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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... 

In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical...