Breaking the mass law for broadband sound insulation through strongly nonlinear interactions

Sound transmission through panels is governed by the well-known mass law in the mid-frequency range. This paper reveals a possibility of breaking this density-dominant law through strongly nonlinear interaction, while broadening the bandwidth for effective sound insulation. For this purpose, a basic model is established, and corresponding exact analytical methods for bifurcation and stability analyses are proposed. Influences of four typical types of nonlinear interactions on the wave insulation are analytically and numerically investigated. We find that, by introducing strongly nonlinear interactions at appropriate locations, the nonlinear model can not only break the barrier imposed by the mass law, but also entails broadband sound insulation by 2-3 times relative to the optimal linear model. Meanwhile, the sound insulation valley due to the coincident effects can also be eliminated. With bifurcation and effective mass, we clarify that the enhanced wave insulation of the strongly nonlinear models arises from the broader band of super mass induced by strongly nonlinear local resonances, which depends on the bifurcation of periodic solutions. The proposed models and the findings provide a solid basis and new possibilities for wave insulation in complex nonlinear structures and nonlinear acoustic metamaterials.