Chapter 25 Model-Based Decision Support Methods Applied to the Conservation of Musical Instruments: Application to an Antique Cello R. Viala, V. Placet, S. Le Conte, S. Vaiedelich, and S. Cogan Abstract In musical instrument making and restoration domains, the variability of the materials and the irreversibility of the changes are issues for the experimental study of the impact of design changes and restorations on musical instruments. In addition, the analytical methods based on simplified geometries and models are not sufficiently detailed for the study of complex structures and phenomena. The virtual prototyping, and its different capabilities, can be a powerful method for instrument makers and museum curators as a decision support tool. Nevertheless, the accuracy of the model is an important matter to assess good predictions. In the case of antique and unique instruments, it is sometimes hard to obtain exhaustive geometrical properties. Similarly, it is also difficult to evaluate the material properties of full instruments, and this uncertainty may have a strong impact on the output features of the numerical models. In this study, a numerical model of cello is developed using finite element method. It is used to evaluate the impact of a modification of a geometrical property on dynamical features. It is shown that the lack of knowledge on the arching height of the top and back plates of a cello has a strong impact on the computed dynamical properties of the cello. Secondly, the model is considered with and without repair cleats and defects like galleries excavated by wood-boring insects. It is observed that the bridge admittance exhibits discrepancies above 220 Hz which is in the low frequencies domain of the model and quantify the impact of repairs. This model capability is a starting point for further simulations accounting for material and geometrical uncertainties and to assess the confidence level of a model for restoration issues. Keywords Musical acoustics · Virtual prototyping · Dynamical modelling · Cultural heritage conservation · Finite element model 25.1 Introduction Generally applied in industrial and research domains, model-based decision support has been used for decades as a powerful tool. Considering uncertainties and finely modeled geometries, it can be used for the virtual prototyping of parts and structures. In the musical instrument domain, these methods can be used as a support for the design of new instruments. Moreover, it can also be used for the conservation and restoration of antique and valuable instruments. Many models of musical instruments have been developed for decades, especially violins since the 1980s [1]. More recently, models have been developed for the reverse engineering of a violin [2] or the study of dynamics and acoustics of violin body [3] and the way geometric properties interacts. Models have also been developed to screen material properties of the wooden constituents of the violin [4] and as a decision support tool for violins and guitars [5]. It must be highlighted that curators deal with unique and irreplaceable instruments, which represents a main difference with usual industrial products, for which the critical aspects mostly deal with security and cost concerns. Musical instruments are made with different pieces of wood whose mechanical properties may be hard to evaluate and represent a considerable R. Viala ( ) · V. Placet · S. Cogan Department of Applied Mechanics, University of Bourgogne-Franche-Comté, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, Besançon, France e-mail: romain.viala@univ-fcomte.fr S. Le Conte · S. Vaiedelich Equipe Conservation Recherche, Musée de la musique, Paris, France Centre de Recherche sur la Conservation (CRC), Muséum National d’Histoire Naturelle, CNRS, Ministère de la Culture, Paris, France © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_25 223
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