Free and forced linear dynamics of a homogeneous model for beam-like structures

A homogeneous shear beam model is used here to address the free and forced dynamic behavior of a multi-story building. After a brief recall of the model, which is taken from the literature, and the hypotheses on which it is grounded, discussion on the free dynamics is carried out, highlighting the intriguing organization of the natural frequencies and modes in triplets, as functions of the wave-number. Then, the properties of the undamped and proportionally damped forced response to external loads is evaluated, and a discussion on the effects of the tip mass related to the top story is addressed. A case-study is analyzed to show the reliability of the homogeneous model, after comparing the outcomes with those provided by F.E.M. procedures applied to the corresponding multi-d.o.f. structure.