Model-Based Decision Support Methods Applied to the Conservation of Musical Instruments: Application to an Antique Cello

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 wedges 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.

Fast estimation of wood elastic constants using least- squares

“…ν yx = ν xy E y /E x [15]. The proposed method allows measuring three such constants, via (2). Given the small variation of Poisson's ratios across specimens [5], one may fix ν xy according to tabulated values, and therefore extract E x , E y and G xy .…”

“…The problem of determining the elastic constants of wood emerges in various applications in sound synthesis and luthiery. Possible applications vary from the virtual prototyping of musical instruments, allowing for faster and more efficient product development processes [1], to model-aided conservation of historical instruments [2] and to sound synthesis purposes requiring accurate input data to generate realistic models [3]. Often, the elastic constants of woods are approximated from literature [4,5].…”

A Review of Finite Element Studies in String Musical Instruments

“…The cello is a bowed musical instrument which is less studied in the literature. Viala et al [74] recently performed an eigenmode FEM analysis on an antique cello, concluding that the geometric accuracy of the developed model highly affects the accuracy of the simulation results of the antique cello model. This study concludes that the numerical models can simulate the effect of the restorer's and instrument maker's decisions on the instrument's final dynamical behavior.…”

Model-predicted geometry variations to compensate material variability in the design of classical guitars

“…These simplified approaches allow us to obtain the values for the eigenfrequencies of the system in 1/1000th of the time compared to traditional FEM simulations without significant loss of accuracy, allowing us to perform optimisations in a reasonable time 6,8 . The traditional approach has been used in a variety of musical instruments, from the kantele 9 to the viola da gamba 10 , with numerous studies focusing on string instruments [4][5][6][7][8][11][12][13][14][15][16][17] .…”