On the adoption of canonical quasi-crystalline laminates to achieve pure negative refraction of elastic waves.

A way to achieve negative refraction of elastic anti-plane shear waves is a transmission across an interface between a homogeneous substrate and a periodic transverse laminate. To achieve negative refraction, the frequency of the source should be lower than the upper limit of the second transition zone (TZ) of the harmonic spectrum of the laminate. An effective way to control the location of TZ is to consider a configuration for the laminate, a concept that originates from the properties of quasi-crystalline sequences among which the Fibonacci one is a particular case.

On the universality of the frequency spectrum and band-gap optimization of quasicrystalline-generated structured rods.

The dynamical properties of periodic two-component phononic rods, whose elementary cells are generated adopting the Fibonacci substitution rules, are studied through the recently introduced method of the toroidal manifold. The method allows all band gaps and pass bands featuring the frequency spectrum to be represented in a compact form with a frequency-dependent flow line on the surface describing their ordered sequence. The flow lines on the torus can be either closed or open: in the former case, (i) the frequency spectrum is periodic and the elementary cell corresponds to a canonical configuration, (ii) the band gap density depends on the lengths of the two phases; in the latter, the flow lines cover ergodically the torus and the band gap density is independent of those lengths.

An interface model for the periodontal ligament.

A nonlinear interface constitutive law is formulated for modeling the mechanical behavior of the periodontal ligament. This gives an accurate interpolation of the few available experimental results and provides a reasonably simple model for mechanical applications. The model is analyzed from the viewpoints of both mathematical consistency and effectiveness in numerical calculations.