Equality-based weighted residual formulation for the forced vibration of a beam with an attached friction damper
Résumé
An equality-based weighted residual (E-WR) formulation is proposed to analyze the periodic responses of systems subject to frictional occurrences. A cantilever beam with an attached friction damper is considered to investigate the effectiveness of friction at mitigating response amplitudes and assessing the effect of damper mass. The system is a common simplified model of a bladed disk sector with an attached platform wedge or ring damper [1]. Friction, governed by Coulomb's classical law, is expressed as a nonsmooth equality condition, augmenting the equations of motion into a mixed displacement-contact force formulation. Periodic solutions are obtained via a standard Ritz-Galerkin procedure using classical Fourier functions. The method employs an exact equality representation of Coulomb's law for interfaces with mass, avoiding common assumptions like regularization, penalization, or massless interfaces. Unlike existing frequency-time methods [2, 3], it operates entirely in the frequency domain, eliminating the need for time-domain calculations of contact forces during nonlinear solver iterations. The approach proves to be compact, robust, accurate, and void of convergence or numerical issues up to large numbers of harmonics. Intricate stick-slip response behaviors dictated by Coulomb's law are captured.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|---|
| Licence |