Mathematical Analysis of Flexural Vibration for a Functionally Graded Material Plate and Vibration Suppression by Flexural Wave Control

In this paper, flexural vibrations of rectangular plates and beams which are consisted of functionally inhomogeneous materials due to cyclic loadings of external force and temperature change are analyzed mathematically. Interference between the flexural vibration due to cyclic loading and that due to cyclic heating is discussed. The amplification effect by loading frequency is also discussed for the deflection and stresses of the beam and the plate. Furthermore, a control problem of the flexural vibration of the FGM beam by the method of wave control is considered. In order to remove progressive wave in flexural waves excited by cyclic loading, intensity and phase lag of control force are derived on the basis of the active sink method. Then, the validity of wave control for the flexural vibration suppression of the FGM beam is discussed