Deflection control of functionally graded material beams with bonded piezoelectric sensors and actuators

An analytical solution is developed for analysis of functionally graded material (FGM) beams containing two layers of piezoelectric material, used as sensor and actuator. The properties of FGM layer are functionally graded in the thickness direction according to the volume fraction power law distribution. The equations of motion are derived by using Hamilton's principle, based on the first-order shear deformation theory. By using a displacement potential function, and assumption of harmonic vibration, the equations of motion have been solved analytically. Finally, the effects of FGM constituent volume fraction in the peak responses for various volume fraction indexes have been graphically illustrated