Improved frequency-dependent damping for time domain modelling of linear string vibration

Charlotte Desvages, Stefan Bilbao, Michele Ducceschi

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


Lossy linear stiff string vibration plays an important role in musical acoustics. Experimental studies have demonstrated the complex dependence of decay time with frequency, confirmed bydetailed modelling of dissipated power in linear strings. Losses at a particular frequency canbe expressed as a function of the physical parameters defining the system; damping due toair viscosity is predominant at low frequencies, whereas internal friction prevails in the higherfrequency range. Such a frequency domain characterisation is clearly well-suited to simulationmethods based on, e.g., modal decompositions, for experimental comparison or sound synthesis.However, more general string models might include features difficult to realise with such models,in particular nonlinear effects. In this case, it is useful to approach modelling directly in thespace-time domain. This work is concerned with the translation of the frequency domain damping characteristics to a space-time domain framework, leading, ultimately, to a coupled system ofpartial differential equations. Such a system can be used as a starting point for a time-steppingalgorithm; an important constraint to ensure numerical stability is then that of passivity, or dissipativity. Candidate loss terms are characterised in terms of positive real functions, as a startingpoint for optimisation procedures. Simulation results are presented for a variety of linear strings.
Original languageEnglish
Title of host publicationProceedings of the 22nd International Congress on Acoustics
Number of pages10
Publication statusPublished - 5 Sep 2016


  • physical modelling
  • sound synthesis
  • finite difference
  • passive systems

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