Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities

Linear and nonlinear vibration problems of elastically end restrained beams made of functionally graded materials (FGMs) are investigated in this present paper. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration behavior of beams having porosities in this investigation. The rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The differential transformation method (DTM) is employed to solve linear and nonlinear vibration responses of FGM beams with different kinds of elastic supports. The effects of material property distribution, spring constants and porosity volume fraction on linear and nonlinear frequencies of FGM beams are also presented and discussed in detail.