Examination of polarization coupling in a plucked musical instrument string via experiments and simulations

Abstract

In this article, the transient motion of a realistically plucked guitar string is studied experimentally and numerically in both transversal polarizations. The frequency dependent damping and suitable initial conditions are identified in the experiment and used in a simulation. For this reason an experimental set-up consisting of a string, an excitation mechanism and two laser Doppler vibrometers is developed. The excitation mechanism performs a realistic and reproducible plucking motion with a plectrum. Two laser Doppler vibrometers are used to measure the string oscillation transversally in two polarizations. The experimental set-up makes it possible to measure the string’s motion under reproducible conditions and, hence, at different positions for the same oscillation. This capability renders the identification of suitable initial conditions, i.e., initial displacement and velocity as well as the pre-tension, for a string model possible. Furthermore, a finite element model for the string is developed that takes into account the oscillation in both transversal planes of polarization and the coupling between them. Finally, the model results are in good agreement with the measurements. With help of the numerical model it can be vividly shown that the coupling between the polarizations of the oscillation is due to a torsional movement of the string on the saddle.

Port-Hamiltonian Fluid-Structure Interaction Modeling and Structure-Preserving Model Order Reduction of a Classical Guitar

“…The modeling of a guitar without strings can be found e.g. in [8,14] and the modeling of strings in [7,15]. Port-Hamiltonian representations of acoustic models are presented for instance in [34] for the vocal apparatus and for a Rhodes piano in [19].…”

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] .…”