Three-dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels

Elasticity solution for free vibrations analysis of functionally graded fiber orientation and volume fraction cylindrical panel is presented, using differential quadrature method. The orthotropic panel is simply supported at the edges and assumed to have arbitrary variations of fiber orientation and volume fraction in the radial direction. Suitable displacement functions that identically satisfy the simply supported boundary conditions are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method to obtain the natural frequencies. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. Numerical results are presented for an orthotropic cylindrical panel with arbitrary variations of fiber orientation and volume fraction in the shell's thickness and compared with discrete laminates composite panels. The interesting and new results show that normalized natural frequency of the functionally graded fiber orientation cylindrical panel is smaller than that of a discrete laminate composite panel and close to that of a 4-layer. In contrast, the normalized natural frequency of a functionally graded fiber volume fractions is larger than that of a discrete laminated and close to that of a 2-layer.