2D Dynamic Directional Amplification (DDA) in Phononic Metamaterials

Phononic structures with unit cells exhibiting Bragg scattering and local resonance present unique wave propagation properties at wavelengths well below the regime corresponding to bandgap generation based on spatial periodicity. However, both mechanisms show certain constraints in designing systems with wide bandgaps in the low-frequency range. To face the main practical challenges encountered in such cases, including heavy oscillating masses, a simple dynamic directional amplification (DDA) mechanism is proposed as the base of the phononic lattice. This amplifier is designed to present the same mass and use the same damping element as a reference two-dimensional (2D) phononic metamaterial. Thus, no increase in the structure mass or the viscous damping is needed. The proposed DDA can be realized by imposing kinematic constraints to the structure's degrees of freedom (DoF), improving inertia and damping on the desired direction of motion. Analysis of the 2D lattice via Bloch's theory is performed, and the corresponding dispersion relations are derived. The numerical results of an indicative case study show significant improvements and advantages over a conventional phononic structure, such as broader bandgaps and increased damping ratio. Finally, a conceptual design indicates the usage of the concept in potential applications, such as mechanical filters, sound and vibration isolators, and acoustic waveguides.