We report on the experimental study of the propagation of surface guided waves in a periodic arrangement of pillars on a semi-infinite medium. Samples composed of nickel pillars grown on a lithium niobate substrate were prepared and wide bandwidth transducers were used for the electrical generation of surface elastic waves. We identify a complete band gap for surface guided waves appearing at frequencies markedly lower than the Bragg band gap. Using optical measurements of the surface vibrations and by comparison with a finite element model, we argue that the low frequency band gap arises because of local resonances in the pillars. When resonance is reached, the acoustic energy is confined inside the pillars and transmission through the array is strongly reduced. At higher frequencies and inside the Bragg band gap, the incident surface elastic waves are almost completely reflected and the observed exponential decay of the transmission is similar to the case of phononic crystals made of holes in a substrate.

We investigate theoretically the propagation of acoustic waves in a two-dimensional array of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the band structure of the periodic array and of the transmission of waves through a finite length array, we show that the phononic crystal can support a number of surface propagating modes in the nonradiative region of the substrate, or sound cone, as limited by the slowest bulk acoustic wave. The modal shape and the polarization of these guided modes are more complex than those of classical surface waves propagating on a homogeneous surface. Significantly, an in-plane polarized wave and a transverse wave with sagittal polarization appear that are not supported by the free surface. In the band structure, guided modes define band gaps that appear at frequencies markedly lower than those expected from the Bragg interference condition. We identify them as originating from local resonances of the individual cylindrical pillars and show their dependence on the geometrical parameters, in particular with the height of the pillars. The transmission of surface acoustic waves across a finite array of pillars shows the signature of the locally resonant band gaps for surface modes and their dependence on the symmetry of the source and its polarization. Numerical simulations are performed by using the finite element method and considering silicon pillars on a silicon substrate.

International audienceThe complex band structure of a phononic crystal is composed of both propagating and evanescent Bloch waves. Evanescent Bloch waves are involved in the diffraction of acoustic phonons at the interfaces of finite phononic crystal structures. They are shown to arise both because of band gaps, where they directly measure the exponential decrease upon transmission, and because of the frustrated nature of higher-order diffracted waves at low frequencies. These diffracted evanescent Bloch waves become propagative as the frequency increases thus populating higher frequency bands. These results should apply as well to any periodic medium supporting the propagation of waves

International audienceWe investigate stop band properties of a theoretical cubic array of iron spheres connected to a bulk of concrete via iron or rubber ligaments. Each sphere moves freely within a surrounding air cavity, but ligaments couple it to the bulk and facilitate bending and rotational motions. Associated low frequency local resonances are predicted by an asymptotic formula. We find complete stop bands in the range [16,21][16,21] Hz (resp. [6,11][6,11] Hz) for 7.4 m (resp. 0.74 m) diameter iron spheres with a 10 m (resp. 1 m) center-to-center spacing, when they are connected to concrete via steel (resp. rubber) ligaments. The scattering problem shows that only bending modes are responsible for damping: rotational modes are totally overwritten by bending modes. Regarding seismic applications, we consider soil as a host medium, in which case the low frequency stop band can be enlarged through ligaments of different sizes that allow for well separated bending and rotational modes. We finally achieve some damping of elastodynamic waves from 8 to 49 Hz for iron spheres 0.74 m in diameter, connected to soil with six rubber ligaments of optimized shapes. These results represent a preliminary step in the design of seismic shields placed around, or underneath, foundations of large civil infrastructures

The propagation of surface acoustic waves in two-dimensional phononic crystals of pillars on a surface is investigated experimentally for hexagonal and honeycomb lattice symmetries. A random array of pillars is also compared to the periodic phononic crystals. Taking into account that the geometrical and physical characteristics of the pillars are the same in all cases, it is shown that the locally resonant band gap in the low frequency range is almost independent of periodicity and resilient to randomness. In contrast, the Bragg band gap disappears with the random array.