Accuracy Analysis of Donnell & Sanders Theories for Free Vibration of Thick Functionally Graded Cylindrical Shell in Various Boundary Conditions

Functionally Graded cylindrical structures, because of their good mechanical ability and their high heat resistance capability, are noteworthy in structural designers view. So, possessing an efficient analysis method for vibration of such structures is so important. In this paper, free vibration of functionally graded cylindrical shell is analyzed based on Donnell and Sanders theories. Also, the first order shear deformation theory is used for displacement field. FG material properties change through the thickness direction according to a power law distribution function. Equations of motion are solved with state space method and as an advantage, numerical results are calculated for every classical boundary conditions. Numerical Results are compared with literature and 3D finite element model and good agreement are observed. Also, effects of geometry and material parameters change on natural frequencies are studied for different boundary conditions. In some cases, one of the theories has major error which is mentioned.