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Advances in Nano Research Volume 16, Number 6, June 2024 , pages 565-577 DOI: https://doi.org/10.12989/anr.2024.16.6.565 |
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Fluid bounding effect on FG cylindrical shell using Hankel's functions of second kind |
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Khaled Mohamed Khedher, Shahzad Ali Chattah, Mohammad Amien Khadimallah, Ikram Ahmad, Muzamal Hussain, Rana Muhammad Akram Muntazir, Mohamed Abdelaziz Salem, Ghulam Murtaza, Faisal Al-Thobiani, Muhammad Naeem Mohsin, Abeera Talib and Abdelouahed Tounsi
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| Abstract | ||
| Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used. | ||
| Key Words | ||
| fluid-filled; Hankel's functions; MATLAB; Sender's shell theory; strain energy | ||
| Address | ||
| Khaled Mohamed Khedher: Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia Shahzad Ali Chattah: Department of Chemistry, Government College University Faisalabad, 38000, Pakistan Mohammad Amien Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Ikram Ahmad: Department of Chemistry, University of Sahiwal, Sahiwal, 57000, Faisalabad, Pakistan Muzamal Hussain and Ghulam Murtaza: Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Faisalabad, Pakistan Rana Muhammad Akram Muntazir and Abeera Talib: Department of Mathematics, Lahore leads University, 54792, Lahore Mohamed Abdelaziz Salem: Department of Mechanical Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia Faisal Al-Thobiani:8Marine Engineering Department, Faculty of Maritime Studies, King Abdulaziz University, Jeddah, Saudi Arabia Muhammad Naeem Mohsin: Institute for Islamic Theological Studies, University of Vienna, Schenkenstrabe 8-10,1010, Vienna Abdelouahed Tounsi: Faculty of Technology Civil Engineering Department, Materials and Hydrology Laboratory University of Sidi Bel Abbes, Algeria/ Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia | ||