Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials

Abstract

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system is evaluated by using the perturbation method and Floquet-Bloch theorem to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials (2D AM). A quantitative study of wave amplitude is carried out to reveal the limits of the proposed method. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations, group velocity, negative effective mass of unit-cell are related to wave amplitude. Furthermore, the dual wave vector, bifurcation of periodic solutions and chaotic band are observed in the nonlinear systems. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials.

Isotacticity in chiral phononic crystals for low-frequency bandgap

“…Inspired by the inertial amplification, more and more novel studies are proposed. For instance, an octahedron structure was built to isolate the special omnidirectional elastic waves [40]; incorporating inertial amplification structures in continuous beams to manipulate the transverse wave [41,42]; a 2D thin plates embedded the classical inertial amplifier structures was proposed to modulate lowfrequency and broad lamb waves [43,44]; the low-frequency vibration isolation of the corrugated-core 3 / 26 sandwich panels can be enhanced through embedding the inertial amplification system [45]; a levertype inertial amplification system can achieve the broadband isolation for the surface wave which is induced by the seismic [46,47]; the combination of the inertial amplification and local resonance can improve the extremely narrow effective attenuation of the classical local resonance bandgap [48] and release the dependence on lowering stiffness and increasing mass for low-frequency local resonance bandgap [49]； the multiple, broadband and highly attenuative bandgaps can be obtained by a system with inertial amplification, local resonance, and Bragg scattering affect simultaneously [50]. However, in the last two decades, the design strategies [42,45,[51][52][53][54][55] have been limited to the form of the classical inertial amplification sub-structure.…”

Low Frequency Band Gap and Wave Propagation Properties of a Novel Fractal Hybrid Metamaterial

“…Acoustic metamaterials are artificial subwavelength structures with unconventional dynamic properties and remarkable functions, including local resonance metamaterials, [1][2][3][4][5][6][7][8][9] Helmholtz resonance metamaterials, [3] and membrane-type metamaterials [4,5] and other materials that can effectively achieve low-frequency attenuation, aroused the interest of a large number of researchers. Liu et al [10] used a high-density mass wrapped in a soft rubber material to form a local resonance unit using a simple cubic lattice form and Zhao et al [11] studied the dispersion relationship and wave propagation properties in nonlinear resonator two-dimensional acoustic metamaterials, and the results can be used to tune wave propagation in nonlinear acoustic metamaterials, providing some ideas for nonlinear research. The propagation of elastic waves in origami-inspired lattices was also studied, and it was found that origami-inspired lattices provided a new method for designing vibration-isolating structures.…”