Free vibration of rotating FGM conical shell with smart patches

In this paper, free vibrations of rotating conical shell with smart patches are investigated. Shell is considered as a thin-wall and equations of motion are obtained from the energy method. Patches are in pairs on the inner and outer shell and play role of sensor and actuator in control of the system. Number of these patches are four. Using classical theory, Love strain- displacement relations, stress-strain relations, and guessed answer with known Location functions and unknown time functions, and Lagrange equation, governing equation of motion as ODE are obtained. The benefit of this method is the non-use of Hamilton's principle and get involved in differentiation and partial integrals. Natural frequencies with and without smart patches in two boundary conditions are compared with results of previous studies and then effect of angular velocity, patches area, boundary conditions and non-homogeneous index of both functionally graded material (shell and smart material) on natural frequency are investigated.