Applied Mathematics and Mechanics

, Volume 39, Issue 11, pp 1587–1604 | Cite as

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

  • Yanqing WangEmail author
  • Chao Ye
  • J. W. Zu


The free thermal vibration of functionally graded material (FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise (UTR), nonlinear temperature rise (NLTR), and linear temperature rise (LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the strain-displacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover, the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Key words

functionally graded material (FGM) cylindrical shell porosity free vibration thermal load Rayleigh-Ritz method 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MechanicsNortheastern UniversityShenyangChina
  2. 2.Key Laboratory of Ministry of Education on Safe Mining of Deep Metal MinesNortheastern UniversityShenyangChina
  3. 3.Schaefer School of Engineering and ScienceStevens Institute of TechnologyHobokenUSA

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