Natural Frequencies of Porous Orthotropic Two-Layered Plates Within the Shear Deformation Theory

Abstract

This paper analyzes the natural frequencies of porous orthotropic laminated compo-site plates with two different porosity models based on the higher-order shear defor-mation theory. The fundamental relations of natural frequency analysis are derived by using the virtual work principle and hyperbolical shear deformation theory. The obtained partial differential equations system is reduced to an ordinary differential equations system via approximation functions suitable for simply supported bounda-ry conditions and the Galerkin method. After some mathematical operations, the natural frequency equation of porous orthotropic laminated composite plates is ob-tained in the framework of hyperbolical shear deformation theory. The natural fre-quency equation based on the classical laminated plate theory can be determined by ignoring the shear strains in the theoretical formulations. After two validation studies by using appropriate results in the literature, parametric analyses are performed to show the sensitivity of natural frequencies to shear deformation, porosity model, orthotropy, layer sequence, and geometric properties.