Project description
Some musical instruments, such as the violins of Antonio Stradivari or the guitars of Antonio de Torres, have achieved near-mythical status among musicians and luthiers alike. These myths persist, although in the meantime several studies have proven that violin makers today are capable of building instruments of comparable quality. Nevertheless, musicians are able to detect very small differences between instruments, and thus even seemingly identical instruments differ audibly in sound. The origin of these differences lies, at least in part, in the natural variability of wood as an orthotropic biological material, where density, stiffness, and damping properties fluctuate not only between trees, but across the grain of a single plate.
At the Institute of Engineering and Computational Mechanics, we seek to turn this complexity into something measurable, predictable, and controllable. Our work combines high-resolution experimental techniques with finite element modeling, model order reduction, and optimization to characterize, simulate, and ultimately control the acoustic behavior of classical guitars, spanning from the properties of the raw wood to the sound field radiated into the room.
The foundation of our work is the identification of the instrument's dynamic behavior through experimental modal analysis. Vibration measurements are performed using laser Doppler vibrometry, yielding the eigenfrequencies, eigenmodes, and modal damping ratios of individual components as well as fully assembled instruments. These modal parameters constitute both the validation basis for our numerical models and the primary input for subsequent material identification procedures.
Selected Publications
- Brauchler, A; Ziegler, P.; Eberhard, P.: An Entirely Reverse-Engineered Finite Element Model of a Classical Guitar in Comparison with Experimental Data. The Journal of the Acoustical Society of America, Vol. 149, No. 6, p. 4450-4462, 2021.
[ DOI: 10.1121/10.0005310 ]
Identifying the material properties of a wooden instrument from vibration measurements is an inverse problem of considerable complexity, given the orthotropic character of wood and the geometric intricacy of the structure. We address this through model updating procedures, in which the parameters of a detailed finite element model are adjusted to minimize the discrepancy between numerically predicted and experimentally measured modal data. Uncertainty quantification methods are employed to account for measurement noise and model imperfections, yielding possibilistic rather than deterministic characterizations of the material parameters.
Selected Publications
- Brauchler, A; Hose, D.; Ziegler, P.; Hanss, M.; Eberhard, P.: Distinguishing Geometrically Identical Instruments: Possibilistic Identification of Material Parameters in a Parametrically Model Order Reduced Finite Element Model of a Classical Guitar. Journal of Sound and Vibration, Vol. 535, p. 117071, 2022.
[ DOI: 10.1016/j.jsv.2022.117071 ]
The acoustic variability between instruments of identical design originates in the natural variability of the material parameters of the woods employed. We investigate whether this variability can be systematically compensated through targeted geometric modifications, such that instruments built from different wood specimens converge toward a prescribed acoustic target. The design variables in this formulation include the outline geometry of the guitar body, the thickness of the plates, and the dimensions of the internal bracing elements. To render this optimization computationally tractable, parametric model order reduction is employed, enabling efficient evaluation of the objective function across the high-dimensional design space.
Selected Publications
- Cillo, P.; Ziegler, P.; Eberhard, P.: Reducing tonal variability in guitars: An efficient framework for soundboard shape optimization.
Proceedings of Meetings on Acoustics, Vol. 58, No. 1, p. 035001, 2025.
[ DOI:10.1121/2.0002052 ] - Nandalal, T. D.; Cillo, P.; Ziegler, P.; Eberhard, P.: Geometrically parameterized reduced-order finite element model for guitar soundboard shape optimization.
Acta Acustica, Vol. 9, No. 56, 2025.
[DOI: 10.1051/aacus/2025040] - Brauchler, A.; Gonzalez, S.; Vierneisel, M.; Ziegler, P.; Antonacci, F.; Sarti, A.; Eberhard, P.: Model-Predicted Geometry Variations to Compensate Material Variability in the Design of Classical Guitars. Scientific Reports, Vol. 13, No. 1, p. 12766, 2023.
[ DOI: 10.21203/rs.3.rs-2014605/v1 ]
The acoustic response of string instruments originates from the energy transfer between the vibrating string, the wooden instrument body, and the internal air cavity. This interaction forms a coupled dynamic system that requires high-fidelity modeling of all subsystems to accurately capture the complex vibro-acoustic behavior of the instrument. We develop detailed finite element models of the guitar string and the instrument body, including its acoustic interaction with the enclosed air cavity. These subsystems are coupled through an explicit constraint-based framework that enforces the kinematic coupling conditions without introducing auxiliary variables as in conventional coupling formulations. Combined with a reduced-order formulation, this approach reduces computational overhead while maintaining physical consistency. This enables the simulation of the full transient response of the system, from the initial excitation at the plucking point of the string to the resulting vibration of the instrument body.
The structural vibration of the guitar body constitutes the boundary condition for the acoustic problem in the surrounding medium. We develop boundary element models of the exterior air domain to simulate the pressure field radiated by the vibrating instrument, closing the simulation chain from material parameters and geometry to the sound field perceived by the listener.
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