Axisymmetric free vibration and stress analyses of saturated porous annular plates using generalized differential quadrature method

The current study presents free vibration and stress analyses of an annular plate which is made of saturated porous materials based on the first order shear deformation plate theory which accounts for the shear deformation effects. The pores are distributed in the thickness direction according to three different types, namely, porosity nonlinear nonsymmetric distribution, porosity nonlinear symmetric distribution, and porosity monotonous distribution. Employing Hamilton's principle and variational formulation, the motion equations are derived and solved via the generalized differential quadrature method as a highly accurate and rapid convergence numerical method for various boundary conditions. The results are validated with simpler cases in the literature and different parameters of the structures such as pores distribution, porosity, pressure of fluids within the pores, and also the aspect ratio of the plate is considered and discussed regarding their effects on the results. It is seen that enhancing the porosity coefficient which means increasing the void volume, reduces the structure's stiffness more than its density and so the frequency and stresses decrease. The findings of this work may be useful to design structures with desired mechanical properties.