Xavier Boutillon

Model for piano hammers: Experimental determination and digital simulation

To explain the clearly nonlinear character of the interaction between a piano hammer and the strings it hits, a model for the hammer is proposed consisting of a point mass and a nonlinear, hysteretic spring that describes the action of the felt. Experimental determinations of force are fitted with an expression of generic form F=a(Δy)α, where α takes values such as 2.1, 3.5, and 5. Numerical simulations of hammer and string motions based on this model are found to be in good agreement with experimental measurements.

Damping by branching: a bioinspiration from trees

Man-made slender structures are known to be sensitive to high levels of vibration due to their flexibility which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong climatic events, yet with minor or no damage in most cases. A new damping mechanism inspired by the architecture of trees is identified here and characterized in the simplest tree-like structure, a Y-shaped branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism that we call damping-by-branching. It originates in the geometrical nonlinearities so that it is specifically efficient to damp out large amplitudes of motion. A more realistic model, using flexible beam approximation, shows that the mechanism is robust. Finally, two bioinspired architectures are analyzed, showing significant levels of damping achieved via branching with typically 30% of the energy being dissipated in one oscillation. This concept of damping-by-branching is of simple practical use in the design of very slender and flexible structures subjected to extreme dynamical loadings.

High-resolution modal analysis

Usual modal analysis techniques are based on the Fourier transform. Due to the Delta T .Delta f limitation, they perform poorly when the modal overlap mu exceeds 30%. A technique based on a high-resolution analysis algorithm and an order-detection method is presented here, with the aim of filling the gap between the low- and the high-frequency domains (30% < mu < 100%). A pseudo-impulse force is applied at points of interests of a structure and the response is measured at a given point. For each pair of measurements, the impulse response of the structure is retrieved by deconvolving the pseudo-impulse force and filtering the response with the result. Following conditioning treatments, the reconstructed impulse response is analysed in different frequency-bands. In each frequency-band, the number of modes is evaluated, the frequencies and damping factors are estimated, and the complex amplitudes are finally extracted. As examples of application, the separation of the twin modes of a square plate and the partial modal analyses of aluminium plates up to a modal overlap of 70% are presented. Results measured with this new method and those calculated with an improved Rayleigh method match closely.

Numerical and experimental modal analysis of the reed and pipe of a clarinet

A modal computation of a complete clarinet is presented by the association of finite-element models of the reed and of part of the pipe with a lumped-element model of the rest of the pipe. In the first part, we compare modal computations of the reed and the air inside the mouthpiece and barrel with measurements performed by holographic interferometry. In the second part, the complete clarinet is modeled by adjoining a series of lumped elements for the remaining part of the pipe. The parameters of the lumped-resonator model are determined from acoustic impedance measurements. Computed eigenmodes of the whole system show that modal patterns of the reed differ significantly whether it is alone or coupled to air. Some modes exhibit mostly reed motion and a small contribution of the acoustic pressure inside the pipe. Resonance frequencies measured on a clarinet with the mouthpiece replaced by the cylinder of equal volume differ significantly from the computed eigenfrequencies of the clarinet taking the actual shape of the mouthpiece into account and from those including the (linear) dynamics of the reed. This suggests revisiting the customary quality index based on the alignment of the peaks of the input acoustical impedance curve.

A novel haptic interface for musical keyboards

A novel haptic interface for musical keyboards is presented. The piano key has an embedded active damping system based on magneto-rheological (MR) fluids that allows to reproduce the dynamic behavior of traditional pianos. The MR fluid is encapsulated into a mechanical sealing to avoid leakage. A slider is attached to the back of the key and shears the MR fluid. When a magnetic field is applied across the MR fluid, chains of particles are aligned along the magnetic field lines. The strain of the chains will create a resistant force that can be controlled on real time. An analytical model of the whole system is presented and compared to experimental results.

Audio, visual, and audio-visual egocentric distance perception by moving subjects in virtual environments

We present a study on audio, visual, and audio-visual egocentric distance perception by moving subjects in virtual environments. Audio-visual rendering is provided using tracked passive visual stereoscopy and acoustic wave field synthesis (WFS). Distances are estimated using indirect blind-walking (triangulation) under each rendering condition. Experimental results show that distances perceived in the virtual environment are systematically overestimated for rendered distances closer than the position of the audio-visual rendering system and underestimated for farther distances. Interestingly, subjects perceived each virtual object at a modality-independent distance when using the audio modality, the visual modality, or the combination of both. WFS was able to synthesise perceptually meaningful sound fields. Dynamic audio-visual cues were used by subjects when estimating the distances in the virtual world. Moving may have provided subjects with a better visual distance perception of close distances than if they were static. No correlation between the feeling of presence and the visual distance underestimation has been found. To explain the observed perceptual distance compression, it is proposed that, due to conflicting distance cues, the audio-visual rendering system physically anchors the virtual world to the real world. Virtual objects are thus attracted by the physical audio-visual rendering system.

