Dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string. - Archive ouverte HAL Access content directly
Conference Papers Year : 2013

Dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string.

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Abstract

We study the implicit time discretization of Tim- oshenko prestressed beams. This model features two types of waves: flexural and shear waves, that propa- gate with very different velocities. We present a novel implicit time discretization adapted to the physical phenomena occuring at the continuous level. Af- ter analyzing the continuous system and the two branches of eigenfrequencies associated with the standing modes, the classical θ-scheme is studied. A dispersion analysis recalls that θ = 1/12 re- duces the numerical dispersion, but yields a severely constrained stability condition for our application. Therefore we propose a new θ-like scheme based on two parameters adapted to each wave velocity, which reduces the numerical dispersion while relaxing this stability condition. Numerical experiments success- fully illustrate the theoretical results on the specific cas of a realistic piano string. This motivates the extension of the proposed approach for more chal- lenging physics.
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Dates and versions

hal-00873632 , version 1 (16-10-2013)

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  • HAL Id : hal-00873632 , version 1

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Juliette Chabassier, Sébastien Imperiale. Dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string.. WAVES 13 : 11th International Conference on Mathematical and Numerical Aspects of Waves, Jun 2013, Tunis, Tunisia. ⟨hal-00873632⟩
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