Title: Low-frequency wide band-gap elastic/acoustic meta-materials using the K-damping concept,
Abstract: The terms "acoustic/elastic meta-materials" describe a class of periodic
structures with unit cells exhibiting local resonance. This localized resonant
structure has been shown to result in negative effective stiffness and/or mass
at frequency ranges close to these local resonances. As a result, these
structures present unusual wave propagation properties at wavelengths well
below the regime corresponding to band-gap generation based on spatial
periodicity, (i.e. "Bragg scattering"). Therefore, acoustic/elastic
meta-materials can lead to applications, especially suitable in the
low-frequency range. However, low frequency range applications of such
meta-materials require very heavy internal moving masses, as well as additional
constraints at the amplitudes of the internally oscillating locally resonating
structures, which may prohibit their practical implementation. In order to
resolve this disadvantage, the K-Damping concept will be analyzed. According to
this concept, the acoustic/elastic meta-materials are designed to include
negative stiffness elements instead or in addition to the internally resonating
added masses. This concept removes the need for the heavy locally added heavy
masses, while it simultaneously exploits the negative stiffness damping
phenomenon. Application of both Bloch's theory and the classical modal analysis
at the one-dimensional mass-in-mass lattice is analyzed and corresponding
dispersion relations are derived. The results indicate significant advantages
over the conventional mass-in-a mass lattice, such as broader band-gaps and
increased damping ratio and reveal significant potential in the proposed
solution. Preliminary feasibility analysis for seismic meta-structures and low
frequency acoustic isolation-damping confirm the strong potential and
applicability of this concept.