The so-called locally resonant acoustic metamaterials (LRAMs) are a new kind of artificially engineered materials capable of attenuating acoustic waves. As the name suggests, this phenomenon occurs in the vicinity of internal frequencies of the material structure and can give rise to acoustic bandgaps. One possible way to achieve this is by considering periodic arrangements of a certain topology (unit cell), smaller in size than the characteristic wavelength. In this context, a computational model based on a homogenization framework has been developed from which one can obtain the aforementioned resonance frequencies for a given LRAM unit cell design in the sub-wavelength regime, which is suitable for low-frequency applications. Aiming at validating both the proposed numerical model and the local resonance phenomena responsible for the attenuation capabilities of such materials, a 3D-printed prototype consisting of a plate with a well selected LRAM unit cell design has been built and its acoustic response to normal incident waves in the range between 500 and 2000 Hz has been tested in an impedance tube. The results demonstrate the attenuating capabilities of the proposed design in the targeted frequency range for normal incident sound pressure waves and also establish the proposed formulation as the fundamental base for the computational design of 3D-printed LRAM-based structures.