## Physics-based methods for modeling nonlinear vibrating strings,” Acta Acustica united with (2005)

Venue: | Acustica |

Citations: | 4 - 0 self |

### BibTeX

@ARTICLE{Pakarinen05physics-basedmethods,

author = {Jyri Pakarinen and Vesa Välimäki and Matti Karjalainen},

title = {Physics-based methods for modeling nonlinear vibrating strings,” Acta Acustica united with},

journal = {Acustica},

year = {2005},

pages = {312--325}

}

### OpenURL

### Abstract

Nonlinearity in the vibration of a string is responsible for interesting acoustical features in many plucked string instruments, resulting inacharacteristic and easily recognizable tone. For this reason, synthesis models have to be capable of modeling this nonlinear behavior, when high quality results are desired. This study presents two novel physical modeling algorithms for simulating the tension modulation nonlinearity in vibrating strings in a spatially distributed manner. The first method uses fractional delay filters within a digital waveguide structure, allowing the length of the string to be modulated during run time. The second method uses a nonlinear finite difference approach, where the string state is approximated between sampling instants using similar fractional delay elements, thus allowing run-time modulation of the temporal sampling location. The magnitude of the tension modulation is evaluated from the elongation of the string at every time step in both cases. Simulation results of the two models are presented and compared. Real-time sound synthesis of the kantele, a traditional Finnish plucked-string instrument with strong effect of tension modulation, has been implemented using the nonlinear digital waveguide algorithm. PACS no. 43.75.Gh, 43.75.Wx 1.

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Citation Context ...he two one-polarizational vibrations are denoted by fy(n) and fz(n). Theconnection from the elongation approximation block to the output simulates the direct coupling of the TM to the instrument body =-=[20]-=-. A scaling coefficient, denoted by C, isused to control the amount of this coupling. The output of the whole two-polarization string model is finally presented as a force signal fout(n) excerted to t... |

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Citation Context ...This paper discusses and compares two physical models for simulating the behavior of the nonlinear string: a spatially distributed nonlinear digital waveguide string recently developed by the authors =-=[3]-=-, and a new spatially distributed nonlinear finite difference string model, created as a part of a Master’s Thesis work at Helsinki University of Technology [4]. Since the purpose of physics-based mod... |

2 |
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2 |
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2 |
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2 |
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Citation Context ...e nonlinear DWG waveguide has noreal stability problems when synthesis of natural plucked-instrument sounds are desired. We studied the stability of the NFDTD algorithm using the Von Neumann analysis =-=[39]-=- in the time-invariant case, i.e. parameter a of equation (26) was kept constant. The basic idea of this method is to calculate the spatial Fourier spectrum of the system under discussion at two conse... |

1 |
Boutillon: Model for piano hammers: Experimental determination and digital simulation
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(Show Context)
Citation Context ...phenomena fall out of the scope of this paper. The hammer-string nonlinearity is mainly due to the compression of the hammer felt, and it is covered in many earlier studies [9], [10], [11], [12], and =-=[13]-=-, to name few. The bow-string nonlinearity is mainly caused by the stick-slip contact between the string and the bow. Also this interaction is coveredinmanystudies,[14],[15], and [16] present some of ... |

1 |
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