# Using Mechanical Metamaterials in Guitar Top Plates: A Numerical Study
## 1 Introduction  
In the last few decades, scientists have focused on the theoretical, experimental, and numerical study of mechanical metamaterials, which exhibit unique mechanical properties derived from their structure rather than their composition [1]. An illustrative overview of different types of mechanical metamaterials and the state-of-the-art in this field can be found in [2, 3, 4, 5, 6]. In particular, a major challenge in the last ten years has been how to obtain lightweight mechanical metamaterials while maintaining their stiffness [3, 7, 8]. This is a topic that could deeply change the way we make musical instruments, as one is looking precisely for that combination of light weight and stiffness.  
Traditional Western wooden instruments have been historically built using the materials available to craftspeople in their region. Norway Spruce (_Picea abies_) has been a favourite of makers since the middle ages, for everything from piano soundboards to violin top plates. Wood, though, presents a high degree of variability when it comes to its mechanical properties [9]. This results in unpredictable and inconsistent mechanical response across different samples of the same wood species [10]. Furthermore, the specific kind of woods that are most used in instrument making are prone to shortages due to deforestation or climate-change-related habitat shrinkage [11, 12, 13]. The possibility ofdeliberately engineering the vibrational behaviour of a material would be, therefore, of great interest for the design of musical instruments. Indeed, not only could it help deal with the issues of the availability and variability of wood, but it could constitute a new tool in the luthier's arsenal, allowing for the development of innovative instrument designs. Mechanical metamaterials, by their very nature, could constitute one such tool. However, very few studies have been conducted on their application to musical instruments [14; 15] and even less to string instruments. Notably, in [16], one of us showed that the application of a tunable mechanical metamaterial to the soundboard of an acoustic guitar allows for controlled modification of its frequency response.  
Further work [17] has demonstrated that the elastic behaviour of thin, rectangular wooden plates can be purposefully altered by carving patterns of holes. Inspired by simple geometries of widely studied mechanical metamaterials [18; 19; 20; 21], the authors in [17] propose a novel method of manipulating the properties of thin wood plates. There, they studied the influence of elliptical and circular holes in rectangular wooden plates, both by simulations and experiments. They demonstrated that the mechanical parameters of the plate and, in particular, the longitudinal and radial moduli of elasticity can be controlled by changing the geometry of the holes, thus obtaining light, yet stiff plates and effectively creating a tunable metamaterial. This is a promising result for instrument making, as it could open the possibility for luthiers and manufacturers to directly control and tune the mechanical properties of the soundboards, resulting in greater consistency between instruments and allowing for innovative and better-performing instrument designs.  
The objective of this article is to study the effect of those mechanical metamaterials when used on the top plate of a classical guitar. We set out to study how they would impact the sound of the instrument, as well as the structural integrity under the tension of the strings and the sound production. Our goal is to find out whether these mechanical metamaterials can produce differently sounding instruments and how much control they allow over the final response of the guitar.