Evaluation of a robust dynamic vibration absorber based on negative stiffness and internal resonance against seismic excitation

In this study, a nonlinear absorber that works with a negative stiffness is introduced to control vibration and its effect on reducing earthquake damage is investigated. Negative stiffness increases structural softness and damping. Also, due to its inherent nonlinear nature, negative stiffness can cause internal resonance and transfer vibration energy from a directly excited vibrating mode to a higher frequency mode. Using these features can be effective in reducing vibration. First, to investigate the dynamic behavior in conditions without internal resonance and with 1:3 internal resonance, the proposed absorber is added to a nonlinear main system and when the system is under external resonance due to harmonic excitation, the negative stiffness parameter of the absorber for conditions with and without Internal resonance is adjusted. The mathematical model of the system is presented and the governing differential equations are derived. The governing equations are solved by the Multiple Scale method, the answers and their stability are examined, discussed and compared. Then, by generalizing the absorber ability to structures with general nonlinear behavior, the effect of the proposed absorber on reducing the damage caused by near and far from the fault earthquakes is studied by numerical simulation and for cases where under an earthquake record, The absorber intensifies the damage to the structure and loses its reliability, an active control loop is proposed and its effect is investigated.