In this paper

the seismic response of bottom-frame-masonry buildings subjected to the earthquake excitation is investigated.Friction dampers are installed in the bottom frame

and the isolation layer is arranged between the lower bottom frame and the upper masonry structure

forming a bifunctional damping structure.First

the seismic response equation of the energy dissipation structure is solved by the state equation direct integration method.Then

the response of the structure under seismic excitation is analyzed.The results are compared with those of the SAP2000 calculation

indicating a very well agreement.Meanwhile

the forced decoupling method is also adopted to study the seismic response of the structure simultaneously.The results were compared with those of the state equation direct integral method.It indicates that there are good precisions for the first-and second-order vibrations

and there are large deviations for higher order vibrations.The forced decoupling method overestimates the damping effect of the structure.Research results show that this new type of shock-absorbing structure possesses good shock absorption performance

and the state equation direct integration method has strong practicability in analyzing the seismic response of structures.