2020/02/16 by Shrinidhi S. Pandurangi, Pandurangi, Shrinidhi S., Ryan S. Elliott +5
Engineering · #Bladed Disk Vibration Dynamics #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Soft Condensed Matter (cond-mat.soft) #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2002.12454
openalex publication_date 2020/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit the classic stability problem of the buckling of an inextensible,\naxially compressed beam on a nonlinear elastic foundation with a\nsemi-analytical approach to understand how spatially localized deformation\nsolutions emerge in many applications in mechanics. Instead of a numerical\nsearch for such solutions using arbitrary imperfections, we propose a\nsystematic search using branch-following and bifurcation techniques along with\ngroup-theoretic methods to find all the bifurcated solution orbits (primary,\nsecondary, etc.) of the system and to examine their stability and hence their\nobservability. Unlike previously proposed methods that use multi-scale\nperturbation techniques near the critical load, we show that to obtain a\nspatially localized deformation equilibrium path for the perfect structure, one\nhas to consider the secondary bifurcating path with the longest wavelength and\nfollow it far away from the critical load. The novel use of group-theoretic\nmethods here illustrates a general methodology for the systematic analysis of\nstructures with a high degree of symmetry.\n