A Review of Acoustic Metamaterials and Phononic Crystals

“Pendry [74] proposed that metamaterials can be designed by using metamaterials so that the evanescent wave is amplified by the superlens propagation .”

“The film-type acoustic metamaterial unit is a film that is tensioned and fixed on the peritoneal ring, and then a rigid mass unit is fixed on the circular film [41,42].”

“[94] realized the phenomenon of optical extraordinary transmission through a subwavelength hole array.”

“[32] used the "core-shell structur " for the first time to make an acoustic metamaterial.”

“The film-type acoustic metamaterial unit is a film that is tensioned and fixed on the peritoneal ring, and then a rigid mass unit is fixed on the circular film [41,42].”

“In the field of electromagnetics, Leonhardt [84] and Pendry [85] et al.”

“In the calculation of solid [14,19,20], liquidliquid [21,23,24], and solid-gas [25–28] systems, great success was achieved with the band gaps of phononic crystals and acoustic metamaterials.”

“[38] firstly proposed an acoustic metamaterial composed of a periodic one-dimensional Helmholtz resonator cavity with acoustic inductance and capacitance (see Figure 8).”

“[13] buried spherical objects in a matrix material in a periodic lattice structure arrangement.”

“There are three main ways to control vibration and noise [2].”

“The structure was found to have an acoustic band gap in the frequency range of 200–300 Hz [45].”

“(a) Film structure diagram with a semi-circular metal sheet; (b) Broadband sound absorption diagram; (c–e) Sound absorption spectra at 172 Hz, 340 Hz, 813 Hz and displacement relationship of the film system; (f) Graph of sound absorption and displacement [80].”

“[86] determined the existence of a two-dimensional equation solution of transform acoustics with anisotropic mass in cylindrical coordinates, and theoretically discussed the possibility of acoustic stealth (see Figure 26).”

“[87] used the expansion of the Bessel function series in spherical coordinates to solve the scattering problem.”

“In the calculation of solid [14,19,20], liquidliquid [21,23,24], and solid-gas [25–28] systems, great success was achieved with the band gaps of phononic crystals and acoustic metamaterials.”

“Traditional sound insulation materials generally use rigid plates, in order to isolate low-frequency sound waves of hundreds of Hertz [4].”

“[67] studied a phononic focusing phenomenon in the passband over a complete band gap in a 3D hononic crystal and found that the wave propagation depends largely on the frequency and the direction of incidence, an due to the anisotropy of the pr pagation, very large negative refraction occurs.”

“Later, it was found that the structure composed of four layers of thin film materials with different sound insulation frequency bands and different mass masses can achieve 50–1000 Hz wide-band sound insulation, and its sound insulation is as high as 40 dB [46] In 2019, He et al.”

“[97] designed a Mi resonanc system with a curly sp ce structure, as hown i Figure 30a.”

“[88] verified the existence of a 3D acoustic wave stealth solution in fluids and the invariance of acoustic wave coordinate transformation, which established a theoretical basis for the proposed 3D stealth cloak.”

“[90] used two-dimensional composite cylindrical structure to achieve two-dimensional acoustic stealth.”

“Because the plane wave expansion method cannot solve the problem of solid scatterers in a liquid matrix, scholars have proposed a multiple scattering method based on the Korringa-Kohn-Rostoker (KKR) theory in the calculation of the electronic band structure [31].”

“[95] found that the sound wave’s extraordinary transmission behavior through a one-dimensional grating achieves a sound transmittance close to 1.”

“An analog optical metamaterial is designed using a structure much smaller than the sub-wavelength size to obtain an acoustic metamaterial [7].”

“[89] used homogeneous and isotropic materials to achieve t o-di ensional acoustic stealth of concentric alternating layered structure.”

“[76] that can amplify evanescent waves.”

“[57] proposed a hybrid acoustic metamaterial composed of micro-perforated plates (MPP) and curled Fabry-Perot (FP) channels (see Figures 16 and 17), and found that the material works at a frequency greater than 30 times the total thickness.”

“[59] studied bubble resonators, which are single-layer gas inclusions in soft solids.”

“There are some limitations in traditional vibration reduction techniques [3], such as vibration insulation, dynamic vibration absorption and damping vibration absorption.”

“The finite-difference time-domain method [29,30] discretizes partial differential equations by discretizing time and space, transforms the partial differential equations into differential equations, and then uses numerical calculation methods to solve all vibrations at three points during wave propagation.”

