# Using Mechanical Metamaterials in Guitar Top Plates: A Numerical Study
## 4 Discussion  
In this article, we showed by means of simulations that the use of mechanical metamaterials for the top plate of a classical guitar is a feasible option regarding its load-bearing capacity, as well as its dynamic response. The results are extremely relevant as they present a way to, in principle, compensate the intrinsic material variation that characterises wood by modifying the pattern of the metamaterial to suit particular needs. We showed that, for all practical purposes, tops made with metamaterials behave in a way that is indistinguishable from solid wood. By doing so, the variability of wood becomes a treatable feature, much like other design variables of the guitar, and not a given. Using the material as a design parameter could open a realm of possibilities, mostly when used with artificial intelligence approaches [35], such that one can start engineering musical instruments as opposed to crafting them. Figure 4: Sound pressure level of the complete body of the instrument for the solid top and two metamaterial configurations. These were obtained by imposing a normal harmonic load on a circular area with a 2 mm radius on the top surface of the soundboard, located under the bridge, in the middle of the lower bout. (**a**) Absolute value of the SPL. (**b**) Relative difference between the guitar with a solid top and the guitar with a metamaterial top plate. Our results show that the dynamic response, measured via the eigenfrequencies of the instrument, is not very sensitive to the orientation of the metamaterial, i.e., to its longitudinal stiffness. This is consistent with existing studies on the impact of the variation of the mechanical properties of different components on the vibrational response of the guitar. In [36], the density of the top plate is the second-most relevant feature, whereas its stiffness has little relevance. Our findings confirm this, given that, with the patterns we used, the density difference between the two orientations of the holes is negligible, whereas their effective radial and longitudinal stiffnesses will vary considerably. A guitar is not only an instrument that needs to vibrate though, it is also necessary that it bears the load of the strings without breaking or deforming too much so as to influence its playability. Indeed, the orientation of the holes does seem to have a clearer impact on the structure's load-bearing capacity, as we found with our static load simulations. Our findings indicate that metamaterial soundboards with longitudinal holes are better suited to withstand the tension of the strings. Given this advantage, therefore, this choice of orientation seems to be overall preferable. In terms of sound production, though, the picture is more nuanced. There are several studies in the literature that have related the frequency response of an instrument to its perceived quality [33; 37; 38], and this could even influence the quality of the instrument [39]. The results presented there showed that the inclusion of metamaterials would have both positive and negative effects in the sound quality, which need to be balanced by the guitar maker to achieve a desired sound. The introduction of parametric metamaterials allows one such a way to fine-tune the frequency response of the instrument. The implications of these results for contemporary guitar making, and instrument making in general, are far fetching. The constant and sustained habitat reduction that tone-wood suffers due to global warming [12] is not going to be reversed anytime soon: making do with lower-grade woods may be the only possibility to continue making traditional instruments. These results present a straightforward way to use different woods in the construction of guitars by tuning their density and stiffness to a desired, perhaps optimal, value. Conceptualisation, S.G. and C.E. ; methodology, S.G.; software, M.L. and G.L. ; investigation, M.L. ; writing--review and editing, M.L., C.E. and S.G.; visualisation, M.L. ; supervision, S.G.; funding acquisition, C.E., F.A.