Natural frequencies of a thin-walled structures with central intermediate stiffeners or/and variable thickness

The present paper deals with a dynamic analysis of stability of thin-walled beam-columns with central intermediate stiffeners or/and variable thickness when the shear lag phenomenon and the distortional deformations are taken into account. This investigation is concerned with thin-walled structures under axial compression and a constant bending moment. The structures are assumed to be simply supported at the ends. In order to obtain the equations of motion of individual plates, the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s principle, taking into account Lagrange’s description, full Green’s strain tensor for thin-walled plates and Kirchhoff’s stress tensor. The disturbance theory has been applied in order to obtain an approximate analytical solution to the equations. The problem of linear dynamic stability has been solved with the transition matrix method, taking into account Godunov’s orthogonalization. The calculations are carried out for a few beam-columns.