Slow Sound and Critical Coupling to Design Deep Subwavelength Acoustic Metamaterials for Perfect Absorption and Efficient Diffusion

Subwavelength Broadband Perfect Absorption for Unidimensional Open‐Duct Problems

“…Following the e iω t convention (ω = 2π f is the angular frequency), ζ Rad for a baffled circular open duct can be explicitly written as (see, for example, page 186 of [45]) $$\[{\zeta _{{\rm{Rad}}}} = {\left[ {\frac{p}{{{z_0}u}}} \right]_{{\rm{Open}}\;{\rm{end}}}} = 1 - \frac{{{J_1}(2{k_0}{R_{\rm{D}}})}}{{{k_0}{R_{\rm{D}}}}} + {\rm{i}}\frac{{S{H_1}(2{k_0}{R_{\rm{D}}})}}{{{k_0}{R_{\rm{D}}}}}\]$$where J 1 is the first‐order Bessel function of the first kind, SH 1 denotes the first‐order Struve‐H function, and k 0 = ω/ c 0 is the acoustic wavenumber. By using the transfer matrix method, [ 34,35 ] the reflection and transmission coefficients R and T in Equations (2) and thus the absorption coefficient α in Equation (1) can be explicitly expressed as functions of the radiation impedance ζ Rad (i.e., a known function of frequency) as well as the structural parameters of the Helmholtz resonators. Specifically, the acoustic response of each resonator is fully determined by 6 structural parameters: the radius R N and thickness T N of the neck, the depth H C , axial width L x , and circular angle θ C of the cavity, as well as the axial position x HR of the resonator (see Figure 1).…”

“…where J 1 is the first-order Bessel function of the first kind, SH 1 denotes the first-order Struve-H function, and k 0 = ω/c 0 is the acoustic wavenumber. By using the transfer matrix method, [34,35] the reflection and transmission coefficients R and T in Equations ( 2) and thus the absorption coefficient α in Equation (1) can be explicitly expressed as functions of the radiation impedance ζ Rad (i.e., a known function of frequency) as well as the structural parameters of the Helmholtz resonators. Specifically, the acoustic response of each resonator is fully determined by 6 structural parameters: the radius R N and thickness T N of the neck, the depth H C , axial width L x , and circular angle θ C of the cavity, as well as the axial position x HR of the resonator (see Figure 1).…”

“…In the design process of this type of meta-absorbers, the dispersion properties of the employed metamaterial should be precisely controlled. Among the passive design strategies, the use of coupled resonators, of either monopolar or dipolar types, has been extensively studied (see, for example, [25,26,33] , chapter 3 of [34], chapter 5 of [35], etc.). In the unidimensional (1D) reflection problem (either with a rigid boundary [36][37][38] or a soft boundary [39] ), perfect absorption can be realized at a given frequency by using a single resonator.…”

Bioinspired periodic panels optimized for acoustic insulation

“…These solutions may further benefit from the use of (i) phononic crystals (PCs) and (ii) periodic MMs, since these may possess phononic band gaps, i.e. frequency ranges where no free wave propagation is allowed in the solid medium [17]. Such frequency bands arise typically due to the mechanisms of (i) Bragg scattering [18], in which case the frequency range is associated with the periodicity of the medium, and (ii) local resonance [19], where Fano-like interference is capable of opening band gaps in the sub-wavelength scale [20].…”

A foldable underwater acoustic meta-structure with broadband sound absorption at low frequency

“…Meanwhile, the underwater good sound absorption of meta-structures has been proved by experiments (4-20 kHz) 18) and applications. 19) Inspired by airborne meta-structures, to overcome the high bulk modulus and low viscosity of water, underwater metastructures based on local resonance units have been used to absorb acoustic waves; 17,[20][21][22][23][24][25][26][27][28] most of these structures have performed poorly in terms of thickness and broadband sound absorption at low frequencies. Clearly, the difficulty of developing underwater meta-structures is related to the absorption of low-frequency broadband acoustic waves.…”