On the dynamic behaviour of masonry beam-columns: an analytical approach

The paper presents an analytical approach to the study of the transverse vibrations of masonry beam-columns. Starting with the constitutive equation for beams made of a masonry-like material and the averaged Lagrangian of the system, some explicit approximate solutions are found to the problem of free damped periodic oscillations and forced oscillations in the case of primary resonance on the beam's first mode. In particular, a set of equations is obtained that gives the modulation over time of the system's energy and of the fundamental frequency of the beam's response. The analytical results are compared to those obtained via the finite element code NOSA-ITACA, developed at ISTI-CNR.