Real-time hybrid testing validation of a stiffness-controllable mass damper for reducing vibrations in nonlinear structures

The design of passive tuned mass dampers (TMDs) and the evaluation of their vibration control performance typically rest on the assumption that the primary structure is a linear system. The optimized TMD is then tuned to the natural frequency of the primary structure, enabling the transfer of vibrational energy from the structure to the TMD and its absorption through the damping mechanism of the TMD, thereby reducing vibrations in the primary structure. However, if the structure exhibits nonlinear behavior during an earthquake, causing the natural frequency of the primary structure to vary, the passive TMD may experience a detuning effect, leading to significant degradation in its control performance. To address this challenge, this paper introduces a novel mass damper with controllable stiffness (MDCS) that dynamically adjusts its stiffness to adapt to changes in structural frequency due to nonlinear responses. This feature enables the MDCS to maintain optimal performance under nonlinear conditions. First, a mathematical model of a nonlinear structure with an MDCS was established, and a least input energy method (LIEM) control law suitable for nonlinear structures was developed to minimize the total energy of the nonlinear structure and the MDCS. This study verified the theoretical model and the LIEM control algorithm by conducting real-time hybrid testing (RTHT) using a physical lever-type MDCS mechanism in combination with a nonlinear numerical (substructure) model. The RTHT results demonstrated that the MDCS provides superior vibration reduction and reduced stroke in nonlinear structures compared to passive TMDs, marking a significant advancement in vibration control for seismic applications.