Free vibration of FGM cylindrical shells with holes under various boundary conditions

Free vibration analysis of functionally graded material (FGM) cylindrical shells with holes was studied in this paper. The variational equation was founded firstly, and the unified displacement mode-shape function of the shells with various boundary conditions was put forward then. The general analytical expressions of natural frequency and mode-shape solutions given by functional variation and characteristic value analysis, which can be applied to FGM cylindrical shells with holes of arbitrary functionally graded distribution along the thickness direction and different boundary conditions. Non-dimensional frequencies of shell with holes of different shape, number, location were given in the end of this paper.