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Pré-Publication, Document De Travail Année : 2023

Harmonic Balance based Nonsmooth Modal Analysis of unilaterally constrained discrete systems

Résumé

Nonsmooth Modal Analysis of a unilaterally constrained one-dimensional bar with constant cross-sectional area was recently proposed. The corresponding formulation took advantage of the d'Alembert solution available for such systems and does not require any space semi-discretization of the governing equations. However, it is unable to cope with non-constant cross-sectional area bars, for instance. The present work suggests a formulation relying on various space semi-discretization methodologies (such as finite elements, Rayleigh-Ritz techniques, component mode synthesis, modal superposition and reduced-order models) where the complementarity Signorini condition, reflecting the unilateral contact constraint, is enforced in a weighted residual sense in time through the Harmonic Balance Method. Importantly, the Newton impact law, classically required for uniqueness purposes in a dynamics framework, is here explicitly ignored in the formulation and attendant solution strategy and is, instead, implicitly satisfied in a weighted residual sense. It corresponds to a restitution coefficient e=1 as required for energy preservation and existence of periodic solutions. Periodic responses are investigated in the form of classical energy-frequency backbone curves along with the associated displacement fields. It is found that for the constant cross-section benchmark system, the results compare well with existing works and the proposed methodology stands as a viable option in the field of interest when semi-discretization in space is required.
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Dates et versions

hal-03970830 , version 1 (02-02-2023)
hal-03970830 , version 2 (28-09-2023)

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  • HAL Id : hal-03970830 , version 1

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Tianzheng Lu, Mathias Legrand. Harmonic Balance based Nonsmooth Modal Analysis of unilaterally constrained discrete systems. 2023. ⟨hal-03970830v1⟩
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