Analysis of the modal frequency of a functionally graded cylindrical shell

The modal frequencies of a functionally graded material (FGM) cylindrical shell with different geometry dimensions and material constituents are studied under eight boundary conditions. The main goal is to reveal the influencing mechanism of different factors on the modal frequencies of the FGM shell. Firstly, the Voigt model is used to describe the properties of FGM. Secondly, the motion equation of the FGM shell is derived using Hamilton’s principle. Thirdly, the modal frequency equation of the FGM shell is obtained based on a trigonometric function for the eight boundary conditions. Lastly, the effects of geometry dimension, material constituents, and boundary conditions on the modal frequencies of the FGM shell are analyzed through case studies. Results indicate that the modal frequencies obtained are good agreement with those from previous literature and the finite element method. The geometry dimensions of the FGM shell, the material constituents of the FGM, and the boundary conditions are crucial to the modal frequencies. This work can serve as a reference for the design of FGM and optimization of the structure of FGM shells.