Viscous-to-viscoelastic transition in phononic crystal and metamaterial band structures

Elastoacoustic wave propagation in a biphasic mechanical metamateriala)

Humans are sensitive to air-borne sound as well as to mechanical vibrations propagating in solids in the frequency range below 20 kHz. Therefore, the development of multifunctional filters for both vibration reduction and sound insulation within the frequency range of human sensitivity is a research topic of primary interest. In this paper, a high-contrast biphasic mechanical metamaterial, composed of periodic elastic solid cells with air-filled voids, is presented. By opening intercellular air-communicating channels and introducing channel-bridging solid-solid couplings, the frequency dispersion spectrum of the metamaterial can be modified to achieve complete and large bandgaps for acoustic and elastic waves. From a methodological viewpoint, the eigenproblem governing the free wave propagation is solved using a hybrid analytical-computational technique, while the waveform classification is based on polarization factors expressing the fraction of kinetic and elastic energies stored in the solid and fluid phases. Based on these theoretical results, a mechanical metafilter consisting of an array of a finite number of metamaterial cells is conceived to provide a technical solution for engineering applications. The forced response of the metafilter is virtually tested in a computational framework to assess its performance in passively controlling the propagation of broadband sound and vibration signals within solid and fluid environments. Quantitative results synthesized by transmission coefficients demonstrate that the metafilter can remarkably reduce the transmitted response in the frequency band of human sensitivity.

Physics of surface vibrational resonances: pillared phononic crystals, metamaterials, and metasurfaces

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.

Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling

Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.

Non-reciprocal acoustics in a viscous environment

It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken P symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry (T symmetry) holds. Viscous losses break T symmetry, adding a non-reciprocal contribution to the transmission coefficient. The non-reciprocal transmission spectra for a phononic crystal of metallic circular cylinders in water are experimentally obtained and analysed. The surfaces of the cylinders were specially processed in order to weakly break P symmetry and increase viscous losses through manipulation of surface features. Subsequently, the non-reciprocal part of transmission is separated from its asymmetric reciprocal part in numerically simulated transmission spectra. The level of non-reciprocity is in agreement with the measure of broken P symmetry. The reported study contradicts commonly accepted opinion that linear dissipation cannot be a reason leading to non-reciprocity. It also opens a way for engineering passive acoustic diodes exploring the natural viscosity of any fluid as a factor leading to non-reciprocity.

Reduced Linear Constrained Elastic and Viscoelastic Homogeneous Cosserat Media as Acoustic Metamaterials

We consider the reduced constrained linear Cosserat continuum, a particular type of a Cosserat medium, for three different material behaviors or symmetries: the isotropic elastic case, a special type of elastic transversely isotropic case, and the isotropic viscoelastic case. Such continua, in which stresses do not work on rates of microrotation gradients, behave as acoustic metamaterials for the (pure) shear waves and also for one branch of the mixed wave in the considered anisotropic material case. In elastic media, those waves do not propagate for frequencies exceeding a certain threshold, whence these media exhibit a single negative acoustic metamaterial behavior in this range. In the isotropic viscoelastic case, dissipation destroys the bandgap and favors wave propagation. This curious effect is, probably, due to the fact that the bandgap is associated not with the dissipation, but with the wave localization which can be destroyed by the viscosity. The dispersion curve is now decreasing in some part of the former bandgap, above a certain frequency, whence the medium is a double negative acoustic metamaterial. We prove the existence of a boundary wavenumber in the viscoelastic case and estimate its value. Below the characteristic frequency corresponding to the boundary of the elastic bandgap, the wave attenuation (logarithmic decrement) is a growing function of the viscous dissipation parameter. Above this frequency, the attenuation decreases as the viscosity increases.

Maximizing wave attenuation in viscoelastic phononic crystals by topology optimization

The viscoelasticity of constituent materials has a significant effect on the dispersion relation of waves in viscoelastic phononic crystals (PCs). This paper extends the bi-directional evolutionary structure optimization (BESO) method to the design of viscoelastic PCs with the maximum attenuation and stiffness. The attenuation factor is calculated by the k(ω)-method, and the effective elasticity matrix of composite PCs is extracted by the homogenization theory. The inverse design of viscoelastic PCs is formulated with a topology optimization problem, which is then solved by the proposed BESO method. Generally, BESO re-distributes the material phases of viscoelastic PCs within the primitive unit cell step by step based on sensitivity analysis. The optimization process is stopped until the optimized viscoelastic PC with the maximum attenuation factor and the desirable bulk modulus is achieved. Numerical examples are systematically presented for the propagation of out-of-plane or in-plane waves, and combined out-of-plane and in-plane waves at various frequencies. Novel topological patterns of the optimized viscoelastic PCs are obtained and discussed.