Abstract: In order to reduce the seismic response of the multistorey reinforced concrete frame building structure， the nonlinear system motion equation which involved the contribution of the TMD and LRB is established. The equations which consist of nonclassical damping， asymmetry stiffness and mass are obtained by expanding the firstorder vibration mode of structure， and the equations are decoupled using the complex modal theory. The program is compiled for solving the problem how to acquire the analytical solutions of random seismic response of structure. The validity of this algorithm was verified by comparing with calculation results of deterministic algorithms. The consequences indicate that the TMD and LRB united control could decrease the seismic response of main structure more obviously than TMD control， for instance， displacement and acceleration.

Key words: multistorey building, tuned mass damper, lead rubber bearing, complex modal, random seismic response