Coupling structure interconnected by hysteretic dampers appears to be an effective method to mitigate structural seismic response. In the paper, the random seismic response is evaluated through the pseudo-excitation principle incorporated with stochastic equivalent linearization method without by solving the Lyapunov differential equation. For which, the seismic excitation is limited to be shot noise process and the computation burden should not be neglected while structural freedoms are large. In the paper, it is supposed that the structures keep elastic all the time and the hysteretic dampers are represented with versatile Bouc-Wen model. With the participation of assistant augment and reduced matrices which are correlated with the location of hysteretic dampers, the unidirectional excitation of one component and spatial excitation of multiple components are derived and the relationship between the pseudo-excitation and pseudo-response is deduced. Then, a pseudo-excitation closed-form expression for the system random response is established. Consequently, the stationary random seismic response of two shear type structure interconnected with hysteretic dampers is analyzed. The structural stationary seismic responses for two methods agree well. parametric studies for the hysteretic dampers and the optimum way to install the hysteretic dampers are also discussed.

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