Energy conserving schemes for the simulation of musical instrument contact dynamics
Shranjeno v:
| izdano v: | arXiv.org (Jan 7, 2015), p. n/a |
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| Izdano: |
Cornell University Library, arXiv.org
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| Teme: | |
| Online dostop: | Citation/Abstract Full text outside of ProQuest |
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| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 2081603828 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 024 | 7 | |a 10.1016/j.jsv.2014.11.017 |2 doi | |
| 035 | |a 2081603828 | ||
| 045 | 0 | |b d20150107 | |
| 100 | 1 | |a Chatziioannou, Vasileios | |
| 245 | 1 | |a Energy conserving schemes for the simulation of musical instrument contact dynamics | |
| 260 | |b Cornell University Library, arXiv.org |c Jan 7, 2015 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument. | |
| 653 | |a Musical instruments | ||
| 653 | |a Simulation | ||
| 653 | |a Sound generation | ||
| 653 | |a Equations of motion | ||
| 653 | |a Newton methods | ||
| 653 | |a Finite difference method | ||
| 653 | |a Impact loads | ||
| 653 | |a Formulations | ||
| 653 | |a Collisions | ||
| 653 | |a Algorithms | ||
| 653 | |a Mathematical models | ||
| 653 | |a Stability analysis | ||
| 653 | |a Analytic functions | ||
| 653 | |a Strings | ||
| 653 | |a Nonlinear equations | ||
| 653 | |a Contact force | ||
| 653 | |a Computer simulation | ||
| 700 | 1 | |a Maarten van Walstijn | |
| 773 | 0 | |t arXiv.org |g (Jan 7, 2015), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2081603828/abstract/embedded/6A8EOT78XXH2IG52?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/1501.01493 |