Modeling and simulation of a grand piano

被引:40
作者
Chabassier, Juliette [1 ]
Chaigne, Antoine [2 ]
Joly, Patrick [1 ]
机构
[1] INRIA Rocquencourt, Poems Team, F-78153 Le Chesnay, France
[2] ENSTA ParisTech, Dept Mech Engn UME, F-91761 Palaiseau, France
关键词
LONGITUDINAL VIBRATIONS; MECHANOACOUSTIC PIANO; NUMERICAL-SIMULATION; STRING VIBRATIONS; SOUNDBOARD; TONE; GENERATION; DISPERSION; STABILITY; DESIGN;
D O I
10.1121/1.4809649
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
A time-domain global modeling of a grand piano is presented. The string model includes internal losses, stiffness, and geometrical nonlinearity. The hammer-string interaction is governed by a nonlinear dissipative compression force. The soundboard is modeled as a dissipative bidimensional orthotropic Reissner-Mindlin plate where the presence of ribs and bridges is treated as local heterogeneities. The coupling between strings and soundboard at the bridge allows the transmission of both transverse and longitudinal waves to the soundboard. The soundboard is coupled to the acoustic field, whereas all other parts of the structure are supposed to be perfectly rigid. The acoustic field is bounded artificially using perfectly matched layers. The discrete form of the equations is based on original energy preserving schemes. Artificial decoupling is achieved, through the use of Schur complements and Lagrange multipliers, so that each variable of the problem can be updated separately at each time step. The capability of the model is highlighted by series of simulations in the low, medium, and high register, and through comparisons with waveforms recorded on a Steinway D piano. Its ability to account for phantom partials and precursors, consecutive to string nonlinearity and inharmonicity, is particularly emphasized. (C) 2013 Acoustical Society of America.
引用
收藏
页码:648 / 665
页数:18
相关论文
共 39 条
[1]  
Anderssen R., 2007, MATH SCI, V32, P71
[2]  
[Anonymous], STL QPSR
[3]   FROM TOUCH TO STRING VIBRATIONS .2. THE MOTION OF THE KEY AND HAMMER [J].
ASKENFELT, A ;
JANSSON, EV .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1991, 90 (05) :2383-2393
[4]  
Balmes E., 2006, P 24 IMAC C EXP STRU, V3, P1314
[5]   Generation of longitudinal vibrations in piano strings: From physics to sound synthesis [J].
Bank, B ;
Sujbert, L .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2005, 117 (04) :2268-2278
[6]   Perception of longitudinal components in piano string vibrations [J].
Bank, Balazs ;
Lehtonen, Heidi-Maria .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2010, 128 (03) :EL117-EL123
[7]   Stability of perfectly matched layers, group velocities and anisotropic waves [J].
Bécache, E ;
Fauqueux, S ;
Joly, P .
JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 188 (02) :399-433
[8]   The simulation of piano string vibration: From physical models to finite difference schemes and digital waveguides [J].
Bensa, J ;
Bilbao, S ;
Kronland-Martinet, R ;
Smith, JO .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2003, 114 (02) :1095-1107
[9]   Conservative numerical methods for nonlinear strings [J].
Bilbao, S .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2005, 118 (05) :3316-3327
[10]   The influence of the soundboard on piano tone quality [J].
Bilhuber, PH ;
Johnson, CA .
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1940, 11 (03) :311-320