Active vibration control of rotating FGM conical shell via piezoelectric patches

In this paper, control of forced vibration amplitude of a rotating FGM conical shell is studied using FGPM patches. Four piezoelectric patches are placed inner and outer of the shell. In order to obtain the system dynamic equations, the energy method and the classical plate theory are used and simply supported boundary conditions are considered. Each system variable is considered as an expression by separation of variables with variable-time coefficients. Subsequently by substitution the considered responses in the energy functions and finally using the Lagrange equation, the governing equations of the system are obtained. Natural frequencies are compared with the result of previous researches in the case of non-rotating and rotating shell. Also to control vibration, velocity feedback is used so that sensor voltage, which is dependent on the surface, thickness, and location of each sensor, is calculated and used in the actuator voltage. In the following section, control of the system is done for first mode and then convergent system, which in both cases, Closed-loop system well dampens amplitude of forced vibrations.