Free Vibration Analysis of Functionally Graded Material Plates With Distributed Patch Mass Using Third Order Shear Deformation Theory

Free vibration analysis of a rectangular and simply supported functionally graded material plate with distributed masses is presented. The Poisson’s ratio of the FGM plate is assumed to be constant, but the Young’s moduli vary continuously throughout the thickness direction according to the volume fraction of constituent defined by power-low function. The Hamilton’s Principle, using third order shear deformation theory, is applied to the simply supported rectangular plate. The displacement of the plate is postulated by a double Fourier series. The effects of size and location of the distributed patch mass on the response of the plate are also presented. A thorough comparison with well known published results is presented for the case of free vibration of unloaded plates and good agreement is observed.

Keywords:

Functionally graded material plate , Third order shear deformation theory , free vibration , distributed mass