A Chebyshev–Ritz solution for size-dependent analysis of the porous microbeams with various boundary conditions

This research proposes a Chebyshev–Ritz solution for analysing the size-dependent behaviour of porous microbeams. The displacement field is based on the higher-order beam theory, while the size-dependent effect is accounted for using the modified couple stress theory. Moreover, porous microbeams’ elasticity moduli and mass density are assumed to be graded in the thickness direction according to four distinct distribution patterns. The open-cell metal foam exemplifies a characteristic mechanical attribute that facilitates the determination of the interrelation between coefficients of density and porosity. To derive the governing equations, the Lagrange’s principle is employed. Four types of boundary conditions, including clamped–clamped, clamped-simply supported, clamped-free, and simply-supported, along with four porosity distribution types of the beam, are considered. The Chebyshev polynomial is developed to analyse the porous microbeams’ buckling, free vibration, and bending. Furthermore, the study discusses the impacts of the material length scale parameter, porosity, slenderness, boundary condition, and porosity type on their mechanical responses. Finally, some novel results are presented, which can serve as benchmarks for future studies.