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In this paper the influence of microstructure on the free vibration of geometrically similar heterogeneous beams with free-free boundary conditions was numerically investigated to identify and quantify any effect of beam size on transverse modal frequencies when the microstructural scale is comparable to the overall size. ANSYS Mechanical APDL was used to generate specific unit cells at the microstructural scale comprised of two isotropic materials with different material properties. Unit cell variants containing voids, inclusions and strata were considered. At the macroscopic scale, four beam sizes consisting of one, two, three or four layers of defined unit cells were represented by repeatedly regenerating the unit cell as necessary. In all four beam sizes the aspect ratio was kept constant. Changes to the volume fractions of each material were introduced while keeping the homogenized properties of the beam fixed. The influence of the beam surface morphology on the results was also investigated.
The numerical results were compared with the analytical results from solution to Timoshenko beam, modified Timoshenko beam (based on single layer theories and incorporating specific heterogeneities into the governing equations) and nonlocal Timoshenko beam. In nonlocal Timoshenko beams the Eringen’s small length scale coefficients where estimated for some of the studied models.