Anti-seismic performances of the hybrid energy dissipation structure(HEDS)composed of an isola-tion interlayer with lateral stopping viscoelastic dampers(VEDs)under random excitation were systematically investigated.Firstly,the seismic motion equations for the HEDS subjected to the double-filtered white noise ex-citation(DFWNE)were established,and the filtering equation of the DFWNE was used to accurately transform the dynamic calculation of the HEDS based on the DFWNE into white noise excitation problems to be easily tackled with concise closed-form solutions.Secondly,based on the complex mode method and the properties of the Dirac function for white noise excitation,a concise closed-form solution of the variance and 0th-to 2nd-or-der spectral moments of the series of responses(structural displacements,interlayer displacements,and damp-er damping forces)of the HEDS,was derived.Finally,based on the verification of the correctness of the pro-posed closed solution through numerical examples,the influencing factors on the seismic performances of the HEDS were studied.The results show that,the structural responses of floors above the isolation layer increase with the stiffness of the isolation layer;while the damping parameter of the VED have different effects on the interlayer displacement and structural displacements of floors above the isolation layer,i.e.,the structural dis-placement can reach the minimum under certain damping parameter of the VED,but the interlayer displacement increases with the damping parameter of the VED.This study can provide reference for the design of HEDSs.
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