TY - JOUR TI - Static and dynamic analysis of periodic lattice structures with applications to acoustic cloaks of the pentamode type DO - https://doi.org/doi:10.7282/T3FJ2JM3 PY - 2015 AB - As a first step towards producing pentamode acoustic cloaks, so named for the type of elasticity required, periodic lattice structured materials are designed that mimic the acoustic properties of water. This material is termed Metal Water and is analyzed in detail. The requirements considered are matching of density and wave speed, this produces a type of metamaterial that couples acoustic wave energy from a background fluid into an elastic medium without reflection. General elastodynamic, scattering, and acoustic cloaking theories are reviewed. In application to scattering, a new method is developed for cylindrically layered elastic media, which combines impedance and matricant propagator matrices in a stable integration scheme. A variety of techniques are used to estimate and improve the homogenized material properties associated with Metal Water. Dispersion curves are found by the application of Bloch-Floquet theory where a new approach that utilizes Euler-Bernoulli beams is developed. Results are compared against finite element methods capable of more accurately determining homogenized properties. Several designs are proposed in two and three dimensions with detailed studies including dispersion curve analysis as well as statically determined properties. KW - Mechanical and Aerospace Engineering KW - Acoustical engineering KW - Dispersion LA - eng ER -