Modeling the grand piano . Numerical Aspects
نویسندگان
چکیده
This paper deals with the discretization of the global piano model described in [2]. We have to solve a complex system of coupled equations, where each subsystem has different spatial dimensions, which poses specific difficulties. The hammer-strings part is a 1D system governed by nonlinear equations. The soundboard is a 2D system with diagonal damping. The acoustic field is a 3D problem in an unbounded domain. Energy based methods allow to build an accurate and a priori stable scheme.
منابع مشابه
The Virtual Piano Action: Design and Implementation
The design of a virtual piano action composed of a keyboard of motorized keys and a realtime mechanical system simulation is presented. Using this simulator, we have re-created certain aspects of the feel of the grand piano by numerically integrating the equations of motion of a simpli ed piano action in real time in a human-in-the-loop simulation scheme. In this paper, the simulation of the re...
متن کاملAcoustics of pianos: physical modeling, simulations and experiments
The outlines of a recently developed model of a grand piano are summarized. Using dedicated numerical methods, the main vibratory and acoustic variables of each constitutive part of the instrument (strings, bridge, soundboard, sound pressure) are simulated in the time-domain. The obtained waveforms are analyzed and compared with experimental data derived from measurements on a Steinway D grand ...
متن کاملDynamical Modeling of the Grand Piano Action
The grand piano action is modeled as a set of four rigid bodies using Kane’s method. Computerized symbol manipulation is utilized to streamline the formulation of the equations of motion so that several models can be considered, each of increasing detail. Various methods for checking the dynamical model thus derived are explored. A computer animation driven by simulation of the equations of mot...
متن کاملSimulation of a non-smooth dynamical model of the piano key
The grand piano action has been developped empirically and provides a remarkably accurate control of the hammer velocity and the impact time [1]. The numerical simulation of the action is necessary to improve numerical keyboards and to better understand haptic controllability. Following previous efforts [2, 3], we propose a simulation based on an explicit model and a solver of non-smooth dynami...
متن کاملModeling the grand piano
A global model of a piano is presented. Its aim is to reproduce the main vibratory and acoustic phenomena involved in the generation of a piano sound from the initial blow of the hammer against the strings to the radiation from soundboard to the air. One first originality of the work is due to the string model which takes both geometrical nonlinear effects and stiffness into account. Other sign...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013