Mechanics Based Characterization of Elastic Metamaterials

In bandgap engineering there is a shortage of systematic design approach which enables one to select design variables to achieve bandgap in desired frequency range. Tools that can address this can open new areas of interest, especially since phononic crystals with low frequency bandgaps have multitude of applications in attenuation of structural vibration. Furthermore, mechanics-based characterization of phononic crystals had not seen much progress in the recent years while a lot of applied research had been conducted on phononic materials with material phase periodicity and other factors taken into consideration. This work aims to propose a systematic characterization approach of elastic metamaterials based on potential and kinetic energy of the system. Based on the characterization a number of design changes have been suggested and analyzed to achieve modulated phonon bandgaps while preserving the existing bandgaps. Numerical analysis was conducted on a simple cubic truss lattice featured with local resonator system consisting of mass and spring which provides needed elasticity to the structure towards achieving phonon bandgaps in different frequency ranges. Potential energy was found to be predominantly stored in the truss and the spring while masses were subjected to kinetic energy. To reveal the nature of the potential energy, deformation modes of the truss and the spring were analyzed and decomposed into four fundamental modes of deformation, i.e. axial, flexure, torsion and transverse shear. Characterization of the kinetic energy of the masses was done by using deformation fields from an isolated mass spring system as basis functions and projecting the crystal deformation fields onto the basis functions which yields modal participation of the local resonator in the crystal during Bloch mode analysis. Design changes were proposed guided by the potential and kinetic energy characterization to facilitate wider bandgap in the higher frequency with an engineered bandgap in the lower frequency. A parametric study was conducted on seven geometric parameters to comprehend the characterizations on a broad range of phononic crystals. Three design principles were proposed using the findings from the parametric study that motivates better decision making towards obtaining desired material property from locally resonant elastic metamaterials.