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A spatially periodic structure of heterogeneous elastic rods that periodically oscillate along their axes is proposed as a time-modulated phononic crystal. Each rod is a bi-material cylinder, consisting of periodically distributed slices with significantly different elastic properties. The rods are imbedded in an elastic matrix. Using a plane wave expansion, it is shown that the dispersion equation for sound waves is obtained from the solutions of a quadratic eigenvalue problem over the eigenfrequency ω. The coefficients of the corresponding quadratic polynomial are represented by infinite matrices defined in the space spanned by the reciprocal lattice vectors, where elements depend on the velocity of translation motion of the rods and Bloch vector k. The calculated band structure exhibits both ω and k bandgaps. If a frequency gap overlaps with a momentum gap, a mixed gap is formed. Within a mixed gap, ω and k acquire imaginary parts. A method of analysis of the dispersion equation in complex ω−k space is proposed. As a result of the high elastic contrast between the materials in the bi-material rods, a substantial depth of modulation is achieved, leading to a large gap to midgap ratio for the frequency, momentum, and mixed bandgaps. 

Abstract Recently, additive manufacturing (AM) fabrications are commonly applied to produce acoustic metamaterials or phononic crystals (PnCs) as tools for complex geometrical designs. However, the material properties of those additive manufactured materials are less involved in the core portion of those PnC designs. Here we report a purely materials-driven, temperature switchable PnC in which Bragg gaps appear or vanish as the lattice medium toggles between liquid water and solid ice. Six widely used AM polymers were acoustically characterized, where stereolithography (SLA) resins showed an impedance mismatch of ≈50% with water but <1% with ice, whereas inkjet agar gel exhibited the opposite trend. A 10 × 10 SLA resin PnC therefore displayed >20 dB on/off contrast at 145 kHz and around 300 kHz when cycled across 0 °C, confirmed experimentally and with plane wave and simulation models. Unlike previous thermally tuned PnCs that depend on volumetric swelling or liquid metal infiltration, the present approach preserves geometry, requires no external actuators and operates with sub 1 °C stability. This simple, robust strategy lays the foundation for band pass filters, steerable lenses and non-reciprocal acoustic circuits that can be frozen or thawed on demand. 

We demonstrate analytically, numerically, and experimentally that a 2D supercrystal (SC)—an elastic structure of solid rods with two distinct spatial periods embedded in a viscous fluid—exhibits very high acoustic absorption. Smaller diameter rods arranged in a 2D lattice with a smaller period serve as an effective medium with high viscosity for a set of larger rods arranged in a lattice of much larger period. The enhancement of acoustic absorption is due to strong viscous friction within a narrow layer with high gradients of velocity formed around each scatterer. The SC as a whole is considered in the homogenization limit of frequencies where it behaves as a metafluid with an effective speed of sound and effective viscosity. Analytical results for the effective parameters are calculated for any Bravais lattices and arbitrary cross-sections of the rods. Experimental measurements of acoustic absorption in a supercrystal with hexagonal lattices for both types of rods are in a good agreement with analytical and numerical results. Published by the American Physical Society2024 

Propagation and attenuation of sound through a layered phononic crystal with viscous constituents is theoretically studied. The Navier–Stokes equation with appropriate boundary conditions is solved and the dispersion relation for sound is obtained for a periodic layered heterogeneous structure where at least one of the constituents is a viscous fluid. Simplified dispersion equations are obtained when the other component of the unit is either elastic solid, viscous fluid, or ideal fluid. The limit of low frequencies when periodic structure homogenizes and the frequencies close to the band edge when propagating Bloch wave becomes a standing wave are considered and enhanced viscous dissipation is calculated. Angular dependence of the attenuation coefficient is analyzed. It is shown that transition from dissipation in the bulk to dissipation in a narrow boundary layer occurs in the region of angles close to normal incidence. Enormously high dissipation is predicted for solid–fluid structure in the region of angles where transmission practically vanishes due to appearance of so-called “transmission zeros,” according to El Hassouani, El Boudouti, Djafari-Rouhani, and Aynaou [Phys. Rev. B 78, 174306 (2008)]. For the case when the unit cell contains a narrow layer of high viscosity fluid, the anomaly related to acoustic manifestation of Borrmann effect is explained. 

Defect mode induced energy trapping at the bandgap frequency of a phononic crystal has been widely explored. Unlike this extensively used mechanism, this work reports the use of nonreciprocity in the transmission band to trap energy inside a phononic crystal cavity. Passive nonreciprocity is due to natural viscosity of the background liquid (water) and asymmetry of aluminum scatterers. The level of nonresonant energy trapping was compared for three cavities with different symmetry. Enhancement of energy trapping at a frequency of 624 kHz was observed experimentally for the cavity where nonreciprocity suppresses acoustic radiation into environment. Experimental results were further investigated and confirmed using finite element numerical analysis. 

A reconfigurable phononic crystal (PnC) is proposed where elastic properties can be modulated by rotation of asymmetric solid scatterers immersed in water. The scatterers are metallic rods with a cross section of 120◦ circular sector. Orientation of each rod is independently controlled by an external electric motor that allows continuous variation of the local scattering parameters and dispersion of sound in the entire crystal. Due to asymmetry of the scatterers, the crystal band structure possesses highly anisotropic band gaps. Synchronous rotation of all the scatterers by a definite angle changes the regime of reflection to the regime of transmission and vice versa. The same mechanically tunable structure functions as a gradient index medium by incremental, angular reorientation of rods along both row and column, and, subsequently, can serve as a tunable acoustic lens, an acoustic beam splitter, and finally an acoustic beam steerer. 

The square lattice phononic crystal (PnC) has been used extensively to demonstrate metamaterial effects. Here, positive and negative refraction and reflection are observed simultaneously due to the presence of Umklapp scattering of sound at the surface of PnC and square-like equifrequency contours (EFCs). It is found that a shift in the EFC of the third transmission band away from the center of the Brillouin zone results in an effectively inverted EFC. The overlap of the EFC of the second and third band produce quasimomentum-matching conditions that lead to multi-refringence phenomena from a single incident beam without the introduction of defects into the lattice. Additionally, the coupling of a near-normal incident wave to a propagating almost perpendicular Bloch mode is shown to lead to strong right-angle redirection and collimation of the incident acoustic beam. Each effect is demonstrated both numerically and experimentally for scattering of ultrasound at a 10-period PnC slab in water environment. 

Abstract Rapid thermokinetics associated with laser-based additive manufacturing produces strong bulk crystallographic texture in the printed component. The present study identifies such a bulk texture effect on elastic anisotropy in laser powder bed fused Ti6Al4V by employing an effective bulk modulus elastography technique coupled with ultrasound shear wave velocity measurement at a frequency of 20 MHz inside the material. The combined technique identified significant attenuation of shear velocity from 3322 ± 20.12 to 3240 ± 21.01 m/s at 45 $$^\circ$$ ∘ and 90 $$^\circ$$ ∘ orientations of shear wave plane with respect to the build plane of printed block of Ti6Al4V. Correspondingly, the reduction in shear modulus from 48.46 ± 0.82 to 46.40 ± 0.88 GPa was obtained at these orientations. Such attenuation is rationalized based on the orientations of $$\alpha ^\prime$$ α ′ crystallographic variants within prior columnar $$\beta$$ β grains in additively manufactured Ti6Al4V.