Discrete-Time Conserved Quantities for Damped Oscillators

Vasileios Chatziioannou, Maarten van Walstijn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.
Original languageEnglish
Title of host publicationProceedings of the 3rd Vienna Talk on Music Acoustics
EditorsAlexander Mayer, Vasileious Chatziioannou, Werner Goebl
PublisherUniversity of Music and Performing Arts Vienna
Pages135-139
Number of pages5
Publication statusPublished - Sep 2015
EventVienna Talk 2015 on Music Acoustics "Bridging the Gaps" - Vienna, Austria
Duration: 16 Sep 201519 Sep 2015

Conference

ConferenceVienna Talk 2015 on Music Acoustics "Bridging the Gaps"
CountryAustria
CityVienna
Period16/09/201519/09/2015

Bibliographical note

Peer-reviewed paper

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