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 are evaluated by using the perturbation method to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials. A quantitative study of wave amplitude is carried out to determine the maximum allowable wave amplitude for the whole structures under the assumption of small parameters. 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 and group velocity of unit cell are related to wave amplitude. Furthermore, the dual-wave vector is observed in the nonlinear systems. Numerical simulations validate the dispersion analytical results. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials.
Highlights
Lightweight periodic lattices [1] have been developed and used in disparate engineering applications for many decades [2] owing to their distinguished properties such as high specific strength, high stiffness, and multi-functional potential [3, 4]
To further illustrate the wave propagation in nonlinear 2D acoustic metamaterials (AM) as controlled by the wave amplitude, we study the group velocities of the considered nonlinear system at several specific normalized frequencies, on a set of values of wave amplitude A1
We consider a type of nonlinear two-dimensional acoustic metamaterials
Summary
Lightweight periodic lattices [1] have been developed and used in disparate engineering applications for many decades [2] owing to their distinguished properties such as high specific strength, high stiffness, and multi-functional potential [3, 4]. LR bandgaps can happen at wavelengths which are much larger than the lattice size, yielding low-frequency vibration/noise attenuation and wave filtering [14, 15] In such linear configurations, the resulting attenuation bandwidth and wave propagation in AM are limited by the parameters of material and structure, i.e. masses of local resonators [16], which is typically aimed to be minimized in most applications that require lightweight and the wave propagation of linear systems cannot be tuned in active or passive ways. Khajehtourian and Hussein [35] studied the approximate dispersion characteristics of a one-dimensional nonlinear locally resonant metamaterial rod based on the transfer matrix method. The case of a linear spring mass resonator is considered, further investigation is dedicated to the case of a nonlinear spring mass resonator
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