Optimal location of FG actuator/sensor patches on an FG rotating conical shell for active control of vibration

In this paper, the optimization of piezoelectric patch positions is conducted in order to improve vibration performance of an FG-truncated conical shell. This investigation is done based upon a new optimization trend on a rotating cone for the first time, as well as, the piezoelectric material has been considered functionally graded. The vibration model is based on the classical theory, and the governing equation is obtained using the Lagrange equation. The sensor voltage change rate is selected as feedback signal to vibration control. Four different piezoelectric sets considered with different numbers of piezoelectric Patches. The settling time of the system and position of the piezoelectric patches in longitudinal direction is assumed as an objective function and optimization variable, respectively. Optimization is carried out using sequential quadratic programming and pattern search algorithms. Also, the symmetrical and asymmetrical layouts of the piezoelectric patches in order to study the settling time have been considered. Then, the effect of piezoelectric lengths and arcs on the settling time has been studied. The results show that the best position for piezoelectric placement is in a range between the middle and the base of the cone.