effects of power-law distribution and exponential with uniform pressures on vibration behavior of reinforced cylindrical shell made of functionally graded materials under symmetric boundary conditions

in this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. the fgm shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. these constituents are graded through the thickness direction, from one surface of the shell to the other and are controlled by power-law volume fraction distribution. the reinforced fgm shell equations with ring and uniform pressure are established based on first order shear deformation theory. the governing equations of motion were employed, using energy functional and by applying ritz method. the boundary conditions represented by end conditions of the fgm cylindrical shell are simply supported-simply supported, clamped-clamped and free-free. effects of the different values of the power-law exponent, uniform pressure, reinforced ring and different symmetric boundary conditions on natural frequencies characteristics are studied. to check the validity of the present study, the results obtained are compared with those available in the literature.