| Free vibration and the free vibration of rotating functionally graded cylindricalshells have been investigated theoretically,numerically,experimentally in thispaper.The effects of the shells and geometric parameters, volume fraction, boundaryconditions, constituent materials on the functionally graded cylindrical shells isstudied.The study provides appropriate analytical methods and theoretical basis fordesign of functionally graded cylindrical shells and open the way for the deepstudy.The main work in this paper is as following aspects:At the beginning,the advances in the research of free vibration of functionallygraded cylindrical shells are reviewed comprehensively.The main comments aresystematically remark on the rotating functionally graded cylindrical shells.Studybackground and involved elementary theory of this thesis are emphatically expatiated.This research investigates free vibration of functionally graded materials (FG)thin cylindrical shells in the paper. The modulus of elasticity of FG cylindrical shells isassumed to vary according to a power law distribution in terms of the volume fractionsof the constituents in the thickness direction. Based on Love’s theory, expressions ofthe internal force, displacement, strain and curvature of FG cylindrical shells are builtup. The shell eigenfrequency equation is derived by the Rayleigh-Ritz method. Themodal functions are introduced to analyze the frequency characteristics of cylindricalshells for simply supported-simply supported, free-simply supported boundaryconditions by numerical examples. The influence of material characteristics andgeometrical parameters for the natural frequencies is further discussed.Based on Love’s first approximation theory, expressions of the strain-displacement and curvature-strain are built up and the Rayleigh-Ritz method is used toderive the shell eigenfrequency equation. The natural frequencies under three differentboundary conditions with S-S, F-S and C-C were investigated as the examples.Effectof volume fraction and material components on the free vibration of functionally graded cylindrical shells is studied in this paper.Based on Love’s first approximation theory, differential equation are built up.Freevibrations of two types rotating FG cylindrical shells under S-S boundary condition,different L/Rratios and r ad/s are studied in this paper.Effect of volume fraction, axial wave number, circumferential wave number, materialcomponents and boundary conditions on the free vibration of rotating functionallygraded cylindrical shells is studied in this paper. Based on Love’s theory, differentialequation are built up and used to derive the shell eigenfrequency equation. Effect ofvolume fraction and etc to the natural frequencies were investigated as theexamples,and the forces under S-S boundary condition were analysed in this paper. |
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