Abstract:
Up to around 1.1 kHz, the soundboard of the piano behaves like a homogeneous plate whereas upper in frequency, it can be described as a set of waveguides defined by the ribs. In consequence: a) The acoustical coincidence phenomenon is deeply modified in comparison with that occurring in homogeneous plates since the dispersion curve of a waveguide can present none, one, or two coincidence frequencies. This may result in a nonuniformity of the soundboard radiation in the treble range, corresponding to the so-called killer octave, where a good sustain is difficult to obtain. b) The mobility (mechanical admittance) in the direction normal to the soundboard can be synthesised with only a small number of parameters. It compares well with published measurements (Giordano, JASA, 1998), in particular the step-like falloff of the local impedance due to the localisation of the waves between ribs. c) The synthesised mobility has the same features as those which can be derived independantly, according to Skudrzyk (JASA, 1980) and Langley (JSV, 1994). This approach avoids the detailed description of the soundboard, based on a very large number of parameters. It can be used to predict global changes of the driving point mobility, and possibly of the sound radiation in the treble range, resulting from structural modifications.

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 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 flim that is determined by the wood characteristics and by the distance between ribs. Above flim, 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 flim, 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.

Abstract:
The vibrations of the soundboard of an upright piano in playing condition are investigated. It is first shown that the linear part of the response is at least 50 dB above its nonlinear component at normal levels of vibration. Given this essentially linear response, a modal identification is performed in the mid-frequency domain [300-2500] Hz by means of a novel high resolution modal analysis technique (Ege, Boutillon and David, JSV, 2009). The modal density of the spruce board varies between 0.05 and 0.01 modes/Hz and the mean loss factor is found to be approximately 2%. Below 1.1 kHz, the modal density is very close to that of a homogeneous isotropic plate with clamped boundary conditions. Higher in frequency, the soundboard behaves as a set of waveguides defined by the ribs. A numerical determination of the modal shapes by a finite-element method confirms that the waves are localised between the ribs. The dispersion law in the plate above 1.1 kHz is derived from a simple waveguide model. We present how the acoustical coincidence scheme is modified in comparison with that of thin plates. The consequences in terms of radiation of the soundboard in the treble range of the instrument are also discussed.

Abstract:
The piano soundboard transforms the string vibration into sound and therefore, its vibrations are of primary importance for the sound characteristics of the instrument. An original vibro-acoustical method is presented to isolate the soundboard nonlinearity from that of the exciting device (here: a loudspeaker) and to measure it. The nonlinear part of the soundboard response to an external excitation is quantitatively estimated for the first time, at \approx -40 dB below the linear part at the ff nuance. Given this essentially linear response, a modal identification is performed up to 3 kHz by means of a novel high resolution modal analysis technique (Ege et al., High-resolution modal analysis, JSV, 325(4-5), 2009). Modal dampings (which, so far, were unknown for the piano in this frequency range) are determined in the midfrequency domain where FFT-based methods fail to evaluate them with an acceptable precision. They turn out to be close to those imposed by wood. A finite-element modelling of the soundboard is also presented. The low-order modal shapes and the comparison between the corresponding experimental and numerical modal frequencies suggest that the boundary conditions can be considered as blocked, except at very low frequencies. The frequency-dependency of the modal density and the observation of modal shapes reveal two well-separated regimes. Below \approx 1 kHz, the soundboard vibrates more or less like a homogeneous plate. Above that limit, the structural waves are confined by ribs, as already noticed by several authors, and localised in restricted areas (one or a few inter-rib spaces), presumably due to a slightly irregular spacing of the ribs across the soundboard.

Abstract:
The grand piano is one of the most important instruments in western music. Its functioning and details are investigated and understood to a reasonable level, however, differences between manufacturers exist which are hard to explain. To add a new piece of understanding, we decided to investigate the effect of ribs mounted on a soundboard. Apart from pianos, this is important to a wider class of instruments which radiate from a structured surface. From scattering theory, it is well-known that a regular array of scatterers yields a band structure. By a systematic study of the latter, the effect of the ribs on the radiated spectrum is demonstrated for a specially manufactured multichord mimicking topologically a piano soundboard. To distinguish between radiated sound and sound propagated inside the board we use piezopolymers, an innovative, non-invasive technique. As a result we find a dramatic change in the spectrum allowed to propagate in the soundboard which is consequently radiated. An explanation by a simple model of coupled oscillators is given with a very nice qualitative coincidence.

