Optimal passive control of adjacent structures interconnected with non-linear hysteretic devices

In this paper, the optimal passive control of adjacent structures interconnected by nonlinear hysteretic devices is studied. For nonlinear devices the versatile Bouc–Wen model is adopted, whereas for seismic excitation a Gaussian zero mean white noise and a filtered white noise are used. To solve nonlinear equations of motion a simplified solution is carried out using a stochastic linearization technique. The problem of the optimal design of the devices is studied and solved in the case of a simple two-degrees-of-freedom model. In the optimization problem, an energy criterion associated with the concept of optimal performance of the hysteretic connection is used. The energy performance index is defined as a measure of the ratio between the energy dissipated in the device and the seismic input energy on the structure. Only two parameters are considered in the optimization problem of the device yielding force and elastic stiffness. The rigid and elastic plastic models for the device are studied and compared. The design procedure leads to very simple indications on the optimal values of the device's mechanical parameters; these optimal values substantially depend only on the mass and stiffness ratio between the two structures. Finally, some concise results about the effectiveness of the hysteretic connection for the seismic response mitigation of coupled structures are also given.