A system of several fraction laws for the identification of rotating response of FG shell

Ahmad Yahya , Muzamal Hussain , Mohamed A. Khadimallah , Khaled Mohamed Khedher , K.S. Al-Basyouni , Emad Ghandourah , Essam Mohammed Banoqitah , Adil Alshoaibi

Abstract

The problem is formulated by applying the Kirchhoff's conception for shell theory. The longitudinal modal displacement functions are assessed by characteristic beam ones meet clamped-clamped end conditions applied at the shell edges. The fundamental natural frequency of rotating functionally graded cylindrical shells of different parameter versus ratios of length-to-diameter and height-to-diameter for a wide range has been reported and investigated through the study with fractions laws. The frequency first increases and gain maximum value with the increase of circumferential wave mode. By increasing different value of height-to-radius ratio, the resulting backward and forward frequencies increase and frequencies decrease on increasing height-to-radius ratio. Moreover, on increasing the rotating speed, the backward frequencies increases and forward frequencies decreases. The trigonometric frequencies are lower than that of exponential and polynomial frequencies. Stability of a cylindrical shell depends highly on these aspects of material. More the shell material sustains a load due to physical situations, the more the shell is stable. Any predicted fatigue due to burden of vibrations is evaded by estimating their dynamical aspects.

Key Words

cylindrical shell; Kirchhoff's conception; polynomial; strain, stainless steel

Address

Ahmad Yahya — Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O.Box 80204, Jeddah 21589, Saudi Arabia
Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Mohamed A. Khadimallah — Civil Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University, BP 655, Al-Kharj, 16273, Saudi Arabia; Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia
Khaled Mohamed Khedher — Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia; Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia
K.S. Al-Basyouni — Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Emad Ghandourah — Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O.Box 80204, Jeddah 21589, Saudi Arabia
Essam Mohammed Banoqitah — Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah P.O.Box 80204, Jeddah 21589, Saudi Arabia
Adil Alshoaibi — Department of Physics, College of Science, King Faisal University, Al-Hassa, P.O. Box 400, Hofuf 31982, Saudi Arabia

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