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

We investigate the eects of warping on the dynamic stability of non-trivial equilibrium congurations 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 nonlinear, hyper-elastic, and distinguish the roles of the centroids and shear centres; inertial actions account for warping, too. By centred nite dierences, the warping inertial action is found ineective 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 eects of warping and of coupling constitutive coecients.