Distinguishing geometrically identical instruments: Possibilistic identification of material parameters in a parametrically model order reduced finite element model of a classical guitar

Brauchler, Alexander; Hose, Dominik; Ziegler, Pascal; Hanss, Michael; Eberhard, Peter

doi:10.1016/j.jsv.2022.117071

Cited by 9 publications

(22 citation statements)

References 32 publications

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“…We focused on these material properties since they have been proved to be important for determining the vibroacoustic properties of complete instruments 23,[27][28][29] . Indeed, their correlation with the first modes of the instrument is found to be higher than others 30 . Moreover, luthiers usually focus on the Young's modulus along the principal dimensions of the wedge as they can infer them empirically 31 and they are used to define acoustic indicators for instruments (e.g.…”

Section: Resultsmentioning

confidence: 73%

The impact of alkaline treatments on elasticity in spruce tonewood

Malvermi

Albano

González

et al. 2022

Sci Rep

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It is commonly believed that violins sound differently when finished. However, if the role of varnishes on the vibrational properties of these musical instruments is well-established, how the first components of the complete wood finish impact on the final result is still unclear. According to tradition, the priming process consists of two distinct stages, called pre-treatment and sizing. The literature reports some recipes used by old Cremonese luthiers as primers, mainly based on alkaline aqueous solutions and protein-based glues. In this manuscript, we analyze the impact of these treatments on the mechanical properties of the material. The combination of two pre-treatments and three sizes is considered on nine different plates. We compare the vibrational properties before and after the application and assess the effects of the different primers, also supported by finite element modeling. The main outcome is that the combination of particular treatments on the violin surface before varnishing leads to changes not only to the wood appearance, but also to its vibrational properties. Indeed pre-treatments, often considered negligible in terms of vibrational changes, enhance the penetration of the size into the wood structure and strengthen the impact of the latter on the final rigidity of the material along the longitudinal and radial directions.

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Section: Resultsmentioning

confidence: 73%

The impact of alkaline treatments on elasticity in spruce tonewood

Malvermi

Albano

González

et al. 2022

Sci Rep

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“…Previous results on the use of metamaterials for thin wooden plates 27 show that, to a certain degree, the density and stiffness of the plates can be purposefully controlled. By matching the density and the longitudinal stiffness of the top and the back plate, we can be certain that the modifications of the braces will be minimal 6 . The implications of these results are far-reaching in the field of instrument making: By quantifying how close we can come to a desired vibrational response with a given material, we have taken guesswork out of the equation in guitar-making.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, a projection-based Krylov approach for parametric model order reduction was applied to reduce the number of degrees of freedom in an efficient surrogate model to n = 600 while keeping a good approximation of the full-order model's results up to 1000 Hz. This was reached by matching the transfer function of 4 inputs and outputs distributed over the plate at 20 frequency shifts equally distributed in the frequency range and 60 parameter expansion points created with a Sobol sequence as explained in 6 . General information on model order reduction can be found in 43,44 while a review of parametric model order reduction techniques is given in 45 , and the used software is described in 46 .…”

Section: Materials Parameter Identificationmentioning

confidence: 99%

“…The material parameter identification follows the approach described in detail in 6 . Detailed finite element models of the guitar plates act as the key pieces of the approach 40,41 .…”

Section: Materials Parameter Identificationmentioning

confidence: 99%

“…The starting point for our research lies with the recent advances in simplified FEM simulations for musical instruments, be they for guitars with model order reduction methods 5,6 or violins with neural networks 7 . 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] .…”

Section: Introductionmentioning

confidence: 99%

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

Brauchler

González

Vierneisel

et al. 2022

Preprint

Self Cite

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Musical instrument making is often considered a mysterious form of art, its secrets still escaping scientific quantification. There is not yet a formula to make a good instrument, so historical examples are regarded as the pinnacle of the craft. This is the case of Stradivari’s violins or Torres guitars that serve as both models and examples to follow. Geometric copies of these instruments are still the preferred way of building new ones, yet reliably making acoustic copies of them remains elusive. One reason for this is that the variability of the wood used for instruments makes for a significant source of uncertainty -- no two pieces of wood are the same. In this article, using state-of-the-art methodologies, we show a method for matching the vibrational response of two guitar top plates made with slightly different materials. To validate our method, we build two guitar soundboards: one serving as a reference and the second acting as a copy to which we apply model-predicted geometry variations. The results are twofold. Firstly, we can experimentally validate the predictive capabilities of our numerical model regarding geometry changes. Secondly, we can significantly reduce the deviation between the two plates by these precisely predicted geometry variations. Although applied to guitars here, the methodology can be extended to other instruments, e.g. violins, in a similar fashion. The implications of such a methodology for the craft could be far-reaching by turning instrument-making more into a science than artistic craftsmanship and paving the way to accurately copy historical instruments of a high value.

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On shift selection for Krylov subspace based model order reduction

Frie

Eberhard

2023

Multibody Syst Dyn

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Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequently, moment matching based on Krylov subspaces is used for the reduction. There, the transfer functions of the full system and of the reduced system are matched at distinct frequency shifts. The selection of these shifts, however, is not trivial. In this contribution we suggest an algorithm that evaluates an increasing number of shifts iteratively until a reduced model that approximates the full model in a subspace with very low approximation error is found. Thereafter, the projection matrix that spans this subspace is decomposed with singular value decomposition and only most important directions are retained. In this way, small reduced models with good approximation properties that do not exceed a predefined error bound can be found or low-error models for a given reduced order can be generated. The evaluation of more shifts than necessary and further reduction by means of singular value decomposition is the novelty of this contribution. In this paper, this novel approach is extensively studied and, furthermore, applied to the numerical example of an industrial helicopter model.

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Distinguishing geometrically identical instruments: Possibilistic identification of material parameters in a parametrically model order reduced finite element model of a classical guitar

Cited by 9 publications

References 32 publications

The impact of alkaline treatments on elasticity in spruce tonewood

The impact of alkaline treatments on elasticity in spruce tonewood

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

On shift selection for Krylov subspace based model order reduction

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