluation of Ritz-polynomial mixed with ring terms |
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Mohamed A. Khadimallah, Muzamal Hussain, Muhammad Nawaz Naeem, Amjad Qazaq, Abdulaziz Alqahtani and Abdelouahed Tounsi
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| Abstract | ||
| Here the Rayleigh - Ritz method has been applied to derive the shell vibration frequency equation. This equation has been formed as an eigenvalue problem form. MATLAB software package has been utilized for extracting shell frequency spectra. Nature of materials used for construction of cylindrical shells also has visible impact on shell vibration characteristics. For isotropic materials, the physical properties are same everywhere, the laminated and functionally graded materials vary from point to point. Here the shell material has been taken as functionally graded material. Moreover, the impact of ring supports around the shell circumferential has been examined for the various positions along the shell axial length. These shells are stiffened by rings in the tangential direction. These ring supports are located at various positions along the axial direction round the shell circumferential direction. These variations have been plotted against the locations of ring supports for three values of exponents of volume fraction law. For three conditions, frequency variations show different behavior with these values of exponent law. The influence of the positions of ring supports for simply supported end conditions is very visible. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. | ||
| Key Words | ||
| Lagrangian functional; ring supports; volume fraction; FGM | ||
| Address | ||
| (1) Mohamed A. Khadimallah, Amjad Qazaq, Abdulaziz Alqahtani: Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia; (2) Mohamed A. Khadimallah: Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia; (3) Muzamal Hussain, Muhammad Nawaz Naeem: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan; (4) Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; (5) Abdelouahed Tounsi: Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia. | ||