Acoustical modeling, prototypes and sound synthesis for piano soundboards – MAESSTRO

The compromise between the sound level, the sound duration and other sound parameters of the piano depends on the local mobility of the soundboard. This parameter depends in particular on local variations of the thickness of the plate, on the height and on the width of stiffeners. An analytical model capable of estimating the local mobility according to the mechanical and geometrical characteristics of the soundboard will take into account these variations. A simplified model yielding global descriptors of the dynamics will be improved. The radiated sound will be computed on the basis of the predicted vibration.
The computer-aided sound tool (function: to restitute sound modifications induced by the modifications of the architecture of a soundboard) will gather computation modules developed in laboratories. Ergonomy will be looked after, in particular for the input of data related to instrument making (material, geometry, etc.) and the exchange of standardized information between modules. The software will be tested by comparing sound, its outcomes, and differences between a traditional table and modified tables ( traditional invoice) or in new architectures. It is aimed at being used by makers and scientists (integration of new scientific findings).
The elaboration of tables in composite materials will be supported by the dynamic modeling: dispersion curves and structural damping of sandwich plates, on one hand, optimization of the dynamics by control of the local anisotropy and stiffness (transposition to vibration criteria of a polar method of optimization of the stiffness and the specific resistance). Genetic algorithms will be used to identify the structures and optimal sequences of layers. Mechanical and dynamical tests will be performed on test-plates and soundboard prototypes (made in heated pre-preg in vacuum, and with cores manufactured by means of a 3D digital manufacturing tool).

A code for computing the eigenmodes of the soundboard has been written, yielding the vibration and sound radiation of the soundboard under the action of a string: soundboard of any geometrical shape, orthotropic material, stiffeners parallel to one of the main directions of orthotropy, all structural elements being homogeneous. For the computation of the radiated sound, the soundboard is considered to be in a plane baffle. An important measurements campaign has been performed on a Pleyel P131 soundboard (with bridge, unstrung).
The programs for evaluating the static response of the soundboard to a unit pressure (necessary for evaluating the localization «landscape«) and its normal modes have been written for orthotropic plates without stiffeners but with local adds-on such as masses or holes. The programs can also take into account heterogeneous boundary conditions. The localization of the vibration predicted by the landscape of localization, as observed on the computed normal modes, is not very marked for plausible distributions of heterogeneous elements.
First models of soundboardshave been done. A first modal prediction was tried and compared to measurements. This highlighted the difficulty to predict damping. An original method of characterization of sandwich plates, based on the prediction of the dispersion laws of anisotrope materials is under development.

The benefits of MAESSTRO are expected in piano and other instruments and in acoustical engineering.
Substantial productivity gains are expected for in piano making and repair (for example: major cracks in soundboards, flat instead of normally arched soundboard, due to wood aging): the computer-aided sound sofware will help to test several solutions at no making costs. Also, the restoration of historical keyboard instruments (pianos, harpsichords, etc.) for which one can barely experiment, will also benefit from this virtual lutherie.
French instrument makers did not take, until now, the initiative of a project as ambitious as MAESSTRO. Its potential impact is important since it is an original attempt to establish bridges between the scientific modelling and the practice of these professionals. Outcomes are expected in the long term for other instruments - harp, guitar - at the price of more or less important adaptations.
The improvement of vibration models is also of interest within the framework of physically-based sound synthesis. This sound synthesis approach allows in particular «virtual lutherie«: synthesizing sounds of instruments which we cannot be build for physical reasons, or which cannot be sounded directly anymore for reasons of museum preservation.
MAESSTRO may also have an impact in industrial structural acoustics. Predicting the localization of vibrations in mechanical structures (which may cause fatigue, for example) would help limit their impact. To control the local anisotropy of a structure is important in composite structures design (generally only the main directions of anisotropy of the constituent material can be assessed). The optimization method will allow to identify optimal directionsfor composite orientation.

Comparisons between measured and predicted vibroacoustics characteristics of an upright piano soundboard, Trévisan, Margerit, Ege, Laulagnet, Vienna Talk 2015.
Caractérisation vibraoacoustique d’une table d’harmonie de piano droit, Margerit P., Trévisan B., Ege K., Laulagnet B., Congrès français de mecanique, Lyon 2015.

The french piano manufacturing network became gradually depopulated of its industrial actors and of piano makers able of designing and building a piano from A to Z. SPCP is the last company in this situation, designing pianos for other (foreign) firms and manufacturing high-end grand pianos.
The design of pianos is based on empirical knowledge and has progressed through marginal improvement of existing schemes. A recent innovation of S. Paulello (bridge agraffes that couples strings to the soundboard) eliminates the needs that the string exerts a static force normal to the board. The disappearance of the corresponding large downward stress allows the evolution of the traditional architecture of the soundboard (prestressed arch with stiffeners) in the direction of lightening, favorable to loudness. S. Paulello has already started to develop flat boards, without stiffeners, in sandwich structures. In order to exploit the potential of this innovation, a renewal of the designing methods is required to prevent the construction of a large number of prototypes without future.
MAESSTRO aims at completing knowledge of the vibroacoustics of the piano soundboard, to provide a sound synthesis software for CAD of musical instrument soundboards, and to propose new architectures of piano soundboards (sandwich structure, including composites) and methods for their optimization.
The knowledge that we have recently acquired on the vibroacoustics of the soundboard includes a semi-analytical model, with a small number of parameters, and a numerical model with a large number of parameters, both valid up to several kHz. A work in progress at LVA aims to adapt to the case of the piano an analytical approach of the vibrations of orthotropic ribbed structures. Finally, a decisive step was taken recently by a researcher involved in the project for the prediction of the localization of the vibration (Anderson’s localization) in heterogeneous or irregular systems. The targeted knowledge consists in taking into account the local characteristics of the soundboard in the description of its vibration, predicting the localization and extending to the radiation problem the small-number-of-vibratory-parameters model.
The best piano sound syntheses (sampling or numerical modeling of the whole vibroacoustical problem) are inadequate for the design aid (by nature or because of too long computing duration). The sound synthesis method proposed here is focused on manufacturers’usage in order to reflect as well as possible the changes made in the sound by structural modifications. It will integrate the knowledge already acquired and provided by MAESSTRO.
Manufacture of soundboards in composite materials (guitars, bowed instruments, harpsichords, some pianos) dates back practically to the appearance of these materials but design methods were most often limited to the imitation of the dynamical properties of wood, completed with empiricism. Recent models and parameters describing successfully the soundboard vibration on a broad frequency range provide design and optimization criteria. Recent optimization methods for laminates (genetic algorithms) will be transposed to these vibratory criteria and several sandwich boards will be made in this way, implemented and tested. The technology implemented will enable local variations of stiffness and anisotropy directions.
Economical impact of MAESSTRO is expected in piano manufacturing – small series of a baby grand model of high quality in composite materials, design of an upright piano model with stable tuning for music schools – for other string instruments manufacturing and in vibro-acoustical industrial applications.