Dynamics of a fg porous microbeam with metal foam under deformable boundaries

Abstract

In this study, the deformable boundary and porosity effects on the free vibration characteristics of functionally graded restrained Rayleigh microbeams made of metal foam subjected to two-parameter elastic foundations are studied by presenting an eigenvalue analysis for the first time. Porosity distribution of the functionally graded restrained microbeam is supposed to change along the height of the metal foam. Nonlocal strain gradient elasticity theory is employed to take into consideration size effects. A system of linear equations is obtained based on Fourier sine series through Stokes' transformation and they are employed to construct the eigenvalue problem. The detailed formulations are given and several mathematical problems are solved to investigate the effect of the different parameters such as strain gradient, nonlocal effect, material distribution profile, spring parameter, elastic medium and rotary inertia on the free vibration frequencies of the functionally graded restrained microbeams embedded in an elastic matrix in detail. It is explicitly figured out that the free vibration response of a restrained microbeam is influenced by these all parameters.