calculation of natural frequencies of bi-layered rotating functionally graded cylindrical shells

In this paper, an exact analytical solution for free vibration of rotating bilayered cylindrical shell composed of two independent functionally graded layers was presented. the thicknesses of the shell layers were assumed to be equal and constant. the material properties of the constituents of bi-layered fgm cylindrical shell were graded in the thickness direction of the layers of the shell according to a volume fraction power-law distribution. in order to derive the equations of motion, the sanders’ thin shell theory and rayleigh- ritz method were used. also the results were extracted by considering coriolis, centrifugal and initial hoop tension effects. effects of rotating speed, geometrical parameters, and material distribution in the two functionally graded layers of the shell, circumferential and longitudinal wave number on the forward and backward natural frequencies were investigated. a comparison of the results was made with those available in the literature for the validity and accuracy of the present methodology.