Free vibration analysis of multilayered composite cylinder consisting fibers with variable volume fraction

In this paper, free vibration of a fiber reinforced composite cylinder in which volume fraction of its fibers vary longitudinally, is studied using a semi-analytical method. The distribution of volume fraction of fiber in base matrix is based on power law model. A micromechanical model is employed to represent its mechanical properties including elastic and physical properties of this composite cylinder. In addition, kinematically the first order shear deformation shell theory is employed for strain field. Then, weak form formulation and spatial approximations of variables are utilized to discretize the equations of motion. Different problems are solved in which primarily the validity of the results obtained for natural frequencies are evaluated by those similar results reported in the literature and with other commercial F.E. code for different boundary conditions. Furthermore, for different values of volume fractions and under various boundary conditions, computed natural frequencies of this composite cylinder with variable volume fraction of fiber are compared with the traditional one in which the volume fraction of fiber is constant throughout the structure. In spite the fact that average volume fraction of fiber and the layer fiber orientation are the same in both configurations, numerical results show that using variable volume fraction of fiber affects the shell natural frequencies and its mode shapes.