3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid

The free vibration of an arbitrarily thick orthotropic piezoelectric hollow cylinder with a functionally graded property along the thickness direction and filled with a non-viscous compressible fluid medium is investigated. The analysis is directly based on the three-dimensional exact equations of piezoelasticity using the so-called state space formulations. The original functionally graded shell is approximated by a laminate model, of which the solution will gradually approach the exact one when the number of layers increases. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement at the interface. Analytical frequency equations are derived for different electrical boundary conditions at two cylindrical surfaces. As particular cases, free vibration of multi-layered piezoelectric hollow cylinder and wave propagation in infinite homogeneous cylinder are studied. Numerical comparison with available results is made and dispersion curves predicted from the present three-dimensional analysis are given. Numerical examples are further performed to investigate the effects of various parameters on the natural frequencies.