Emergence of metadamping in thin-walled mono-symmetric metabeam: Homogenization approach

The paper presents a unified homogenization-based methodology to estimate the damping enhancement, known as metadamping, for a thin-walled mono-symmetric beam (TWMSB) having periodically placed damped resonators. The dispersion equation for a damped TWMSB with a damped resonator, incorporating the influence of warping and two types of damping, namely strain-rate and velocity-dependent viscous damping, is derived. The wavenumber-dependent damped frequency and damping ratio are obtained from the band structure of a unit cell utilizing the free wave approach. The energy dissipation profile, obtained from the coefficient of energy decay, matches closely with the envelope of the time domain response. The variation of total damping ratio and coefficient of energy decay with the long wave sound speed for a beam with and without a resonator is studied. The influence of the mass and the stiffness of the resonator on the overall damping ratio of the system is investigated. The findings reveal that even with only a 2% damping ratio in the resonator, a significant enhancement in the overall dissipation can be perceived. A trade-off is observed between spatial attenuation and temporal attenuation as the damping of the resonator increases. This study is helpful for the application of transient vibration control often encountered in the event of blast, impact, and earthquake. [Display omitted] •Metadamping on a damped thin-walled mono-symmetric metabeam is investigated.•Dispersion relation is obtained using the homogenization approach.•Resonator damping significantly enhances the damping of the metabeam.•Higher damping is achieved in a stiffer metabeam incorporating a resonator.