Natural Frequencies Analysis of a Rotating Tapered Timoshenko Beam Made of Functionally Graded Material with Actuated Piezoelectric Layer

In this research, the free vibration of rotating tapered Timoshenko beam with piezoelectric layer has been studied. It is assumed that the beam is made of Functionally Graded Materials (FGM) through the thickness direction and the boundary condition is a cantilever attached to the hub. The first-order shear deformation theory has been used to drive governing equations. At first, the total energy of the system such as potential and kinetic energies for the beam and piezoelectric layer has been derived, and then the natural frequencies of the beam have been determined by the Ritz approach based on minimizing the total system energy. After verifying the results by comparing them with other research, the effects of some parameters such as hub radius, rotational speed, taper ratios, rotary inertia, material gradient, piezoelectric voltage, and beam thickness on the natural frequencies of the tapered Timoshenko beam have been studied in detail. The results showed that with increasing the angular velocity of the beam, the natural frequency increases so that as the increasing velocity increases, the natural frequency increases with a steeper slope.