Critical and post-critical galloping behavior of base isolated coupled towers

Nonlinear analysis of two base isolated tall buildings, close to each other, coupled at the tip with a nonlinear viscous device and under the effect of wind, is addressed. The partial differential equations of motion are written with reference to a system constituted by two equivalent beam-like elements, and the modal features are evaluated both in presence and absence of wind which, besides nonlinear terms, provides non-proportional damping contributions. A reduced order system is then proposed to carry out an extensive parametric analysis, which is finalized to pick parameter values, like stiffness and damping of the isolation devices, which correspond to lowered amplitude of oscillations. Finally, a perturbation analysis on the continuum model is performed, for an in-depth evaluation of the post-critical response of the system, valid in a small interval of the constitutive parameter values.