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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]

The chiral metamaterials have been well applied in engineering applications, but the chiral structure of a single material is difficult to achieve low-frequency sound insulation or vibration reduction. Therefore, a new chiral lattice structure is proposed in this paper. Based on the Bloch's theorem, finite element analysis is carried out, and the energy band structures of different types of structures are calculated. The principle of band gap generation of Model No.1 is emphatically analyzed. The effect of geometric parameters on the band gap is discussed. In addition, the propagation characteristics of elastic waves with a specific frequency in the structure are explored. Finally, according to the corresponding relationship between the finite element simulation of vibration transmission in finite period structures and the band gap frequency range, it is verified that the structure can effectively restrain the vibration transmission. The research results show that the structure has excellent broadband gap performance in the frequency range of 3000 Hz, and has a certain filtering effect on vibration transmission. [ABSTRACT FROM AUTHOR]