Warping and Ljapounov stability of non-trivial equilibria of non-symmetric open thin-walled beams

•We studied how warping and non-symmetries affect the global stability of non-trivial equilibrium paths for open profiles.•We proved that the postulated inertial action for warping does not affect the linear dynamics of the considered beams.•We showed that warping affects eigen frequencies.•We showed that warping and constitutive couplings affect the buckling loads: standard formulas may be unreliable.•We found some flutter critical loads, which are not present in the literature.

We investigate the effects of warping on the dynamic stability of non-trivial equilibrium configurations for non-symmetric open thin-walled beams. We use a direct one-dimensional model coarsely describing warping; the rest of the kinematics is exact. Dynamic derives from the balance of power; constitutive relations are non-linear, hyper-elastic, and distinguish the roles of the centroids and shear centres; inertial actions account for warping, too. By centred finite differences, the warping inertial action is found ineffective on the natural angular frequencies. Then, we follow non-trivial equilibrium paths and investigate their Ljapounov stability, by examining the small superposed oscillations. Results for generic, non-symmetric cross-sections are presented and discussed, showing the effects of warping and of coupling constitutive coefficients.