Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Sub-wavelength resonators as seismic Rayleigh waves shield

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure. As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Characterization of a 3D-printed low-cost flexible dielectric material for the realization of innovative WPT wearable applications

The aim of this thesis is to demonstrate that 3D-printing technologies can be considered significantly attractive in the production of microwave devices and in the antenna design, with the intention of making them lightweight, cheaper, and easily integrable for the production of wireless, battery-free, and wearable devices for vital signals monitoring. In this work, a new 3D-printable, low-cost resin material, the Flexible80A, is proposed as RF substrate in the implementation of a rectifying antenna (rectenna) operating at 2.45 GHz for wireless power transfer. A careful and accurate electromagnetic characterization of the abovementioned material, revealing it to be a very lossy substrate, has paved the way for the investigation of innovative transmission line and antenna layouts, as well as etching techniques, possible thanks to the design freedom enabled by 3D-printing technologies with the aim of improving the wave propagation performance within lossy materials. This analysis is crucial in the design process of a patch antenna, meant to be successively connected to the rectifier. In fact, many different patch antenna layouts are explored varying the antenna dimensions, the substrate etchings shape and position, the feeding line technology, and the operating frequency. Before dealing with the rectification stage of the rectenna design, the hot and long-discussed topic of the equivalent receiving antenna circuit representation is addressed, providing an overview of the interpretation of different authors about the issue, and the position that has been adopted in this thesis. Furthermore, two rectenna designs are proposed and simulated with the aim of minimizing the dielectric losses. Finally, a prototype of a rectenna with the antenna conjugate matched to the rectifier, operating at 2.45 GHz, has been fabricated with adhesive copper on a substrate sample of Flexible80A and measured, in order to validate the simulated results.