Direct FE numerical simulation for dynamic instability of frame structures

Abstract

Dynamic instability analysis of structures has been a critical issue in the application of engineering and mechanical designs. Can we directly simulate the dynamic stability of structures like buckling analysis in finite element software? To address this question, in this study, we explore the dynamic instability of frame structures, discretized into finite element structures, through developing a direct FE numerical simulation procedure. Benefiting from the advances of eigenvalue analysis of partial differential equations and finite element technology, a direct numerical simulation procedure is developed by using Floquet theorem, harmonic balance methods and finite element method. Dynamic instability characteristics of frame structures, concerning fundamental vibration, multi-mode coupling vibration and flexural-torsional vibration deformation due to their spatial characteristics, are thoroughly investigated. The results reveal that, the developed procedure can achieve dynamic stability analysis of damped and non-damped structures. Frame's flexural-torsional vibration deformation can significantly enlarge the size and instability intensity of unstable regions, threatening dynamic stability of frame structures. Moreover, damping ratio has a slight impact on instability mitigation of the frame induced by flexural-torsional vibration. Unstable regions of mode-coupling vibration of frame have a hidden attribute. No existing approximate formula can be available to estimate instability regions of frame's flexural-torsional vibration and mode-coupling vibration. The dynamic instability index presented here can characterize unstable regions intuitively. The proposed insights can provide design guidelines for frame structures, the developed direct FE simulation procedure may be insightful for extending to explore instability mechanisms of generalized structures with complex forms owing to parametric resonance.