With the aid of fast development in manufacturing techniques, it is now possible to produce structures with considerable geometrical complexity. In the current investigation, 3D printing machine is utilized to produce beam-type bone implant made of porous polymers with three different periodic cellular topologies. The stress-strain curves and mechanical properties of the bone implants are extracted experimentally corresponding to each porosity shape with various pore sizes. Scanning electron microscope (SEM) is utilized to assess the biological capability in apatite formation on the free surface of the fabricated scaffolds after soaking in the simulated body fluid (SBF). Thereafter, based upon the obtained mechanical properties and using generalized differential quadrature (GDQ) method, the nonlinear primary resonance of bone implants made of the polymer scaffolds and subjected to the soft harmonic excitation is predicted corresponding. The frequency-response and amplitude-response of the bone implants are presented associated with the cubic, spherical and honeycomb periodic cellular topologies and different pore sizes. The analysis of soaked samples in SBF reveals that among different porosity shapes, the samples with cubic and hexagonal porosities have the maximum and minimum permeability, respectively. However, this pattern is vice versa for apatite formation. Moreover, it is seen that for the samples with cubic and hexagonal porosity shapes, the oscillation amplitude as well as the associated excitation frequency at the peak of jump phenomenon are maximum and minimum, respectively.