Free vibration analysis of sandwich beam with porous FGM core in thermal environment using mesh-free approach

Thermally induced free vibration of sandwich beams with porous functionally graded material core embedded between two isotropic face sheets is investigated in this paper. The core, in which the porosity phase is evenly or unevenly distributed, has mechanical properties varying continuously along with the thickness according to the power-law distribution. Effects of shear deformation on the vibration behavior are taken into account based on both third-order and quasi-3D beam theories. Three typical temperature distributions, which are uniform, linear, and nonlinear temperature rises, are supposed. A mesh-free approach based on point interpolation technique and polynomial basis is utilized to solve the governing equations of motion. Examples for specific cases are given, and their results are compared with predictions available in the literature to validate the approach. Comprehensive studies are carried out to examine the effects of the beam theories, porosity distributions, porosity volume fraction, temperature rises, temperature change, span-to-height ratio, different boundary conditions, layer thickness ratio, volume fraction index on the vibration characteristics of the beam.