An acoustic crystal composed of tightly packed spherical particles can exhibit a wide spectrum of acoustic properties with responses varying from linear to highly nonlinear regimes. The physical attractiveness of these crystals resides in the controllability of such acoustic responses by simple manipulation of static pre-compression applied to the material.

Figure 1. The dynamic responses of a 1D phononic crystal were investigated under various nonlinearity conditions. A Granular Crystal composed of 20 stainless steel beads was assembled, guided by four vertical rails.
During the first part of this study, the focus was on the fundamental understanding of the energy transmission through these crystals in relation to the tunable acoustic nonlinearity. To control the degree of nonlinearity, three parameters were varied: pre-compression, striker velocity, and striker mass, maintaining an identical configuration of one-dimensional (1D) granular structures. The transmission gain in the stop/pass frequency band of the granular chain was evaluated as a function of the nonlinearity. The evolution of the frequency band structure was studied as the degree of nonlinearity was changed. The transmission gain of the granular structure shows a remarkable dependence on the structural linearity level.

To combine the frequency filtering response governed by the discrete particles with an amplitude filtering response, a system composed of a highly nonlinear granular chain and a deformable linear medium was assembled. Acoustic wave propagation can be efficiently manipulated and redirected with such added degree of freedom.

Figure 2. As a higher degree of system nonlinearity is imposed on the Granular Chain, it starts to form highly nonlinear solitary waves under a striker impact. This plot reports the smooth transition of wave configurations from linear (top grey curve) to highly nonlinear ones (bottom blue curve) as the system nonlinearity is increased due to the reduction of static pre-compression.
During the second part of the study, a hybrid linear/nonlinear metamaterial was built to allow high-energy transmission only in a selected range of external impact amplitude. In this hybrid structure, the nonlinear granular chain takes the role of transmitting energy when the system is excited with low amplitude impacts, whereas the linear structure performs as an effective shock mitigation medium under large-amplitude impacts, controlled by structural deflections. A strong correlation of transmission gain with external impact amplitudes was verified, showing an order-of-magnitude reduction of transmission gain for large-amplitude impacts compared to that of low-amplitude impacts. The wave propagation and impact mitigation were evaluated in the nonlinear acoustic metamaterial using a combined discrete particle model and a finite element method. Finally, it was verified that the numerical results are in excellent agreement with the experimental results.

The proposed metamaterials are fundamentally different from any other approach to vibration isolation. They do not use active modulation to suppress external vibration/impacts, but rely on passive insulation. Furthermore, they are stiff and load-bearing, present large recovery to external deformation, and do not develop permanent damage in the ranges of excitations studied. The proposed systems are designed to forbid the propagation of waves in selected frequency ranges (also called as band gaps or stop bands). Incident waves in these forbidden frequency ranges experience an exponential decay of their amplitudes (i.e., they are evanescent waves), and they are fully reflected. The presence of nonlinearity in the structure may allow the redirection of part of the incoming energy into allowed modes.

This work was done by Jinkyu Yang and Chiara Daraio of the California Institute of Technology for DARPA. DARPA-0011

This Brief includes a Technical Support Package (TSP).
Nonlinear Acoustic Metamaterials for Sound Attenuation Applications

(reference DARPA-0011) is currently available for download from the TSP library.

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