Elastic buckling and free vibration analyses of porous-cellular plates with uniform and non-uniform porosity distributions

The aim of this research paper is to present the elastic buckling and free vibration analyses of porous-cellular plates based on the first-order shear deformation theory (FSDT). In the porous-cellular plate model, porosities are dispersed by uniform and non-uniform (symmetric and asymmetric) distribution patterns. The material properties, such as Young's modulus and mass density of the porous-cellular plates are assumed to vary along the thickness direction in term of porosity coefficient. First, the dynamic version of Hamilton's principle is applied to derive the Euler-Lagrange equations. Then, in the case of simply supported boundary condition, the critical buckling load and natural frequency of the porous-cellular plates are obtained using the Navier procedure. Furthermore, the reliability of the current formulation is validated by several examples. Finally, a comprehensive examination into the influence of porosity coefficient, porosity distributions, and the geometric parameters on the buckling behavior and vibration response of the porous-cellular plates are performed. Numerical results indicate that the effect of porosity distributions on the structural performance and provide the useful insights into the porosity design to achieve appropriately natural frequency and buckling resistance.