Analysis of nonlinear behavior of viscoelastic damping in musical membranes using physics-informed self-organizing maps - Cristhiam Fidel Martínez Orellanos; Rolf Bader (APL Machine Learning)
This research offers a new analytical tool that unravels the nonlinear relation between the parameters of Viscoelastic Damping (VD) and the resulting frequency spectrum in musical membranes. Understanding how variations in VD parameters influence the resulting sounds is crucial for developing new tools for artistic expression and for designing musical instruments with distinct sound qualities. In the case of membranophones, the external damping is well understood, while the internal damping due to viscoelastic properties of materials remains unclear. In previous research, VD in musical membranes has been modeled using a Finite-Difference Time-Domain (FDTD) model. Nonetheless, analyzing the complex relationships between the large parameter space of the model and the nonlinear behavior of VD is a challenging task. This study addresses this analysis through physics-based machine learning. We employed a FDTD model of a viscoelastically damped membrane to create a physics-informed dataset, which we subsequently analyzed using Self-Organizing Maps (SOMs). Our findings reveal that the damping coefficient is the primary criterion when clustering the data. Furthermore, we found the internal structure of the cluster to depend on the rate of decay of the memory effect, i.e., the rate at which the energy introduced back into the system decreases. The study also demonstrates the benefits of using principal component analysis for the SOM initialization.