Harmonic balance-based nonsmooth modal analysis of unilaterally constrained discrete systems
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...
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Veröffentlicht in: | Nonlinear dynamics 2024-02, Vol.112 (3), p.1619-1640 |
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Sprache: | eng |
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Zusammenfassung: | 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 other 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, an impact law, such as Newton’s impact law, for instance, classically required for uniqueness purposes in a space semi-discrete dynamical framework, is here explicitly ignored in the proposed formulation and is, instead, implicitly satisfied in a weighted residual sense. As required for the existence of periodic solutions, the predicted vibratory responses would then correspond to an energy-preserving impact law in case the latter had to be explicitly implemented. 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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ISSN: | 0924-090X 1573-269X |
DOI: | 10.1007/s11071-023-09014-4 |