Linear Vibration Analysis of Functionally Graded Thick Beams Carrying Porosities under Thermal Load

In the current research, the vibrational behavior in bending of FG beams carrying porosities (PFGBs), exposed to different thermal loads is studied according to an efficient beam theory; the displacement field is determined by a hyperbolic variation of transverse andin-plane displacements through the thickness. The number of unknowns and, consequently the number of governing equations is reduced by decomposing the transverse displacement into shearing and bending components.On PFGB lower and uper faces, the boundary conditions are respected without shear correction. Material mechanical and thermal characteristics depend on the temperature, and change with beam thickness according to a modified mixing law. Even and uneven porosities-distributions through the beam cross-section are used. Hamilton's principle is applied to obtain the motion equations. Boundary conditions Hard and Simply Supported (HSS) are considered to allow beam-buckling. The differential equations system is solved by using the Navier-solution. The temperature and porosity effects on the frequency responses and buckling of HSS-PFGB are shown graphically and numerically, and then discussed in detail