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Abstract The two circular structures with local resonance resonant hammers proposed in this paper have the comprehensive performance of small size, easy fabrication and low frequency vibration and sound damping. In the study, Bloch’s theorem is used to calculate the energy band curves of the two structures and to analyze the vibration forms of the structures at the edge of the band gap. At the same time, the integrated analysis means of phase constant surface, group velocity and phase velocity are innovatively used to explore the real propagation path of waves and provide experience for topology optimization. The position of resonant hammers, the mirror symmetry structure and the size of resonant hammers are adjusted to optimize the band gap for both structures. Finally, the vibration transmission characteristics of the finite period structure are calculated to verify the band gap and evaluate the vibration isolation performance. The results show that the new structure has low-frequency noise reduction performance, and the band gap frequency can be further reduced by topology optimization. This study presents an innovative approach for achieving low-frequency noise reduction, analysis of wave propagation paths and lightweight design. [ABSTRACT FROM AUTHOR]

In this paper, a new class of multi-ligament derived structures is proposed. Based on the finite element method and Bloch's theorem, the bandgap characteristics and transmission properties of different derived structures are comprehensively analyzed, and the bandgap opening and closing mechanism and the vibration and noise reduction capability of the structure are explained by stress cloud diagrams and vibration modes. Then, a better bandgap is obtained by structural optimization and active frequency modulation. Finally, the propagation characteristics of elastic waves in different derived structures are investigated separately. The results show that the multi-ligament derived structure has excellent bandgap performance and can obtain better vibration and noise reduction capability through bandgap adjustment and active strain modulation, which greatly improves its engineering practicality. The comprehensive analysis of wave propagation in this paper provides a theoretical basis and technical means for the improvement and design of metamaterials. [Display omitted] • Bloch's theorem for explaining the band gap of graded maze structure. • Applying active strain to probe the band gap tunability of a structure. • Evaluation of vibration attenuation by transfer function and stress cloud map. • Analysis by group and phase velocity, iso-frequency and wave propagation maps. • Probing the band gap opening mechanism by single cell vibration modal analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new graded maze metamaterial with a single phase is proposed. Based on the finite element method and Bloch's theorem, the bandgap characteristics of graded maze structures in different regions are analyzed, and the mechanism of bandgap opening and closing is explored by vibration patterns. Subsequently, the mechanism of elastic wave propagation within different structures is comprehensively analyzed from four perspectives, such as group velocity and phase velocity. And the damping performance is further verified by frequency response spectra. The results show that the new structure has excellent low-frequency bandgap and damping performance, the local resonance of the graded maze plays an important role in the expansion of the bandgap, and there is directionality and regionality of wave propagation within the structure. This paper provides a new idea for wave propagation control and analysis, and low frequency damping of single-phase materials. • Low frequency bandgap generation through area grading. •Verification of bandgap and noise reduction performance by transfer function. •Analysis by group and phase velocity, iso-frequency and wave propagation maps. •Probing the bandgap opening mechanism by single cell vibration modal analysis. •Evaluation of vibration attenuation capacity with frequency-specific stress clouds. [ABSTRACT FROM AUTHOR]