Dynamics of multicell, thin-walled beams with regular cutouts

In a previous paper, the writers presented a one-dimensional analytical model for the static analysis of multicell, thin-walled beams with nonhomogeneous cross sections. The proposed model accounts for shear deformations due to nonuniform bending and torsion supplementing the primary effects considered by the classical models. Here, the constitutive relations for the beam model are given and the dynamic analysis of the shear core is considered by a proper generalization of the continuous formulation. An algebraic procedure is given to evaluate the equivalent mechanical properties of the cross section. Moreover, a one-dimensional hierarchical finite element formulation is proposed for displacements and rotations. The proposed model is shown to cover the analysis of multicell, thin-walled beams, having regular cutouts, as is typical of shear cores of tall buildings. The applications include solutions to both the continuous and the discrete models.