A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation

A novel quasi-3D hyperbolic theory is presented for the free vibration analysis of functionally graded (FG) porous plates resting on elastic foundations by dividing transverse displacement into bending, shear, and thickness stretching parts. The elastic foundation can be chosen as Winkler, Pasternak or Kerr foundation. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. A Galerkin method is developed for the solution of the eigenvalue problem of the presented quasi-3D hyperbolic plate model. The presented quasi-3D hyperbolic theory is simple and easy to implement since it uses only five-unknown variables to determine fourfold coupled (axial-shear-bending-stretching) vibration responses. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, stiffness of foundation parameters, mode numbers, and geometry on the natural frequencies of imperfect FG plates.