Free Vibration Frequency of Thick FGM Circular Cylindrical Shells with Simply Homogeneous Equation by Using TSDT

The objective of this study is to provide the frequency solutions of free vibration in thick FGM circular cylindrical shells by mainly considering both shear correction coefficient and nonlinear coefficient term. This paper investigates the effects of third-order shear deformation theory (TSDT) and the varied shear correction coefficient on the free vibration of thick functionally graded material (FGM), the circular cylindrical shells with simply homogeneous equation under thermal environment. The approach of derivations are given as follows, the varied value of shear correction coefficient is included in the simple homogeneous equation. The nonlinear term of displacement field of TSDT is also included to derive the simply homogeneous equation, some reasonable simplifications in the elements of homogeneous matrix under free vibration of thick FGM circular cylindrical shells are assumed, thus, the natural frequency can be found. Three parameters effect on the frequency of thick FGM circular cylindrical shells are computed and investigated, they are nonlinear coefficient c1 term, environment temperature and power law index. There are some main conclusions obtained, generally the natural frequency results are in decreasing value with the mode shape numbers for the thicker circular cylindrical shells. The values of natural frequencies are also affected by the nonlinear coefficient term.