A modal method for the simulation of nonlinear dynamical systems with application to bowed musical intruments

Inacio, Octávio José Patrício Fernandes Inácio (2008) A modal method for the simulation of nonlinear dynamical systems with application to bowed musical intruments. University of Southampton, Institute of Sound and Vibration Research, Doctoral Thesis , 256pp.


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Bowed instruments are among the most exciting sound sources in the musical world,
mostly because of the expressivity they allow to a musician or the variety of sounds
they can generate. From the physical point of view, the complex nature of the
nonlinear sound generating mechanism – the friction between two surfaces – is no less
In this thesis, a physical modelling computational method based on a modal
approach is developed to perform simulations of nonlinear dynamical systems with
particular application to friction-excited musical instruments. This computational
method is applied here to three types of systems: bowed strings as the violin or cello,
bowed bars, such as the vibraphone or marimba, and bowed shells as the Tibetan bowl
or the glass harmonica. The successful implementation of the method in these
instruments is shown by comparison with measured results and with other simulation
methods. This approach is extended from systems with simple modal basis to more
complex structures consisting of different sub-structures, which can also be described
by their own modal set.
The extensive nonlinear numerical simulations described in this thesis, enabled some
important contributions concerning the dynamics of these instruments: for the bowed
string an effective simulation of a realistic wolf-note on a cello was obtained, using
complex identified body modal data, showing the beating dependence of the wolfnote
with bowing velocity and applied bow force, with good qualitative agreement
with experimental results; for bowed bars the simulated vibratory regimes emerging
from different playing conditions is mapped; for bowed Tibetan bowls, the essential
introduction of orthogonal mode pairs of the same family with radial and tangential
components characteristic of axi-symmetrical structures is performed, enabling an
important clarification on the beating phenomena arising from the rotating behaviour
of oscillating modes. Furthermore, a linearized approach to the nonlinear problem is
implemented and the results compared with the nonlinear numerical simulations.
Animations and sounds have been produced which enable a good interpretation of
the results obtained and understanding of the physical phenomena occurring in these

Item Type: Thesis (Doctoral)
Subjects: M Music and Books on Music > M Music
Q Science > QC Physics
Divisions : University Structure - Pre August 2011 > Institute of Sound and Vibration Research
ePrint ID: 65914
Accepted Date and Publication Date:
July 2008Made publicly available
Date Deposited: 30 Mar 2009
Last Modified: 27 Mar 2014 18:47
URI: http://eprints.soton.ac.uk/id/eprint/65914

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