Abstract
Passive vibration control systems are characterized by their simple practical design and independence of external power supplies. However, they are usually hindered by their narrow frequency band that cannot handle variable frequency disturbances. Recent research has demonstrated the capability of passive self-tuning resonators through the use of a sliding mass without the need for any external power sources. This work analytically and experimentally investigates the passive self-tuning of a metastructure consisting of a clamped-clamped beam with a sliding mass. The governing equations of motion show that the slider can be driven by Coriolis and centrifugal forces upon applying the excitation force on the structure. To improve the accuracy of our analytical simulations, we derive the exact instantaneous mode shapes and frequencies of the structure and feed them into an adaptive algorithm, which updates the spatial state of the system. Numerical simulations demonstrate that the proposed resonator can tune itself to the excitation frequency as the slider reaches the equilibrium position. This observation suggests that a significant vibration reduction can be obtained using the proposed resonator over a wide frequency band. Experiments are carried out to validate the analytical findings. The proposed structure can be used in different vibration control applications (i.e., aerospace, automotive, and machining), and its model can further be extended to self-adaptive periodic structures (metamaterials).