Concrete structures suffer from crack damage under heavy vibrations, caused by seismic loads. Passive vibration control devices can be used to reduce the damage. The most common device is the tuned-mass-damper (TMD), which is tuned to match the natural frequency of the primary structure. However, under prolonged vibration load, the natural frequency of the concrete structure decreases, reducing the TMD's effectiveness in mitigating vibrations and damage, as it can only target a fixed natural frequency. Therefore, this study will propose and implement the nonlinear energy sink (NES), which is a vibration control device that can adapt to changing frequency, resulting in a larger effective bandwidth than the TMD. As a concrete structure, the cast-in-place double-column piers is seismically loaded with a shaking table with and without NES to observe the vibration and damage-mitigating properties of the NES. More specifically, a magnetic bi-stable NES (MBNES) with a viscous fluid damper (VFD) is designed and built. The bi-stable restoring force allows for a larger bandwidth than conventional NESs, and the magnets and VFD allow for easy manufacturability. An optimization method is proposed to obtain optimal parameters, and the restoring force and damping of the experimentally designed MBNES are verified using the restoring force surface method. The proposed design, optimization and identification procedure are generic and can be applied to any (concrete) civil structure. Shaking table tests are used to verify the robust performance of MBNES under continuous changes in the natural frequency of concrete double-column piers. The experimental results show that the MBNES can effectively mitigate vibrations of the pier and, consequently, reduce the damage of the pier, slow down the decrease of the stiffness of the pier, reduce the curvature and shear deformation of the pier. Numerical analysis results show that MBNES can absorb the energy of the primary structure in a wide frequency bandwidth and has excellent robust performance compared to conventional devices.