Abstract
Here the Rayleigh - Ritz method has been applied to derive the shell vibration frequency equation. This equation has been formed as an eigenvalue problem form. MATLAB software package has been utilized for extracting shell frequency spectra. Nature of materials used for construction of cylindrical shells also has visible impact on shell vibration characteristics. For isotropic materials, the physical properties are same everywhere, the laminated and functionally graded materials vary from point to point. Here the shell material has been taken as functionally graded material. Moreover, the impact of ring supports around the shell circumferential has been examined for the various positions along the shell axial length. These shells are stiffened by rings in the tangential direction. These ring supports are located at various positions along the axial direction round the shell circumferential direction. These variations have been plotted against the locations of ring supports for three values of exponents of volume fraction law. For three conditions, frequency variations show different behavior with these values of exponent law. The influence of the positions of ring supports for simply supported end conditions is very visible. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure.