The confinement of elastic waves within a single defect in a phononic crystal slab is investigated both experimentally and theoretically. The structure is formed by a honeycomb lattice of air holes in a silicon plate with one hole missing in its center. The frequencies and polarizations of the localized modes in the first band gap are computed with a finite element method. A noncontact laser ultrasonic technique is used both to excite flexural Lamb waves and to monitor in situ the displacement field within the cavity. We report on the time evolution of confinement, which is distinct according to the symmetry of the eigenmode.

Aiming at the isolation of low-frequency sound, a kind of thin-film acoustic metamaterialis designed and obtained by implanting PZT into thin film. The finite element method (FEM) of the structure is built, and 1^st–14^th order eigenfrequencies and transmission loss between 20–1200 Hz are calculated. The reliability of finite element calculation is verified experimentally and the existence of adjustable sound insulation peak is monitored in the experiment. The results show that the acoustic metamaterial has good sound insulation performance in a frequency range between 20 and 1200 Hz, and has two sound insulation peaks of more than 50 dB, and there is a sound insulation peak which can be changed by adjusting the parameters of the outer circuit. By analyzing the first resonance mode of simple structure and building its equivalent model, the effect of structural parameter on the sound insulation performance of thin film acoustic metamaterial is investigated theoretically, and the rationality of the equivalent model is verified by the finite element calculation. The sound insulation mechanism of the structure is further illustrated by taking into consideration the eigenfrequencies, transmission loss curve and vibration mode diagrams at various frequencies. It is found that at the resonance frequency, the flapping motion of the film will cause the sound wave in the subsequent propagation to cancell the interference, therefore realizing the attenuation of the sound wave. Based on Fano resonance theory, the reasons for the different characteristics of transmission loss curves at different resonance points are investigated. The PZT and outer circuit can form a LC oscillator. At the resonant frequency of the oscillator, the vibration of the piezoelectric material can absorb the energy of sound wave to cause a sound insolation peak. The resonant frequency of the circuit can be adjusted by changing the parameters of the outer circuit, thereby realizing the adjustability of the sound insulation performance. The influence of eccentricity of piezoelectric mass block on sound insulation performance of material is explored, proving that the sound insulation performance can be further optimized by improving structure. And through the finite element calculation, it is proved that the sound insulation performance of material is adjustable by changing the parameters of the outer circuit. The results provide a theoretical reference for designing the thin film acoustic metamaterials.

Based on the finite element method (FEM), characteristics of the local resonance band gap and the Bragg scattering band gap of two periodically-distributed vibrator structures are studied. Conditions of original anti-resonance generation are theoretically derived. The original anti-resonance effect leads to localization of vibration. Factors which influence original anti-resonance band gap are analyzed. The band gap width and the mass ratio between two vibrators are closely correlated to each other. Results show that the original anti-resonance band gap has few influencing factors. In the locally resonant structure, the Bragg scattering band gap is found. The mass density of the elastic medium and the elasticity modulus have an important impact on the Bragg band gap. The coexistence of the two mechanisms makes the band gap larger. The band gap covered 90% of the low frequencies below 2000 Hz. All in all, the research could provide references for studying the low-frequency and broad band gap of phononic crystal.

To solve the problem of low-frequency noise in the environment, a Helmholtz-type phononic crystal with adjustable cavity structure and labyrinth tubes was designed. The unique design of the labyrinth tube greatly increases the length of the tube, improving low-frequency sound insulation performance, and the design of adjustable cavity structure realizes active regulation of the band structure. The band gap structure and sound insulation characteristics were analyzed by finite element method (FEM) and electro-mechanical-acoustic analogy method. The result shows that, firstly, the structure can generate two complete band gaps in the low-frequency range of 0–500 Hz, and there is a low-frequency band gap with lower limit of 40 Hz. Meanwhile, the structure has excellent sound insulation performance in the range of 0–500 Hz. Secondly, multiple resonant band gaps can be connected by adjusting the structural layout of the cavity through the telescopic screw, so as to achieve the purpose of widening the band gap and active control of environmental noise. Finally, in the periodic arrangement design of the structure, reducing the spacing between cells can effectively increase the bandwidth of band gaps. This design broadens the design idea of phononic crystal and provides a new method to solve the problem of low-frequency noise control.

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