Using a generalized form of Bloch’s theorem, we derive the dispersion relation of a viscously damped locally resonant metamaterial modeled as an infinite mass-in-mass lumped parameter chain. For comparison, we obtain the dispersion relation for a statically equivalent Bragg-scattering mass-spring chain that is also viscously damped. For the two chains, we prescribe identical damping levels in the dashpots and compare the damping ratio associated with all propagating Bloch modes. We find that the locally resonant metamaterial exhibits higher dissipation throughout the spectrum which indicates a damping emergence phenomena due to the presence of local resonance. This phenomenon, which we define as metadamping, provides a new paradigm for the design of material systems that display both high damping and high stiffness. We conclude our investigation by quantifying the degree of metadamping as a function of the long-wave speed of sound in the medium or the static stiffness.
Metadamping in Dissipative Metamaterials
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Hussein, MI, & Frazier, MJ. "Metadamping in Dissipative Metamaterials." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 14: Vibration, Acoustics and Wave Propagation. San Diego, California, USA. November 15–21, 2013. V014T15A051. ASME. https://doi.org/10.1115/IMECE2013-66210
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