Nonlinear dynamics and stability of a homogeneous model of tall buildings under resonant action

A homogeneous model of beam-like structure, roughly portraying  the mechanical behavior of a tall building, is considered to address nonlinear dynamic response in case of external resonant excitation. A  symmetric layout of the building is considered, so as to allow the existence of an in-plane response, whose features are evaluated by means of the Multiple Scale Method and accounting for internal resonance, necessarily occurring in the model. Furthermore, to take into account the three-dimensional nature of the problem, stability of the in-plane response to out-of-plane disturbances is addressed, solving the associated parametrically excited linear system.