EXPERIMENTAL AND COMPUTATIONAL INVESTIGATION IN THE RESONANT VIBRATION OF 3D-PRINTED PLA THIN RECTANGULAR PLATES

When a plate is vibrated at the frequency of a resonant normal mode, the plate exhibits a 2D standing wave pattern with characteristics determined by its geometry, material properties, and boundary conditions. A visualization of these vibrational patterns is popularly called Chladni patterns and is named after late 18^th century German scientist Ernst Chladni. As designers and engineers continue to explore innovative applications for 3D printed materials, it is important to ensure that these fabricated parts possess mechanical resonant frequencies that match those fabricated from traditional processes. As an acknowledgement of a long-standing history here at Northern Illinois University in the study of vibrating elastic plates through the work of Professor Thomas Rossing, the objective of this investigation is to determine the relationship between 3D printing layer height and vibrational response for fused deposition modeled (FDM), polylactic acid (PLA), 3D-printed, thin rectangular plates. Experimental and computational analyses are performed to describe the free vibration of centrally clamped plates with free edge boundary conditions on all four sides indicated (FFFF). In the experimental analyses, 100% infilled specimens of five different 3D printed layer heights were fabricated and driven via a mechanical wave driver across the frequency range of 1-4000 Hz. Experimental visualizations of the standing wave patterns were performed using sand. The relationship between layer height and vibrational response for nine mode shapes was found. In the computational analysis, finite element modal analysis was used on thin rectangular plates possessing standard PLA material properties. It is concluded in this study that by decreasing the fabrication layer height to the minimum layer thickness of 0.05 mm, the experimentally observed resonant frequency for a given mode shape in the 3D printed rectangular plate approaches an approximately 3% deviation from the values calculated by finite element analysis. It is believed that as the layer height decreases, the number of connections in the plates increases, resulting in the increase of homogenous tendencies within the plate body.