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Analyse et modélisation de vibrations non-linéaires de milieux minces élastiques - Application aux instruments de percussion

Abstract : This thesis is devoted to the study of the non-linear vibrations of percussion instruments, such as cymbals and gongs. The idea is to contribute to the writing of a physical model of behaviour, in order, on the one hand to understand the sound production mecanisms, and on the other hand to do sound synthesis. In a first part are presented results from experiments conducted on a chinese tam-tam, when it is subjected to a harmonic forcing of frequency close to a natural frequency. Simple non-linear phenomena are exhibited, such as the dependance of the free-oscillations frequency on the amplitude of the movement, hysteretic resonances, and energy exchanges between normal modes. A second part is devoted to modelize percussion instruments by circular thin elastic plates, with free edge, subjected to large deflections and moderate rotations. The non-linear dynamic analogue of Von-Karman equations is used, and its validity range is discussed. The solution is expanding onto the linear normal modes. The reduction of the problem to a one mode vibration is studied in details. A physical model is derived and confirmed very precisely by experiments. When an asymetric mode is under study, a nonlinear coupling between the two corresponding degenerated modes is predicted, and studied. In the third part, one-degree-of-freedom (DDL) systems are studied. They are composed of articulated rods subjected to large deflections. Through simple arguments, a parallel is drawn between the dynamics exhibited by those systems, and the behaviour of percussion instruments. A physical interpretation of the geometrical non-linearities is first exposed. Then, this 1DDL models shed a new light on the one-mode behaviour of the chinese tam-tam. In particular, the influence of simple gemetrical parameters (such as the thickness and the curvature) on the non-linearities is evaluated.
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Submitted on : Wednesday, July 18, 2012 - 3:50:28 PM
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  • HAL Id : tel-00005656, version 2

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Olivier Thomas. Analyse et modélisation de vibrations non-linéaires de milieux minces élastiques - Application aux instruments de percussion. Mécanique [physics.med-ph]. Université Pierre et Marie Curie - Paris VI; Telecom ParisTech, 2001. Français. ⟨tel-00005656v2⟩

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