Linear acoustic metamaterials (LAMs) are widely used to manipulate sound; however, it is challenging to obtain bandgaps with a generalized width (ratio of the bandgap width to its start frequency) >1 through linear mechanisms. Here we adopt both theoretical and experimental approaches to describe the nonlinear chaotic mechanism in both one-dimensional (1D) and two-dimensional (2D) nonlinear acoustic metamaterials (NAMs). This mechanism enables NAMs to reduce wave transmissions by as much as 20–40 dB in an ultra-low and ultra-broad band that consists of bandgaps and chaotic bands. With subwavelength cells, the generalized width reaches 21 in a 1D NAM and it goes up to 39 in a 2D NAM, which overcomes the bandwidth limit for wave suppression in current LAMs. This work enables further progress in elucidating the dynamics of NAMs and opens new avenues in double-ultra acoustic manipulation.

The introduction of engineered resonance phenomena on surfaces has opened a new frontier in surface science and technology. Pillared phononic crystals, metamaterials, and metasurfaces are an emerging class of artificial structured media, featuring surfaces that consist of pillars—or branching substructures—standing on a plate or a substrate. A pillared phononic crystal exhibits Bragg band gaps, while a pillared metamaterial may feature both Bragg band gaps and local resonance hybridization band gaps. These two band-gap phenomena, along with other unique wave dispersion characteristics, have been exploited for a variety of applications spanning a range of length scales and covering multiple disciplines in applied physics and engineering, particularly in elastodynamics and acoustics. The intrinsic placement of pillars on a semi-infinite surface—yielding a metasurface—has similarly provided new avenues for the control and manipulation of wave propagation. Classical waves are admitted in pillared media, including Lamb waves in plates and Rayleigh and Love waves along the surfaces of substrates, ranging in frequency from hertz to several gigahertz. With the presence of the pillars, these waves couple with surface resonances richly creating new phenomena and properties in the subwavelength regime and in some applications at higher frequencies as well. At the nanoscale, it was shown that atomic-scale resonances—stemming from nanopillars—alter the fundamental nature of conductive thermal transport by reducing the group velocities and generating mode localizations across the entire spectrum of the constituent material well into the terahertz regime. In this article, we first overview the history and development of pillared materials, then provide a detailed synopsis of a selection of key research topics that involve the utilization of pillars or similar branching substructures in different contexts. Finally, we conclude by providing a short summary and some perspectives on the state of the field and its promise for further future development.

We investigate the elastic wave dispersion by a phononic metamaterial plate containing low frequency resonator stubs arranged periodically over the plate. We show that this system not only provides stop bands for wavelengths much larger than the periodicity but also displays negative behavior of its effective mass density under the homogenization assumption. A numerical method is used to calculate the plate's effective dynamic mass density as function of the frequency where the metamaterial is considered as homogeneous plate for these large wavelengths. Strong anisotropy of the effective mass density matrix is observed around the resonance frequencies where the gaps are opened. In these regions, we demonstrate that the effective matrix density components take negative values. For each of these components, the negative behavior is studied by taking into account the polarization of the involved resonant modes as well as their associated partial band gaps opened for each specific Lamb symmetry modes. We found that coupling between Lamb waves and resonant modes strongly affects the effective density of the whole plate especially in the coupling frequency regions of the gaps.

The propagation of Lamb waves in silicon plates coated by a very thin two-dimensional phononic film is studied experimentally. The dispersion curves are measured using a laser ultrasonics technique. The data are then compared to the calculated dispersion curves of the uncoated silicon plate. The overall shapes of the lower-order symmetric and antisymmetric Lamb modes are not altered by the thin phononic film, except by the appearing of frequency band gaps at the edges of both the first and the second Brillouin zone. The influence of the filling fraction on the magnitude of the gaps is investigated experimentally.

We theoretically investigate acoustic metasurfaces consisting of either a single pillar or a line of identical pillars on a thin plate, and we report on the dependence on the geometrical parameters of both the monopolar compressional and dipolar bending modes. We show that for specific dimensions of the resonators, bending and compressional modes may be simultaneously excited. We study their interaction with an antisymmetric Lamb wave, whether or not they occur at the same frequency, with particular consideration for the amplitude and phase of waves emitted by the pillars at resonance. Especially, the analysis of both the amplitude and the phase of the wave at the common resonant frequency downstream from a line of pillars demonstrates that the reemitted waves allow for the transmission with phase shift of π.