This paper presents a type of single-phase double “I” hole phononic crystal (DIH-PnC) structure, which is formed by vertically intersecting double “I” holes. By using the finite element method, the complex energy band curve, special point mode shapes, and different delay lines were calculated. Numerical results showed that DIH-PnC yielded ultra-wide band gaps with strong attenuation. The formation mechanism is attributed to the Bragg-coupled local resonance mechanism. The effects of the pore width in DIH-PnC on the band gaps were further explored numerically. Significantly, as the pore width variable, the position of the local resonance natural frequency could be modulated, and this enabled the coupling between the local resonance and the Bragg mechanism. Subsequently, we introduced this DIH-PnC into the thin-film piezoelectric-on-silicon (TPOS) resonator. The results illustrated that the anchor loss quality factor (Qanc) of the DIH-PnC resonator was 20,425.1% higher than that of the conventional resonator and 3762.3% higher than the Qanc of the cross-like holey PnC resonator. In addition, the effect of periodic array numbers on Qanc was researched. When the Qanc reached 1.12 × 106, the number of the period array in DIH-PnC only needed to be 1/6 compared with cross-like holey PnC. Adopting the PnC based on the coupling Bragg and local resonance band gaps had a good effect on improving the Qanc of the resonator.

In this paper, a novel H-shaped radial phononic crystal (H-RPC) structure is proposed to suppress the anchor loss of a Lamb wave resonator (LWR), which has an ultra-high frequency (UHF) and ultra-wideband gap characteristics. Compared to previous studies on phononic crystal (PC) structures aimed at suppressing anchor loss, the radial phononic crystal (RPC) structure is more suitable for suppressing the anchor loss of the LWR. By using the finite element method, through the research and analysis of the complex energy band and frequency response, it is found that the elastic wave can generate an ultra-wideband gap with a relative bandwidth of up to 80.2% in the UHF range when propagating in the H-RPC structure. Furthermore, the influence of geometric parameters on the ultra-wideband gap is analyzed. Then, the H-RPC structure is introduced into the LWR. Through the analysis of the resonant frequency, it is found that the LWR formed by the H-RPC structure can effectively reduce the vibration energy radiated by the anchor point. The anchor quality factor was increased by 505,560.4% compared with the conventional LWR. In addition, the analysis of the LWR under load shows that the LWR with the H-RPC structure can increase the load quality factor by 249.9% and reduce the insertion loss by 93.1%, while the electromechanical coupling coefficient is less affected.

A new type of stepwise radial metamaterial (SRM) with ultralow-frequency and broadband characteristics is proposed in this study. In contrast to the traditional radial metamaterial (TRM), the proposed structure is periodically arranged in a stepwise shape along the radial direction. The propagation characteristics of Lamb waves in the SRM were investigated using the finite element method. For the numerical analysis, the degeneracy between the bands of the SRM was separated, resulting in the opening of the bandgaps in the ultralow-frequency range. The total bandwidth was 75 times that of the TRM, and the wave attenuation ability was increased by more than 70%. The introduction of a stepwise array in the SRM opened up the local resonance and Bragg scattering bandgaps, and as a result, the SRM exhibited ultralow-frequency broadband characteristics. Furthermore, the influences of the structural parameters of the SRM on the bandgap characteristics were discussed. With the increase in the stepped angle, the coupling relationship between the Lamb wave mode and the local resonance was enhanced, which caused the band structure to shift to a lower frequency. In addition, the hole rotation and shape played important roles in the bandgap tuning. Finally, the experimental sample was processed based on the model, and the vibration propagation characteristics were tested to prove its ultralow-frequency broadband characteristics. The proposed shielding approach could provide a better alternative in the field of ultralow-frequency noise reduction and vibration reduction.

This paper proposes an I-shaped radial elastic metamaterial with ultra-low-frequency broadband characteristics and studies the propagation characteristics of elastic waves in their quasi-static state. Through the calculation of the dispersion relationship, the frequency response function, and the eigenmode displacement field, it is found that the ultra-low-frequency wide band gap can be generated in the quasi-static metamaterial. The wide band gap is mainly caused by modal transitions. The equivalent mass–spring model reveals the modal changes of the I-shaped radial elastic metamaterial under the surface constraints. Furthermore, by studying the directional vibration displacement field of the finite period structure, it is demonstrated that the mechanism of the ultra-low-frequency broadband (0<Reduced frequency(Ω)<0.20) is the local resonance mechanism. Subsequently, the influence of the geometric and the material parameters on the location and width of the band gap is explored numerically. Finally, based on the model, through the hammer modal experiment, it is proven that the quasi-static structure yields an ultra-low-frequency stop band of 0.1–1012 Hz. The research conclusions can be applied to mechanical engineering fields such as ultra-low-frequency vibration reduction.