Free vibration and stability analysis of a functionally graded cylindrical shell embedded in piezoelectric layers conveying fluid flow

A general formula is presented for the free vibration problems of the functionally graded (FG) cylindrical shells embedded in piezoelectric layers conveying fluid flow. The 3D elasticity theory is used to derive cylindrical shell equations of motion. The cylindrical shell is assumed to be multi-layered and is coupled with an incompressible fluid flow, where the fluid-structure interaction is applied at the inner surface of the shell. A potential flow theory is used to model the incompressible fluid flow. Some solutions of the cylindrical shell without fluid are used for model validations. A stability analysis has been performed to establish the instability boundary of the hybrid shell. The results of the free vibration analysis show that the natural frequency decreases with increasing the fluid velocity. The 3D elasticity theory applied here has resulted in high-accurate numerical solutions. A parametric study is performed to establish the effects of the shell thickness to mid-radius, length, and vibrational mode numbers on the critical velocity of the FG shell bonded to piezoelectric layers.