Bifurcation Analysis of Damped Visco-Elastic Planar Beams Under Simultaneous Gravitational and Follower Forces

Angelo Luongo (1) , Francesco d'Annibale (1)

1 DICEAA - Dipartimento di Ingegneria Civile, Edile-Architettura, Ambientale

The mechanical behavior of a non-conservative non-linear beam, internally and externally damped, undergoing codimension-1 (static or dynamic) and codimension-2 (double-zero) bifurcations, is analyzed. The system consists of a purely flexible, planar, visco-elastic beam, fixed at one end, loaded at the tip by a follower force and a dead load, acting simultaneously. An integro-differential equation of motion in the transversal displacement, with relevant boundary conditions, is derived. Then, the linear stability diagram of the trivial rectilinear configuration is built-up in the space of the two loading parameters. Attention is then focused on the double-zero bifurcation, for which a post-critical analysis is carried out without any a-priori discretization. An adapted version of the Multiple Scale Method, based on a fractional series expansion in the perturbation parameter, is employed to derive the bifurcation equations. Finally, bifurcation charts are evaluated, able to illustrate the system behavior around the codimension-2 bifurcation point.

Domaines: Autre

Angelo Luongo, Francesco d'Annibale. Bifurcation Analysis of Damped Visco-Elastic Planar Beams Under Simultaneous Gravitational and Follower Forces. International Journal of Modern Physics B, 2012, 26 (25), pp.1246015-1 - 1246015-6. ⟨hal-00787883⟩