Axi-symmetrical Bending Of FGMs Cylindrical Shells And Free Vibration Of FGMs Cylindrical Shells With Holes

Functionally graded materials (FGMs) are the kind of composite materials that are microscopically inhomogeneous, taking advantage of the merits of constituent materials adequately. By gradually varying the volume fraction of the constituent materials, FGMs possesses the gradient in properties, i.e. the thermal and mechanical properties vary smoothly and continuously from one surface to the other, which eliminates the mismatch of mechanical properties induced by the interface, and mitigates thermal stress concentration in high temperature gradient environment. So, mechanical behavior of functionally graded materials structure becomes a new research direction of structure mechanics. Our research object includes linear bending of FGMs cylindrical shells and free vibration of cylindrical shells with holes. We using analytical method study on perfect cylindrical shells and cylindrical shells with holes which material properties change along thickness direction with power function form. The main research results and conclusions are summarized as follows:1. Governing equations of axi-symmetrical bending for the FGMs cylindrical shells in terms of the displacements in the radial and the axial directions are derived on the bases of classical linear shell theory. The deformation of FGMs cylindrical shell subjected to internal pressure is studied. We obtain analytical solution of the problem by using analytic method. The effects of the gradient parameter of the materials variation on the deformation and internal forces of the FGMs cylindrical shells are examined and discussed in special boundary conditions. Maximal deflection and maximal circumferential internal force occur near ends. For the simply supported conditions, maximal bending moment occurs near ends, whereas for the fixed boundary conditions, maximal bending moment occurs at ends. For the both boundary conditions, the deflection of FGMs shells decreases with the gradient parameter of the materials increasing. We also research the long cylindrical shells subjected to special loads. For one end of the shell subjected to couple and lateral force, and one section of the shell subjected to pressure, the deflection,bending moment and shear force of the shells decrease rapidly as the axial coordinate increasing respectively. This indicates that the loads only have local influence on bending deformation and internal force of the shell. 2. Hamilton's principle and Rayleigh-Ritz method are employed for the analysis of the FGMs shells with holes on the bases of classical linear shell theory. For simply supported boundary conditions, we obtain analytical solution of natural frequencies of FGMs shells. Characteristic curves of natural frequency along opening ratio,ratio of length and radius,ratio of length and width of hole,the gradient parameter of the FGMs, are plotted respectively. The natural frequency of FGMs shell with holes increases as opening ratio,ratio of thickness and radius of the shell and ratio of length and width of hole increases respectively. As the length/width of hole and the gradient parameter of FGMs increases, the natural frequency of FGMs shells with center square hole decreases rapidly. For the same wave number of axial direction, the natural frequency do not change monotonously with circumferential wave numbers.