“Peng, H.; Pai, P. Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression.”

“(a) Image of the cloak machined from an aluminum block; (b) Enlarged view of one segment, highlighted in (a) [91].”

“The sound absorption mechanism of the curly space structure is to allow sound waves to propagate in the coiled space, increasing the propagation time and reducing the effective phase velocity [51,52].”

“(a–c) Evolution of a floating double resonator to a thin film structure; (d) Negative mass density system; (e) Amplified evanescent wave [77].”

“Wave reflections as sm ll as zero ar achi ved [61,62].”

“[34] proposed two types of mass spring structures with local resonators and performed equivalent simulations, and found that they have negative effective elastic modulus and selectiv filtering.”

“[70] used one-dimensional long-period tubes to periodically arrange thin films and open holes on the side to prepare onedimensional double-negative acoustic composites.”

“In the calculation of solid [14,19,20], liquidliquid [21,23,24], and solid-gas [25–28] systems, great success was achieved with the band gaps of phononic crystals and acoustic metamaterials.”

“, Dong et al. [98] proposed an acoustic super lens based on the idea of far-field It was found that the far-field super-resolution of λ / 6 can be achieved by using a multiple signal classification algorithm combined with a supersonic lens.”

“The transfer matrix method [17,18] is a method of converting the wave equation into the form of a transfer matrix equation and solving the eigenvalues.”

“[96] sculpted periodical air grooves on both sides of a copper plate, and also achieved extraordinary sound transmission.”

“[71] designed an acoustic metamaterial with seven flute-like binary molecular clusters.”

“The unit cell of the metamaterial plate: (a) front view, (b) perspective view [48]”

“(a) Fabricated 3D microstructure sample; (b) Photograph of a 3D superlens containing 8 × 9 × 3 microstructures [99].”

“[81] designed an ultra-thin sub-wavelength absorber based on a regular coupling array that can achieve low-frequency absorption.”

“The plane wave expansion method [14,19–22] is the earliest and most widely used method in the theoretical analysis of phononic crystals and acoustic metamaterials.”

“The transfer matrix method [17,18] is a method of converting the wave equation into the form of a transfer matrix equation and solving the eigenvalues.”

“[83] compared the porous acoustic metamaterial with an inverted wedge shape on the plane interface with a uniform melamine layer and a classic wedge-shaped sound absorption material of the same quality.”

“[44] first proposed a membrane structure with additional masses, the so-called membrane with additional weights (MAW), and found that this structure can improve sound insulation in the low frequency range through sound insulation experiments under normal incidence effects.”

“In 2019, Wu [82] proposed an acoustic metamaterial for low-frequency sound absorption consisting of three nested square-opened tubes and opposite opening directions (see Figure 25).”

“Fi tic view of an underwater absorptive metasurface with a finite-thickness steel l t f llo ed by air; (b) A physical realization of the proposed metasurface for perfect absorption [100].”

“[68] proposed the metamaterial properties of a two-phase unit cell traditionally considered to be a non-local resonance type, and demonstrated a hexagonal unit cell composed of two materials.”

“[53] designed a curly space structure composed of a Jerusalem cross groove air matrix periodically arranged in a square lattice.”

“[69] proved through experiments that the simple two-di ensional phononic crystals co posed of aluminum matrix and circular flexible i clusions with square patt rns have negative refractive ch racteristics i the shear mode and longitudinal mode.”

“[48,49] can also suppress low frequency noise (see Figure 12).”

“(a) The unit cell ith spindle-shaped inclusion; (b) Schematic view of proposed PC [60].”

“Schematic diagram of proposed structures: (a) The unit cell of an S-shape slot phononic crystal(PC); (b) Schematic view of the cross-section of the two-dimensional PC [54].”

“Similarly, by changing the internal structure and defects of the phononic crystal, the propagation path of the elastic wave can be artificially adjusted, thereby achieving the purpose of vibration isolation and noise reduction [15].”

“(a) avenumber-frequency representation of the signals measured under the grating for an excitation frequency b longing to the ap; (b) Amplitude versus wav number at fr q ency f = 396 kHz [75].”

“[47] designed a new type of thin film acoustic metamaterial by embedding a piezoelectric mass connected to an external circuit into a tensioned elastic membrane and fixed on a metal frame (see Figure 11).”

“[73] reported anomalous Doppler effects found in two commonly used wind instruments based on flute-type acoustic metamaterials.”