Double zero bifurcation of non-linear viscoelastic beams under conservative and non-conservative loads

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

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

The combined effects of conservative and non-conservative loads on the mechanical behavior of an unshearable and inextensional visco-elastic beam, close to bifurcation, are investigated. The equations of motion and boundary conditions are derived via a constrained variational principle, and the Lagrange multiplier successively condensed, to get integro-differential equations. These latter, with the mechanical boundary conditions appended, are put in an operator-form, amenable to perturbation analysis. A linear stability analysis is carried out in the space of the two loading parameter, displaying the existence of codimension-1 and codimension-2 bifurcations. The influence of both internal and external damping on this scenario is thoroughly investigated. A post-critical analysis is carried out around a double-zero bifurcation, by using an adapted version of the multiple scale method, based on fractional series expansions in the perturbation parameter. The integro-differential problem is directly attacked, so that any a priori discretization is avoided. Emphasis is given to the interaction between the two damping coefficients. This reveals the existence, also in the non-linear range, of a phenomenon of destabilization, so far known only in the linear range.

Domaines: Génie civil

Angelo Luongo, Francesco d'Annibale. Double zero bifurcation of non-linear viscoelastic beams under conservative and non-conservative loads. International Journal of Non-Linear Mechanics, 2013, 55, pp.128-139. ⟨hal-00909808⟩