This letter presents a thin plate structure with an acoustic black hole (ABH) sub-unit to reorient the flexural wave. Different from the previously reported flexural wave metasurface, ABH sub-units are introduced into thin plates in this work, which can control the group velocity of flexural waves and realize their efficient transmission. According to generalized Snell's law, the mechanism of phase shift of transmitted waves across subwavelength sub-units is theoretically revealed. An analysis of the ABH sub-units is established by the finite element method. The deflection and focusing effect of flexural waves are demonstrated. Furthermore, adjusting the black hole section can quickly obtain the transmission phase response in the range of 2π, and it can accurately predict the phase shift and amplitude of the transmitted wave. The results show that the ABH beam-plate structure can effectively control the propagation direction of flexural waves, which provides a modern design idea and method for the manipulation and energy harvesting of the flexural wave.

Anchor loss is usually the most significant energy loss factor in Micro-Electro-Mechanical Systems (MEMS) resonators, which seriously hinders the application of MEMS resonators in wireless communication. This paper proposes a cross-section connection phononic crystal (SCC-PnC), which can be used for MEMS resonators of various overtone modes. First, using the finite element method to study the frequency characteristics and delay line of the SCC-PnC band, the SCC-PnC has an ultra-wide bandgap of 56.6–269.6 MHz. Next, the effects of the height h and the position h₁ of the structural parameters of the small cross-connected plate on the band gap are studied, and it is found that h is more sensitive to the width of the band gap. Further, the SCC-PnC was implanted into the piezoelectric MEMS resonator, and the admittance and insertion loss curves were obtained. The results show that when the arrangement of 4 × 7 SCC-PnC plates is adopted, the anchor quality factors of the third-order overtone, fifth-order overtone, and seventh-order overtone MEMS resonators are increased by 1656 times, 2027 times, and 16 times, respectively.

The time-modulated active medium with linear independent frequency conversion method has been demonstrated to enable wave orientation and reconstruction. However, due to the symmetric scattering field, this technique requires intricate microcircuit designs. To overcome this limitation, this paper proposes a tunable piezoelectric metasurface based on acoustic black holes (ABHs) to redirect flexural wave reflections. The system can convert an incident flexural wave into a reflected wave of any direction and frequency. This is accomplished through the linear time modulation of the sensing signal, which breaks the constraints of Snell’s law inherent in traditional designs and is insensitive to the incident amplitude. The coupling of the ABH damping system with a linear independent frequency conversion mechanism allows for the conversion of an incident flexural wave into a reflected wave in any direction and frequency while also eliminating the influence of second harmonic reflection on the wave field and simplifying the time modulation circuit. In addition, this paper demonstrates arbitrary angle reflection, focusing, beam splitting, and frequency conversion of the incident wave. By improving the flexibility of elastic wave manipulation, this paper introduces a new approach for active control of elastic waves and provides a design method that can be employed in a variety of applications ranging from vibration protection of engineering structures to vibration sensing and evaluation.

In this paper, a radial gradient seismic metamaterial (RGSM) is proposed. The structural unit cell is composed of an external square soil embedded with a triangular-cross-sectioned steel ring, which is filled at different angles of multiple steel rings to form a supercell. The dispersion curve and attenuation spectrum of the unit cell are calculated by the finite element method, and the opening mechanism of the band gap is explained by analyzing the modes at the band gap boundary. The influence of geometric parameters and material parameters on the band gap is further studied, and the optimized supercell radial gradient seismic metamaterial (OS-RGSM) structure is designed through structure and parameter optimization. The ultra-low broadband excellent band gap in the range of 2.35–20 Hz for seismic Lamb waves is realized, and its three-dimensional frequency response and displacement field diagram are calculated. In addition, the attenuation characteristics of the optimized supercell seismic metamaterial on the seismic surface wave are calculated and analyzed. It is found that the attenuation can reach more than 50% in the ultra-low frequency range of 3.5–9 Hz. The seismic wave barrier is verified by the vibration transmission characteristics of RGSM under finite period and dynamic time history analysis. The results show that RGSM can effectively shield from seismic Lamb waves in the ultra-wideband with the starting frequency of 2.35 Hz and can also effectively attenuate the seismic surface wave in semi-infinite space.

In this paper, a novel single-phase double-leaf multi-stage acoustic black hole (SDM-ABH) is proposed. Compared with the traditional double-leaf ABH metamaterials, the unit cell consists of multiple sub-ABH structures arranged in a gradient periodically along the length direction. The energy band structure of the SDM-ABH metamaterial is calculated by the finite element method, and it is found that its weight decreases with the increase in the number of stages, but the bandgap ratio and attenuation both increase. By analysing the vibration modes at special points and the vibration displacement response of finite construction, it is revealed that strong attenuation at a low-frequency broadband is caused by the increase in the number of sub-ABHs that appear to have ABH effects due to the increase in the number of stages. In addition, the effect of structural parameters on the bandgap is investigated, and it is found that SDM-ABH metamaterials can be modulated at low frequencies by changing the truncation thickness and the power exponent of the sub-acoustic black hole, in which the increase in the truncation thickness t leads to the gradual weakening of the ABH effect of the sub-ABH until it disappears. The strong low-frequency attenuation properties of SDM-ABH metamaterials provide a method for a lightweight vibration damping design of metamaterials.