A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities, resting on elastic foundations

Some Functionally Graded Materials contain pores due to the result of processing; this influences their elastic and mechanical properties. Therefore, it may be very useful to examine the vibration behavior of thin Functionally Graded Annular Plates Clamped at both edges including porosities. In the present study, the rule of mixture is modified to take into account the effect of porosity and to approximate the material properties assumed to be graded in the thickness direction of the examined annular plate. A semi-analytical model based on Hamilton’s principle and spectral analysis is adopted using a homogenization procedure to reduce the problem under consideration to that of an equivalent isotropic homogeneous annular plate. The problem is solved by a numerical iterative method. The effects of porosity, material property, and elastic foundations characteristics on the CCFGAP axisymmetric large deflection response are presented and discussed in detail.