  The vibration of various structures such as blades of turbines, helicopters,
and all kinds of rotating robot arms can damage the structures and disrupt
their performance and balance. Thus, investigation of the reduction and control
of vibration of these structures is significant. In this paper, the coupled and
nonlinear vibration of a rotating beam in the presence of the piezoelectric
layer is considered. The Von Karman strain displacements are used for deriving
the potential equation. The nonlinear equations of motion are obtained based on
the Hamilton principle, and two ordinary differential equations are derived by
the Assume Mode method. Besides, a feedback linearization control strategy is
proposed for suppressing the vibration of the rotating beam. According to the
equation of motion, flexural and torsional vibrations are coupled. Therefore,
control of flexural mode can result in control of the whole system.
