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

doi:10.1007/s10483-018-2388-6

Abstract

Abstract:

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 straindisplacement 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: circular plate, large deflection, the modified method of multiple scales, the method of composite expansions, asymptotic solution, free vibration, cylindrical shell, porosity, functionally graded material (FGM), Rayleigh-Ritz method, thermal load

2010 MSC Number:

74H45

Yanqing WANG, Chao YE, J. W. ZU. Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities. Applied Mathematics and Mechanics (English Edition), 2018, 39(11): 1587-1604.

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