Estimation of the Damping Ratio of the Coupled System Based on the Damping Ratios of Two 1-Dof Systems

A number of different structures in industrial facilities are installed on supports. There is the case that the damage occurs by the coupled vibration. The response magnification is obtained from the modal natural frequency and the modal damping ratio of the coupled system in the seismic design. Therefore, the modal natural frequency and the modal damping ratio of the coupled system are required. The natural frequency and the damping ratio of the support and the structure are abtained during the initial design process or by a shaking test. However, the modal natural frequency and the modal damping ratio of the coupled system are not easily obtained. The modal natural frequency of the coupled system can be calculated from theoretical equation, but the modal damping ratio cannot be easily calculated. In the present study, an equation to calculate the modal damping ratio of the coupled system with classic damping is presented. In addition, a simple equation to calculate the modal damping ratio with a non-classic damping system is proposed. This equation is evaluated theoretically. The proposed equation is useful for obtaining the modal damping ratio without performing eigenvalue analysis or a shaking test.