Forced vibration analysis of functionally graded porous deep beams

The purpose of this study is to investigate forced vibration analysis of functionally graded porous deep beams under dynamically load. Mechanical properties of the functionally graded deep beam change in the thickness direction with porosity. The beam theories fail to satisfy in the calculation and the boundary conditions of deep beams. So, the plane solid continua model is used in the calculation of deep beams in order to obtain more realistic results. The governing equations of the problems are obtained by using the Hamilton procedure. In the solution of the problem, finite element method is used within the plane solid continua model. The effects of porosity parameters, material distribution and porosity models on the forced vibration responses of functionally graded deep beams are examined and discussed with porosity effects. Numerical results show that porosity plays very important role in the dynamic responses of the functionally graded deep beam. Choosing the suitable functionally graded material distribution, negative effects of the porosity can be decreased. It is necessary to use the plane solid continua model in modelling the deep beams.