Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than understanding, and a definitive scientific study of the specific relations that exist between shape and vibrational properties is yet to come and sorely missed. In this article, using standard statistical learning tools, we show that the modal frequencies of violin tops can, in fact, be predicted from geometric parameters, and that artificial intelligence can be successfully applied to traditional violin making. We also study how modal frequencies vary with the thicknesses of the plate (a process often referred to as plate tuning) and discuss the complexity of this dependency. Finally, we propose a predictive tool for plate tuning, which takes into account material and geometric parameters.

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.

It has recently been shown that the mechanical properties of thin, rectangular wooden plates can be tuned by carving them with specific patterns of perforations, effectively realising a 2D wooden mechanical metamaterial. Such a material is of great interest for the construction of musical instruments, as it could allow a new degree of creative control for makers. Furthermore, issues with the shrinking supplies of tone-woods could be alleviated as wood samples that don not meet the desired requirements could simply be altered, instead of being discarded. In this work, we study the effect of the use of these metamaterials in the soundboards of classical guitars. By way of simulations, we evaluate their impact on the modal behaviour and on the sound pressure level of the instrument, as well as on its ability to sustain the load exerted by the strings. Our results show that the metamaterials can tune the instrument’s response without compromising its structural integrity. We thus conclude that the use of wooden mechanical metamaterials in the soundboards of classical guitars is feasible and, in many ways, beneficial, not the least since it opens the door to using non-traditional woods with bespoke density and stiffness.

Comparing violins requires competence and involves both subjective and objective evaluations. In this manuscript, vibration tests were performed on a set of 25 violins, both historical and new. The resulting bridge admittances were modeled in the low and mid-frequency ranges through a set of objective features. Once projected into the new representation, the bridge admittances of three historical violins made by Stradivari and a famous reproduction revealed high similarity. PCA highlighted the importance of signature mode frequencies, bridge hill behavior, and signature mode amplitudes in distinguishing different violins.

In instruments of the violin family, the bridge is the part in charge of transferring the vibrational energy of the strings into the body and therefore contributes greatly to the sound of the instrument. The bridge needs to be light enough to efficiently transmit the strings’ movement yet rigid enough to support the static load of the strings. Historically, there have been several attempts at solving this problem with different designs, arriving in the early 1800s at the two current models: the French and the Belgian. Recently, in Cremona, Italy, the Amorim family of luthiers has developed a new cello bridge design. Inspired by their work, we study the influence of the shape of the legs of the cello bridge on its static and vibrational behavior through parametric modeling and simulations using the Finite Element Method. In particular, we perform displacement and modal analysis for different boundary conditions, providing in addition a detailed description of the mode shapes. We also compute and compare Frequency Response Functions for the different geometries. Our results show that shape can indeed be used to control the vibrational and static responses of the cello and consequently tune its sound.