(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
This paper investigates the dynamic responses of clamped-clamped functionally graded material circular cylindrical shell at both ends with small initial geometric imperfection and subjected to complex loads. The small initial geometric imperfection of the cylindrical shell is characterized with the shape of hyperbolic function. The effects of radial harmonic excitation combined with thermal loads are considered. The classical theory and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the functionally gradient material circular cylindrical shell by the Hamilton's principle. The partial differential dynamic equations are truncated by the Galerkin technique, using the modal expansion with the inclusion of axisymmetric and asymmetric modes. The effective material properties vary in the radial direction following a power-law distribution accordance with the volume fractions. The effects of volume fraction indexes, ratios of thickness-radius and length-radius on the first three dimensionless natural frequencies of the perfect cylindrical shell and its counterpart with imperfection are given. The effects of radial external loads, initial geometric imperfections and volume fraction index on the nonlinear dynamic response of the clamped-clamped FGM circular cylindrical shell are discussed by numerical calculation.