Abstract:
The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The analysis of their morphological features suggests that the fractal dimension is a descriptor of a cluster's large-scale structure, whereas the fractal prefactor is a local-structure indicator. For a constant fractal dimension, the prefactor becomes also an indicator of a cluster's shape anisotropy. The hydrodynamic radius of orientationally averaged aggregates was calculated via molecule-aggregate collision rates determined from the solution of a Laplace equation. An empirical expression that relates the aggregate hydrodynamic radius to its radius of gyration and the number of primary particles is proposed. The suggested expression depends only on geometrical quantities, being independent of statistical (ensemble-averaged) properties like the fractal dimension and prefactor. Hydrodynamic radius predictions for a variety of fractal-like aggregates are in very good agreement with predictions of other methods and literature values. Aggregate dynamic shape factors and DLCA individual monomer hydrodynamic shielding factors are also calculated.

Abstract:
Il sistema della mobilità in area urbana è strategico per il funzionamento di qualunque città. Esso è composto da un sistema di parti e di funzioni interrelate strettamente con il territorio di riferimento; tra queste funzioni la sosta rappresenta un’attività primaria e la sua organizzazione e pianificazione un punto nodale di una corretta pianificazione della mobilità: questo a causa, principalmente, della sua caratteristica fondamentale, ossia l’essere attrattore di flussi veicolari. La scelta dei siti dove localizzare le strutture per la sosta e la determinazione delle relative caratteristiche gestionali va effettuata con una particolare attenzione agli impatti sulla organizzazione e sulla vivibilità della città stessa, il che si traduce in una stretta connessione con la pianificazione urbanistica e in una considerazione profonda dei caratteri morfologici delle diverse parti che compongono la città. Diversi sono gli strumenti di programmazione del sistema della mobilità e, al suo interno, della sosta. Il Piano Urbano della Mobilità è l’ultimo nato tra questi ed è uno strumento prevalentemente strategico in quanto agisce sul sistema nel suo complesso ipotizzando una generale razionalizzazione ed evoluzione di reti e mezzi. L’articolo approfondisce i caratteri di questo strumento, a partire dalle previsioni legislative ed in relazione a specifici casi applicativi. In particolare, la prima parte analizza i concetti che sono alla base delle relazioni tra città, mobilità urbana e regolazione della sosta. Nella seconda parte si analizzano gli aspetti normativi, ossia il Piano Urbano della Mobilità, anche in relazione ad uno strumento che lo ha preceduto e che era specificamente indirizzato alla programmazione delle infrastrutture per la sosta, il Programma Urbano dei Parcheggi. La terza parte analizza due casi di applicazione dello strumento, relativi alle città di Ferrara e Perugia con lo scopo di evidenziare le diverse opzioni che si aprono davanti al pianificatore nel momento in cui è necessario applicare lo strumento teorico ad una specifica realtà urbana. Infine, nella quarta parte, sono messe in evidenza alcune delle tecniche e degli strumenti utilizzabili per la risoluzione del problema della sosta in relazione ai tipi di sosta, alle diverse modalità per la sua organizzazione e alle tecniche di gestione indirizzate a favorire comportamenti più corretti in relazione ai diversi ambiti urbani. In the urban areas the mobility system is strategic for its working and it is composed of a series of territorial closely interrelated elements. Among these the p

Abstract:
On the basis of a recently proposed vibro-acoustical model of the piano soundboard (X. Boutillon and K. Ege, Vibroacoustics of the piano soundboard: reduced models, mobility synthesis, and acoustical radiation regime. \emph{submitted to the Journal of Sound and Vibration}, 2011.), we present several models for the coupling between the bridge and the ribbed plate of the soundboard. The models predict the modal density and the characteristic impedance at the bridge as a function of the frequency. Without parameter adjustment, the sub-structure model turns out to fit the experimental data with an excellent precision. The influence of the elastic parameters of wood is discussed. The model predictions are compared for pianos of different sizes and types.

Abstract:
The aim of this study is to examine the mental processes that affect the piano performance. An efficient performance and education of the piano instrument depends on a complex systematic structure of a combination of some musical and technical challenges. To succeed in piano playing, one shall overcome the difficulties systematically over several years. Naturally, this process depends on many variables and the correct organization of the central nervous system plays a very important role on it. Having a complete understanding on the subject matter, it might guide the performance of piano playing and its educationBy the analysis of the historical processes, the activity of playing the piano was initially seen as a pure mechanical activity. However, at the beginning of the 20th Century, scholars had started to consider it not without its physiological and mental elements. This trend has reached today by gradually increasing its importance. Today in the contemporary piano performance and education, the mental processes are not being isolated from the whole matter of subject. In this study, the importance of the practicing methods that are based on correct organization of the central nervous system is set forth and to increase the efficiency of the piano performance, some practicing examples are given.

Abstract:
This paper reviews recent developments in physics-based synthesis of piano. The paper considers the main components of the instrument, that is, the hammer, the string, and the soundboard. Modeling techniques are discussed for each of these elements, together with implementation strategies. Attention is focused on numerical issues, and each implementation technique is described in light of its efficiency and accuracy properties. As the structured audio coding approach is gaining popularity, the authors argue that the physical modeling approach will have relevant applications in the field of multimedia communication.