Sound absorption by a metasurface comprising hard spheres in a soft medium

Asymmetric sound scattering by gratings of monopolar and dipolar resonators in a viscoelastic materiala)

A self-consistent analytical model of a locally resonant coating exhibiting strong asymmetric wave scattering is presented. Gratings of resonant inclusions composed of cavities and hard particles embedded in a soft matrix are translated to the problem of sound scattering by monopolar and dipolar type resonators in a one-dimensional waveguide. Equations of motion for gratings of cavities and hard particles are developed that incorporate added mass, damping, and restoration forces to take into account multiple scattering effects. Expressions for the impedances of the resonators are derived from which the particle velocity fields are obtained. Monopole and dipole strengths are also calculated in terms of polarizability tensor components, which in turn are obtained from a retrieval method. Sound scattering by monopolar and dipolar resonators of different size and distribution within the waveguide are examined. Using detailed understanding of the interaction between groups of resonators, optimized solutions for a new class of acoustic materials can be designed by selecting layers of resonators to produce a given response.

Propagation of elastic waves in correlated dispersions of resonant scatterers

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Scaling relations for sound scattering by a lattice of hard inclusions in a soft mediuma)

Soft elastic materials embedded with resonant inclusions are widely used as acoustic coatings for maritime applications. A versatile analytical framework for resonance scattering of sound waves in a soft material by a lattice of hard inclusions of complex shape is presented. Analogies from hydrodynamics and electrostatics are employed to derive universal scaling relations for a small number of well-known lumped parameters that map resonant scattering of a complex-shaped hard inclusion to that of a sphere. Multiple scattering of waves between inclusions in proximity is also considered. The problem is then treated using an effective medium theory, viz, a layer of hard inclusions is modeled as a homogenized layer with some effective properties. The acoustic performance of hard inclusions for a range of shapes with spheres of the same volume are compared. Results obtained using this approach are in good agreement with finite element simulations.

Weak-form homogenization of two and three-dimensional fluid acoustical systems

A one-dimensional weak-form homogenization method [Muhlestein, J. Acoust. Soc. Am. 147(5), 3584-3593 (2020)] is extended to two and three-dimensional for quasi-static fluid systems. This homogenization approach uses a local multiple-scales approximation to estimate the acoustical fields within a representative volume element, substitutes these approximations into a weak formulation of the mechanics, and then globally homogenizes the system by averaging the integrand of the weak-form integral. An important consequence of including more spatial dimensions is that the local particle velocity does not approach a uniform macroscopic particle velocity. Instead, the effective material properties are used to describe the behavior of the mean particle velocity. A localization tensor may be used to convert from the mean particle velocity to the local particle velocity. The generalized homogenization method is then applied to two special cases. The first case is stratified media, chosen because it has an exact analytical solution. The second case is a cubic lattice of spheres, which has a benchmark solution to compare with. This second case utilizes finite element software to provide estimates of the effective mass density. Finally, three further generalizations to the homogenization method, including extension to finite frequency values, complex media, and elasticity, are briefly discussed.

A simple model for elastic wave propagation in hard sphere-filled random composites

A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.

Homogenization of an acoustic coating with a steel backing subject to an obliquely incident sound

An effective homogenization model for the acoustic coating of underwater structures is important for reducing the complexity of acoustic scattering computation, which arises from the huge difference in scale between the integral structure and the inhomogeneous microstructure of the coating. The main difficulty of this homogenization arises from the oblique-incidence effect of external sound waves and the interface effect between the coating and backing. In this work, a hybrid method, combining the Bloch wave analysis and retrieval technique, is proposed to characterize the acoustic behavior of the voided coating backed with a steel plate under the action of external sound waves with an arbitrary incident angle. The effectiveness of this method is validated by numerical simulations and comparison with the Bloch wave method and the traditional retrieval method. The influence of the shear-wave effect under obliquely incident sound waves and the coupling effect between the coating and the backing on the homogenization model is investigated in detail, providing a comprehensive understanding of the effective acoustic behavior of the coating.

Two-Dimensional Composite Acoustic Metamaterials of Rectangular Unit Cell from Pentamode to Band Gap

Pentamode metamaterials have been receiving an increasing amount of interest due to their water-like properties. In this paper, a two-dimensional composite pentamode metamaterial of rectangular unit cell is proposed. The unit cells can be classified into two groups, one with uniform arms and the other with non-uniform arms. Phononic band structures of the unit cells were calculated to derive their properties. The unit cells can be pentamode metamaterials that permit acoustic wave travelling or have a total band gap that impedes acoustic wave propagation by varying the structures. The influences of geometric parameters and materials of the composed elements on the effective velocities and anisotropy were analyzed. The metamaterials can be used for acoustic wave control under water. Simulations of materials with different unit cells were conducted to verify the calculated properties of the unit cells. The research provides theoretical support for applications of the pentamode metamaterials.