CHABASSIER, Juliette; DURUFLÉ, Marc

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CHABASSIER, Juliette
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]

DURUFLÉ, Marc
Advanced 3D Numerical Modeling in Geophysics [Magique 3D]
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Sound and Vibration. 2014, vol. 333, n° 26, p. 7198-7215

Elsevier

Résumé en anglais

A nonlinear model for a vibrating Timoshenko beam in non-forced unknown rotation is derived from the virtual work principle applied to a system of beam with mass at the end. The system represents a piano hammer shank coupled to a hammer head. An energy-based numerical scheme is then provided, obtained by non classical approaches. A major difficulty for time discretisation comes from the nonlinear behavior of the kinetic energy of the system. Numerical illustrations are obtained by coupling this new numerical scheme to a global energy-preserving numerical solution for the whole piano. These numerical results show that the pianistic touch clearly influences the spectrum of the piano sound of equally loud isolated notes. These differences do not come from a possible shock excitation on the structure, nor from a changing impact point, nor a "longitudinal rubbing motion" on the string, since neither of these features are modeled in our study.< Réduire

Mots clés en anglais

flexible piano hammer shank

piano model

pianistic touch

implicit time discretization

vibrating Timoshenko beam

energy preservation

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Energy based simulation of a Timoshenko beam in non-forced rotation. Application to the flexible piano hammer shank.

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