Advances in nano research

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Simply supported boundary condition for bifurcation analysis of functionally graded material: Thickness control by exponential fraction law

  • Shadi Alghaffari (Department of Port and Maritime Transportation, Faculty of Maritime Studies, King Abdul Aziz University) ;
  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Faisal Al Thobiani (Department of Marine Engineering, Faculty of Maritime Studies, King Abdul Aziz University) ;
  • Hussain Talat Sulaimani (Department of Port and Maritime Transportation, Faculty of Maritime Studies, King Abdul Aziz University)
  • Received : 2021.11.02
  • Accepted : 2022.11.17
  • Published : 2023.04.25
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Abstract

In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects under grant no. (IFPIP-238-980-1443). Therefore, authors gratefully acknowledge the technical and financial support from the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

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