Three-dimensional mechanical admittance: Theory and new measurement method applied to the violin bridge

The mechanical admittance (or mobility) measures the generalized velocities of a system under generalized forces, whereas the impedance measures the forces when velocities are imposed. It is shown that generally, and in cases of practical interest, the experimental determination of the impedance and that of the admittance must comply with different requirements. Therefore, one description cannot be derived from the other unless the degrees of freedom of the system which are not measured are properly dealt with. Some of the experimental methods presented in the literature are discussed along these lines. A new method is proposed for measuring locally the mobility matrix: it is based on comparison with a known mechanical impedance and requires no force measurements. A realization is presented in the case of the bridge of a violin and a quarter-size cello. Theoretical requirements are found to be met between ∼450–1500 Hz for the violin and ∼250–2000 Hz for the cello. Limitations of the method are found to be...

Analytical investigation of the flattening effect: The reactive power balance rule

McIntyre et al. [J. Acoust. Soc. Am. 74, 1325–1345 (1983)], through comprehensive time‐domain analyses of the bowed string mechanisms and various numerical simulations, have first pointed out that the hysteretical character of the sticking–slipping process necessarily induces, under certain end conditions, a flattening effect (the note plays flat as the bow pressure exceeds a given level). Taking advantage of a frequency‐domain analysis, it is demonstrated that the area of the hysteresis cycle has an analytical relation to various physical parameters of the bowed string, leading to the concept of reactive power. The flattening effect appears as a consequence of this relation. Another possible consequence is the observed dependence of the spectrum and intensity of the string vibration on the bow pressing force. Based on realistic assumptions, an algorithm is proposed to connect the flattening effect or the intensity variations to the physical characteristics of the string. Finally, the variations of the fl...

Evaluation of the acoustical stiffness of saxophone reeds under playing conditions by using the reactive power approach

The dynamics of a saxophone reed has been analyzed by means of the simplest model—one pure spring—acceptable for frequencies below the resonance frequency of the reed. As proposed in the context of bowed string dynamics [J. Acoust. Soc. Am. 90, 754–763 (1991)], a reactive power is defined for the air‐column of a saxophone and its reed. When the instrument sustains a harmonic tone, a balance between those two reactive powers can be established, as a generalization onto a multimodal system of the usual condition sin(φ)=0 that a simple oscillator fulfills when it vibrates at its resonance frequency. The stiffness of the reed can be derived from that condition. Experiments were carried out on a saxophone played by a professional musician. The reed stiffness under playing conditions is determined after separate measurements of the input impedance (TMTC method) and of the internal pressure spectrum. Results are comparable with compliance values measured on isolated reeds by other authors.

Vibroacoustics of the piano soundboard: Reduced models, mobility synthesis, and acoustical radiation regime

Abstract In string musical instruments, the sound is radiated by the soundboard, subject to the strings excitation. This vibration of this rather complex structure is described here with models which need only a small number of parameters. Predictions of the models are compared with the results of experiments that have been presented in Ege et al. [Vibroacoustics of the piano soundboard: (non)linearity and modal properties in the low- and mid-frequency ranges, Journal of Sound and Vibration 332 (5) (2013) 1288–1305]. The apparent modal density of the soundboard of an upright piano in playing condition, as seen from various points of the structure, exhibits two well-separated regimes, below and above a frequency f lim that is determined by the wood characteristics and by the distance between ribs. Above f lim , most modes appear to be localised, presumably due to the irregularity of the spacing and height of the ribs. The low-frequency regime is predicted by a model which consists of coupled sub-structures: the two ribbed areas split by the main bridge and, in most cases, one or two so-called cut-off corners. In order to assess the dynamical properties of each of the subplates (considered here as homogeneous plates), we propose a derivation of the (low-frequency) modal density of an orthotropic homogeneous plate which accounts for the boundary conditions on an arbitrary geometry. Above f lim , the soundboard, as seen from a given excitation point, is modelled as a set of three structural wave-guides, namely the three inter-rib spacings surrounding the excitation point. Based on these low- and high-frequency models, computations of the point-mobility and of the apparent modal densities seen at several excitation points match published measurements. The dispersion curve of the wave-guide model displays an acoustical radiation scheme which differs significantly from that of a thin homogeneous plate. It appears that piano dimensioning is such that the subsonic regime of acoustical radiation extends over a much wider frequency range than it would be for a homogeneous plate with the same low-frequency vibration. One problem in piano manufacturing is examined in relationship with the possible radiation schemes induced by the models.