Article Dans Une Revue Journal of Structural Dynamics Année : 2024

A compact, equality-based weighted residual formulation for periodic solutions of systems undergoing frictional occurrences

Résumé

A very compact weighted residual formulation is proposed for the construction of periodic solutions of oscillators subject to frictional occurrences. Coulomb's friction is commonly expressed as a differential inclusion which can be cast into the complementarity formalism. When targeting periodic solutions, existing algorithms rely on a procedure alternating between the frequency domain, where the dynamics is solved, and the time domain, where friction is dealt with. In contrast, the key idea of the present work is to express all governing equations including friction as equalities, which are then satisfied in a weak integral sense through a weighted residual formulation. The resulting algebraic nonlinear equations are solved numerically using an adapted trust region nonlinear solver and basic integral quadrature schemes. To increase efficiency, the Jacobian of the friction forces is calculated analytically in a piecewise linear fashion. The shape functions considered in this work are the classical Fourier functions. It is shown that periodic solutions with clear multiple sticking and sliding phases can be found with a high degree of accuracy. The equality-based formulation is shown to be effective and efficient, and convergence is achieved in all cases considered with reasonable computational cost, including for large numbers of harmonics. Importantly, this new friction formulation does not suffer from the typical limitations or hypotheses of existing frequency-time domain methods for non-smooth systems, such as regularization, penalization, or massless frictional interfaces.

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Est traduit par hal-04521553 Objet présenté à une conférence Mathias Legrand, Christophe Pierre. Résolution par résidus pondérés d'une formulation sous forme d'égalités de systèmes vibratoires avec frottement de Coulomb. 16ème Colloque National en Calcul de Structures (CSMA 2024), CNRS; CSMA; ENS Paris-Saclay; CentraleSupélec, May 2024, Hyères, France. ⟨hal-04521553⟩

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Est une version de hal-04201052 Objet présenté à une conférence Mathias Legrand, Christophe Pierre. Equality-Based Weighted Residual Formulation for Periodic Solutions of Dry Friction Damped Systems. IDETC-CIE 2023, ASME, Aug 2023, Boston, United States. ⟨hal-04201052⟩

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Est une version de hal-03751780 Objet présenté à une conférence Mathias Legrand, Christophe Pierre. Compact weighted residual formulation for periodic solutions of systems undergoing unilateral contact and frictional occurrences. 10th European Nonlinear Oscillations Conference (ENOC 2022), Jul 2022, Lyon, France. ⟨hal-03751780⟩

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Est une version de hal-04201054 Objet présenté à une conférence Mathias Legrand, Christophe Pierre. An Equality-Based Formulation for Vibrating Systems with Friction. Nodycon 2023, Jun 2023, Rome, Italy. ⟨hal-04201054⟩

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Est une version de hal-04201237 Objet présenté à une conférence Mathias Legrand, Christophe Pierre. Compact weighted residual formulation for periodic solutions of systems undergoing frictional occurrences. IUTAM Symposium on Nonlinear dynamics for design of mechanical systems across different length/time scales, Jul 2023, Tsukuba, Japan. pp.152-153. ⟨hal-04201237⟩

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Est complété par swh:1:dir:925849db7fa38d37336bc85c4d56ed8b7b2ed2b7 Logiciel

Exact state of the numerical procedures used in the paper.
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Est complété par hal-04525598 Logiciel Mathias Legrand, Christophe Pierre, Sebastian Mcdonald. Equal[iseR]. 2024, ⟨swh:1:rev:f250761aa2646df3da29c2e1baff9f3a2d0e0641;origin=https://github.com/mlegr/EqualISER;visit=swh:1:snp:93a283d450360c146c0d6d2f02396a68c7b61d16⟩. ⟨hal-04525598⟩

Dates et versions

hal-04189699 , version 1 (29-08-2023)
hal-04189699 , version 2 (29-03-2024)

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Mathias Legrand, Christophe Pierre. A compact, equality-based weighted residual formulation for periodic solutions of systems undergoing frictional occurrences. Journal of Structural Dynamics, 2024, 2, pp.144-170. ⟨10.25518/2684-6500.190⟩. ⟨hal-04189699v2⟩
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