2009/06/15 by Stéphane Junca, Junca, Stéphane, B. Rousselet +1
Engineering · #Bladed Disk Vibration Dynamics #Classical Physics (physics.class-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Structural Health Monitoring Techniques #Vibration and Dynamic Analysis
paper · doi:10.48550/arxiv.0906.2714
openalex publication_date 2009/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study some spring mass models for a structure having a unilateral spring of small rigidity ε. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including a non negligible cumulative effect over a long time: T_\eps ∼ \eps-1 as usual; or, for a new critical case, we can only expect: T_\eps ∼ \eps-1/2. We check numerically these results and present a purely numerical algorithm to compute "Non linear Normal Modes" (NNM); this algorithm provides results close to the asymptotic expansions but enables to compute NNM even when ε becomes larger.