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

  • Yahya, Ahmad (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed A. (Civil Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University) ;
  • Khedher, Khaled Mohamed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Al-Basyouni, K.S. (Mathematics Department, Faculty of Science, King Abdulaziz University) ;
  • Ghandourah, Emad (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Banoqitah, Essam Mohammed (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Alshoaibi, Adil (Department of Physics, College of Science, King Faisal University)
  • Received : 2021.06.11
  • Accepted : 2022.03.10
  • Published : 2022.03.25
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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.

Keywords

Acknowledgement

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. G: 158-135-1442. The authors, therefore, gratefully acknowledge DSR technical and financial support.

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