Various homogenisation schemes for vibration characteristics of axially FG core multilayered microbeams with metal foam face layers based on third order shear deformation theory

This study assesses the significance of homogenisation models in theoretically analysing the vi-brations of three-layered microbeams with a core composed of axially functionally graded (AFG) material and with upper and lower face layers composed of metal foam material, especially when the third order shear deformation beam theory and the modified couple stress theory are used. The material of the core is assumed to vary following a power gradation profile. The range of homogenisation schemes, including the Voigt model, Reuss model, Voigt-Reuss-Hill model, Tamura model, Mori-Tanaka model, lower and upper bounds of Hashin-Shtrikman, and the local representative volume element (LRVE) model, are utilised to approximate the material properties of the AFG core. The upper and lower layers of metal foams are modelled using the closed-cell and open-cell solid porosity models. The coupled motion equations are solved for the natural fre-quencies of the system for the transverse, rotational and axial directions. A software-based finite element analysis (FEA) study of two simplified macrobeam systems was undertaken and the agreement between the FEA and numerical results, using the presented theoretical method, is found to be excellent. It has been confirmed that the homogenisation schemes have a notable effect on the mechanical properties of the AFG core, and hence on the coupled translational -rotational motion's natural frequencies. The largest difference in natural frequencies between different homogenisation schemes is found with a power gradation constant of approximately 0.53. A larger disparity of natural frequencies between different homogenisation methods was seen with an increase in the thickness of the AFG core and the microbeam's length-scale parameter of multilayered porous microbeam. The results of this study highlight the signifi-cance of homogenisation scheme employed when investigating the vibrations of a multilayered microbeam with an AFG core and metal foam porous face layers.