Active control of free and forced vibration of a rotating FG cylindrical shell via FG piezoelectric patches

Abstract

This article aims to study the active control of free and forced vibration of a rotating functionally graded (FG) cylindrical shell using FG piezoelectric patches. Accordingly, this study uses sensors and actuators embedded in the shell’s inner and outer surfaces. Considering classical theory and Love relations, ordinary differential equations of the system are extracted through the energy method and Lagrange equation. The validation part of the study involves comparing the results of this study with previous studies of rotating and nonrotating cylindrical shells. In addition, the convergence of vibration responses of the rotating cylindrical shell is investigated. Using the LQR method and considering the appropriate value for the weighting matrices, the system’s vibration is attenuated, and the required voltage of the actuators is also obtained. Lastly, the effects of parameters such as position and performance index of piezoelectric on the closed-loop response are studied. The results show that changing piezoelectric properties in the form of a power law lead to a quicker decrease in vibration amplitude.

Keywords:

• Rotating shells
• FG cylindrical shells
• piezoelectric patches
• active control of vibration
• LQR method