Spatiotemporal Damping of Dissipative Metamaterial

The concept of spatiotemporal damping is proposed to quantify the inherent wave attenuation property of dissipative metamaterials. The concept of spatiotemporal damping is more general compared to its counterparts in previous studies such as band gap and damping. Spatiotemporal damping results from the coupling effect of energy dissipation and energy scattering, and the coupling mechanism is revealed in this study. The traditional concept of damping only considers the energy dissipation effect, and the traditional concept of band gap only defines the frequency range in which wave propagation is prohibited due to the energy scattering (energy reflection) effect in metamaterials. The proposed concept of spatiotemporal damping covers both energy dissipation and energy scattering (energy reflection), which are intrinsic properties of dissipative metamaterials and are coupled with each other. Taking a two-dimensional square-lattice viscoelastic metamaterial as an example, the coupling mechanism of energy dissipation and energy scattering (energy reflection) is revealed. When the dissipative properties of the components change from low to high, the viscoelastic metamaterial strengthens the effect of energy dissipation at the sacrifice of weakening the effect of energy scattering (energy reflection), and the dominant mechanism of its spatiotemporal damping gradually switches from energy scattering (energy reflection) to energy dissipation. For the case where energy scattering (energy reflection) is dominant, the coupling effect of energy dissipation and energy scattering on spatiotemporal damping can be summarized as peak shaving and valley filling. And for the case where energy dissipation is dominant, the spatiotemporal damping increases with the enhancement of the dissipative performance of the components. The effects of main structural and material factors on the spatiotemporal damping of viscoelastic metamaterials are investigated numerically. This research has broad application prospects in the field of vibration and noise control.