Seismic Response of a Two-Degree-of-Freedom System with Friction Based on the Mass Ratio

The friction force is effective for dissipating seismic energy. Therefore, in recent years, the installation of a frictional isolator in industrial facilities has been investigated. When a system including this isolator is regarded as multi-dof system, however, the seismic response of the system is obtained only by non-linear time history analysis. A great deal of time is required for non-linear analysis. In the present study, the easy estimation of seismic response for a multi-dof system with friction is considered. The seismic response of a multi-dof linear system can be obtained by the response spectrums method. This estimation is based on the modal analysis method. In the present paper, a method of modal separation for a 2-dof system with friction is presented. However, the accuracy of the proposed method depends on the mass ratio γ, the frequency ratio Rƒ and the friction force. The proposed method is compared with 2-dof non-linear time history analysis, and the accuracy of the proposed method is calculated at γ ≤ 0.1 and Rƒ ≤ 3. The present study defines the area within an error of 10% as the applicable area of the modal analysis method for a friction system and shows the range of error over 10%. The proposed method can be useful for obtaining the seismic response of a 2-dof friction system without non-linear time history analysis.