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

• Published in: Applied mathematics and mechanics Vol. 39; no. 11; pp. 1587 - 1604
• Main Authors: Wang, Yanqing, Ye, Chao, Zu, J. W.
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.11.2018; Springer Nature B.V; Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines,Northeastern University, Shenyang 110819, China%Department of Mechanics, Northeastern University, Shenyang 110819, China%Schaefer School of Engineering and Science, Stevens Institute of Technology,Hoboken, NJ 07030, U.S.A; Department of Mechanics, Northeastern University, Shenyang 110819, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Cylindrical shells; Fluid- and Aerodynamics; Functionally gradient materials; Material properties; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Porosity; Rayleigh-Ritz method; Resonant frequencies; Shell theory; Shells; Temperature effects; Thermal analysis; cylindrical shell; Rayleigh-Ritz method; 74H45; porosity; thermal load; O321; free vibration; functionally graded material (FGM)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-018-2388-6

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.