A reduced order model for optimal design of 2-mdof adjacent structures connected by hysteretic dampers

Coupling adjacent structures with supplemental control devices appears to be a useful method to mitigate structural response. In this work, a reduced order model for optimal design of two multi-degree-of-freedom (2-mdof) structures connected by hysteretic dampers is studied. The seismic input is modeled as a Gaussian white-noise stationary stochastic process. Since the passive connection is modeled as a nonlinear hysteretic element, represented by the differential Bouc–Wen law, a stochastic linearization technique is applied in order to simplify the problem. The design procedure is based on replacing the 2-mdof system, with a generalized two single-degree-of-freedom (2-sdof) system, by using the principle of virtual displacements; here, each structure is represented by an elementary oscillator interconnected by a hysteretic device. Once the equivalent structural parameters of the generalized 2-sdof system is known, it is possible to carry out the optimal design of the connection by using simple spectra obtained by the authors in a previous work, where the optimal design of a horizontal hysteretic link connecting a 2-sdof system has been studied and solved. Illustrative examples confirm the entire methodology and also verify the effectiveness of hysteretic connection on seismic response.