Metamaterial plate with compliant quasi-zero-stiffness resonators for ultra-low-frequency band gap

Propagation of elastic waves in metamaterial plates with various lattices for low-frequency vibration attenuation

Auxetic materials and structures have been attracting attention due to their extraordinary mechanical properties that stand out due to their high capacity to absorb energy. Some types of auxetic tubular structures have been studied and designed in diverse engineering fields such as mechanical, aerospace and medical. This manuscript cites more than a hundred papers containing the definitions, designs, structural analyses and optimization, mechanical properties, and specific applications of tubular design of auxetic structures. It can be noted from the present paper that additive manufacturing has been one of the most common manufacturing techniques used in many cases to manufacture tubular structures, and numerical analysis was essential to analyzing the behavior of the structures. The purpose of this paper is to assist researchers and engineers in using the methodology step by step to develop and apply auxetic tubular structures. 

Tubular auxetic structures: A review

Quasi-zero-stiffness metamaterial pipe for low-frequency wave attenuation

Wave propagation characterization of 2D composite chiral lattice structures with circular plate inclusions

In this work, an innovative two-dimensional (2D) hybrid auxetic elastic metamaterial (MODEL I) with reentrant triangular and chiral structures is proposed to open the broaden bandgap for vibration attenuation. Furthermore, the hybrid reentrant-chiral lattice with embedded resonators (MODEL II) shows multiple bandgaps at ultra-low frequency. Based on theoretical lumped mass-in-mass method and finite element method , the bandgap and longitudinal elastic wave attenuation are characterized. There is no complete bandgap in classical reentrant triangular lattice (MODEL 0), while the complete bandgaps width for MODEL I and II account for one forth of the concerned frequency range (0–4500 Hz). What more, the lower boundary of the first bandgap for MODEL II is 56% lower than that of MODEL I. The bandgap formation mechanisms are investigated by analyzing the mode shapes on the dispersion curves , and the frequency-dependent energy flow are studied through the iso-frequency contours, phase and group velocities . Finally, the longitudinal elastic wave attenuation of finite-size lattice of MODEL II illustrates ultra-wide vibration attenuation frequency range in the directional bandgaps. This research provides important clues and theoretical guidance for the design of vibration isolators , beam, plates and other renewed devices.

Vibration characteristics of innovative reentrant-chiral elastic metamaterials

In this paper, the quasi-one-dimensional tetra-chiral metamaterial is proposed for low-frequency broadband vibration attenuation, inspired by the 3D chiral compression-torsion coupling metamaterials. Different from the traditional metamaterials utilizing translational local resonators to induce reaction force to prevent vibration transmission, this paper can realize rotation and translation on a resonator by introducing chiral structure, which is more beneficial for vibration energy dissipation. The band gap mechanism and vibration attenuation characteristics of the proposed metamaterial are studied based on the discrete mass-spring model. The dependences of the band gap characteristics on the parameters are studied in detail as the bigger the chiral angle, the bigger the mass ratio, the smaller the stiffness ratio, the smaller the dimensionless rotational inertia, the wider the band gap. The analytical boundary equations for band gaps are derived to provide guidance for desired band gap design and multiple and ultra-wide band gaps can be obtained by tuning the structural parameters. Through the investigation of eigenstate modes, the mode reversals at dispersion curves intersection and veering are observed, and the interchange mechanism for the boundary equations of dispersion curves is unveiled. The vibration transmission in finite unit cells validates the frequency ranges with high vibration attenuation predicted by band structure. The movement energy analysis and wave packet propagation in finite unit cells also demonstrate the vibration attenuation characteristics of the proposed metamaterial. This study can provide new ideas and theoretical guidance for metamaterial design.

Band gap mechanism and vibration attenuation characteristics of the quasi-one-dimensional tetra-chiral metamaterial

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Vibration characteristics of innovative reentrant-chiral elastic metamaterials

Band gap mechanism and vibration attenuation characteristics of the quasi-one-dimensional tetra-chiral metamaterial