Nonlinear Dynamics of Clamped Initial Imperfect Functionally Graded Material Circular Cylindrical Shell Considering the Axisymmetric Mode (Advances in Applied Mathematics and Mechanics, 2018)
This paper investigates the dynamic responses of clamped-clamped functionallygraded material circular cylindrical shell at both ends with small initial geometricimperfection and subjected to complex loads. The small initial geometric imperfectionof 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 toobtain partial differential equation of the functionally gradient material circular cylindricalshell by the Hamilton's principle. The partial differential dynamic equationsare truncated by the Galerkin technique, using the modal expansion with the inclusionof axisymmetric and asymmetric modes. The effective material properties varyin the radial direction following a power-law distribution accordance with the volumefractions. The effects of volume fraction indexes, ratios of thickness-radius and length-radiuson the first three dimensionless natural frequencies of the perfect cylindricalshell and its counterpart with imperfection are given. The effects of radial externalloads, initial geometric imperfections and volume fraction index on the nonlinear dynamicresponse of the clamped-clamped FGM circular cylindrical shell are discussedby numerical calculation.