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.