6. Vibration Analysis of FGPM Annular Plate

The annular plate structures are the fundamental structure elements which are extensively used in engineering applications such as ultrasonic motors. As discussed in the previous section, if the piezoelectric plate is polarized in the thickness direction and the electric field is applied in the same direction, the deformation is observed in the thickness direction which is due to \(d_{33}\) effect. And if the deformation is observed in the radial direction, it is due to the \(d_{31}\) effect. The literature on vibration analysis of functionally graded piezoelectric material (FGPM) annular plate is available in [1, 2]. It has been observed that most of the FGPM annular/circular plate actuators are based on \(d_{31}\) effect. If the piezoelectric plate is polarized in the radial direction and the electric field is applied in the thickness direction, the deformation is observed due to \(d_{15}\) effect. Parashar [3] demonstrated the modal characteristics of pure piezoceramics plate when the \(d_{15}\) effect is utilized. The vibration behavior of FGPM plate with hole when the \(d_{15}\) effect is utilized is discussed here.