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  Volume 5, Number 4, October 2020 , pages 363-380

On mixing the Rayleigh-Ritz formulation with Hankel
Muzamal Hussain, Muhammad Nawaz Naeem, Aamir Shahzad, Muhammad Taj, Sehar Asghar, Alireza Fatahi-Vajari, Rahul Singh and Abdelouahed Tounsi

    In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are 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. HankelHanke's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.
Key Words
    Langrange functional; fluid-filled; MATLAB; Hankel
Muzamal Hussain,Muhammad Nawaz Naeem:Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Aamir Shahzad:Department of Physics, Govt. College University Faisalabad, Faisalabad 38040, Pakistan
Muhammad Taj:Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, Azad Kashmir, Pakistan
Sehar Asghar:Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Alireza Fatahi-Vajari:Department of Mechanical Engineering, Shahryar Branch, Islamic Azad University, Shahryar, Iran
Rahul Singh :University Department of Mechanical Engineering, Rajasthan Technical University, Kota 324010, India
Abdelouahed Tounsi:Materials and Hydrology Laboratory University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department
,Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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