Abstract
Nonlinear phononic crystals are receiving increasingly greater attention in the field of sound absorption and vibration reduction. In this paper, we use the perturbation method to investigate elastic wave propagation in one-dimensional discrete local resonance nonlinear phononic crystals. The nonlinear force on the inner resonator is expressed in the form of a linear part plus a cubic nonlinear fluctuation. By combining Bloch wave theory and the perturbation method, the nonlinear dispersion relation is obtained by a first-order approximate analytical solution. The results show that the band’s cut-off frequency is not only affected by the degree of nonlinearity but is closely related to the wave amplitude. In addition, the finite element method is used for comparison and verification. Finally, an application example of a wave filter is provided based on the nonlinear characteristics.
Highlights
In 2000, Liu [1] put forward the concept of mass-in-mass structure phononic crystals, which are called local resonance phononic crystals
Thereby, we have proposed a one-dimensional nonlinear phononic crystal with a band gap characteristic related to the vibration amplitude
We focus on the dynamic behavior of a one-dimensional local resonance phononic crystal system containing cubic nonlinear inner springs
Summary
In 2000, Liu [1] put forward the concept of mass-in-mass structure phononic crystals, which are called local resonance phononic crystals. In a linear periodic structure, the principle of local resonance acoustic metamaterials/phononic crystals is to confine the elastic waves of relevant frequencies to an inner spring-mass system. Local resonance phononic crystals can produce band gaps at larger wavelengths with smaller lattice sizes As a result, they have important application prospects in low-frequency sound insulation and vibration reduction. By studying the nonlinearity of the periodic structure, we can reveal more peculiar phenomenon compared with the linear case, which includes nonlinear resonance, bifurcation, mixing, or self-trapping Based on these topics, nonlinear devices have potential new applications, such as frequency conversion and energy harvesting. A perturbation analysis method is applied to the discrete nonlinear local resonant periodic structure to predict the amplitude-dependent dispersion relation. An application example based on the proposed nonlinear phononic crystal is provided
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