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

• Published in: International journal of non-linear mechanics Vol. 55; pp. 128 - 139
• Main Authors: Luongo, A., D'Annibale, F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2013; Elsevier
• Subjects: Beams (structural); Bifurcations; Boundary conditions; Civil Engineering; Damping; Destabilization phenomenon; Engineering Sciences; Internal and external damping; Mathematical analysis; Multiple scale method; Non-conservative loads; Non-linear bifurcations; Nonlinearity; Perturbation methods; Viscoelasticity; Non-conservative loads; Destabilization phenomenon; Internal and external damping; Non-linear bifurcations; Multiple scale method
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2013.05.007

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. •The mechanical behavior of a non-conservative non-linear damped beam is studied.•The linear stability diagram is built and emphasis is given to the role of damping.•A post-critical analysis is carried out by using the MSM.•The non-linear scenario is strongly affected by damping.•Homoclinic and heteroclinic bifurcations are showed.