Tunable solid acoustic metamaterial with negative elastic modulus

International audienceWe report in this letter on a tunable solid acoustic metamaterial with negative elastic modulus by means of piezoelectric composite. The theoretical formulae for one-dimensional layer-stacked metamaterial embedding a piezoelectric material by means of external shunted inductors are presented. The acoustic band structure of the composite is calculated by the transfer matrix method. Results show that a band gap can be opened and tuned by the resonant behavior of the LC circuit. It is found further by the formulae that piezoelectric material with large piezoelectric constant and small elastic modulus will be beneficial for opening a wide band gap. The effective elastic constant of the system is also calculated by the unit-cell-boundary-averaging method. Result shows that the system behaves as an effective medium with a negative elastic modulus. This property is quite different from the typical solid metamaterial achieved by dispersing heavy inclusions coated with a soft layer into a matrix for which only the negative mass density can be obtained

Opening a large full phononic band gap in thin elastic plate with resonant units

International audienceIn this paper, the mechanism for opening a locally resonant band gap in a thin elastic plate is investigated. Two previously suggested structures, which are constructed by periodically drilling holes on elastic plate and then filling them with the rubber-coated masses, or just by periodically stubbing the rubber rods with mass cap on the plate, are revisited. We find that, because of the partial band gaps for in-plane and out-of-plane plate modes cannot be appropriately overlapped, the full band gaps in both of the structures are generally narrow. The reason for this phenomenon is based on the selective coupling between the different resonant patterns of the resonant units and the in-plane and out-of-plane plate modes. Based on the understanding, a new structure with the three-layered spherical resonant units is proposed. Numerical results show that, making use of such kind of resonant units, a large sub-wavelength full band gap can be opened

Computation of Plate Wave Dispersion Diagrams and Surface Wave Velocities Without Explicit Boundary Conditions

Abstract-We discuss the computation of the band structure of plate waves using the plane wave expansion (PWE) method. This method is generally used to formulate eigenvalue problems to compute dispersion diagrams for solid-solid phononic crystals. We show how the free surface boundary condition can be included implicitly in the form of the PWE solution, thus leading to an efficient eigenvalue problem. This generic method for wave dispersion is non-iterative and does not require an initial guess for the solution. Furthermore, surface acoustic wave velocities can be estimated from the slowest wave for large wave vectors. Examples for a single plate and a multilayer plate are given, and extension to piezoelectric materials is discussed

General analytical approach for sound transmission loss analysis through a thick metamaterial plate

International audienceWe report theoretically and numerically on the sound transmission loss performance through a thick plate-type acoustic metamaterial made of spring-mass resonators attached to the surface of a homogeneous elastic plate. Two general analytical approaches based on plane wave expansion were developed to calculate both the sound transmission loss through the metamaterial plate (thick and thin) and its band structure. The first one can be applied to thick plate systems to study the sound transmission for any normal or oblique incident sound pressure. The second approach gives the metamaterial dispersion behavior to describe the vibrational motions of the plate, which helps to understand the physics behind sound radiation through air by the structure. Computed results show that high sound transmission loss up to 72 dB at 2 kHz is reached with a thick metamaterial plate while only 23 dB can be obtained for a simple homogeneous plate with the same thickness. Such plate-type acoustic metamaterial can be a very effective solution for high performance sound insulation and structural vibration shielding in the very low-frequency range

Acoustic superfocusing by solid phononic crystals

International audienceWe propose a solid phononic crystal lens capable of acoustic superfocusing beyond the diffraction limit. The unit cell of the crystal is formed by four rigid cylinders in a hosting material with a cavity arranged in the center. Theoretical studies reveal that the solid lens produces both negative refraction to focus propagating waves and surface states to amplify evanescent waves. Numerical analyses of the superfocusing effect of the considered solid phononic lens are presented with a separated source excitation to the lens. In this case, acoustic superfocusing beyond the diffraction limit is evidenced. Compared to the fluid phononic lenses, the solid lens is more suitable for ultrasonic imaging applications

Subwavelength acoustic focusing by surface-wave-resonance enhanced transmission in doubly negative acoustic metamaterials

International audienceWe present analytical and numerical analyses of a yet unseen lensing paradigm that is based on a solid metamaterial slab in which the wave excitation source is attached. We propose and demonstrate sub-diffraction-limited acoustic focusing induced by surface resonant states in doubly negative metamaterials. The enhancement of evanescent waves across the metamaterial slab produced by their resonant coupling to surface waves is evidenced and quantitatively determined. The effect of metamaterial parameters on surface states, transmission, and wavenumber bandwidth is clearly identified. Based on this concept consisting of a wave source attached on the metamaterial, a high resolution of lambda/28.4 is obtained with the optimum effective physical parameters, opening then an exciting way to design acoustic metamaterials for ultrasonic focused imaging

Hybrid phononic crystal plates for lowering and widening acoustic band gaps

International audienceWe propose hybrid phononic-crystal plates which are composed of periodic stepped pillars and periodic holes to lower and widen acoustic band gaps. The acoustic waves scattered simultaneously by the pillars and holes in a relevant frequency range can generate low and wide acoustic forbidden bands. We introduce an alternative double-sided arrangement of the periodic stepped pillars for an enlarged pillars' head diameter in the hybrid structure and optimize the hole diameter to further lower and widen the acoustic band gaps. The lowering and widening effects are simultaneously achieved by reducing the frequencies of locally resonant pillar modes and prohibiting suitable frequency bands of propagating plate modes