Free vibration behavior of bi-directional functionally graded plates with porosities using a refined first order shear deformation theory

This paper proposes the refined first order shear deformation theory to investigate the free vibration behavior of bidirectional functionally graded porous plates. This theory satisfies the transverse shear stress free conditions at the top and bottom of the plate, thus avoids the need of a shear correction factor. The rule of mixtures is employed to compute the effective material properties and assumed to be graded in both x and z-directions. The equations of motion are derived by means of Lagrange equations to investigate the free vibration response. The displacement functions in axial and transverse directions are expressed in simple algebraic polynomial series form, including admissible functions which are used to fulfill the simply supported boundary conditions. The admissible functions are generated using Pascal’s triangle. The accuracy of the present theory is assessed with the numerical results and is confirmed by comparing with ۳-D exact solutions and with other higher order theories. The influence of thickness ratios, aspect ratios, gradation indexes, type of porosity distribution and the volume fraction of porosity on the free vibration behavior of bi-directional FGPs are discussed in detail. The presented numerical results can be used as benchmark solutions to assess the various plate theories and compare with solutions obtained by other analytical and finite element methods. From the present work, it can be concluded that the present theory allows examining the vibration behavior of bidirectional porous FG plates manufactured in the sintering process.

Keywords:

Bidirectional Functionally graded plates , Porosities , Free Vibration , Rule of Mixtures , Lagrange Equations