Learning from failure: An analysis of a flawed nonlinear acoustic metamaterial design

Acoustic metamaterials (AMMs) are structured systems designed to exhibit specific, often exotic, effective material properties for acoustic wave motion. Most research on AMMs prioritize linear wave behavior, but a growing body of work has focused on nonlinear phenomena. While the primary approach to enhancing the nonlinear response of a system has been to place highly nonlinear inclusions in the system (such as bubbles, cracks, or buckling beams), an alternative approach is to control the linear material properties to enhance the relative strength of the nonlinearity. For example, one may reduce the shock formation distance of a system by reducing the effective mass density and wave speed even if the coefficient of nonlinearity is left unchanged. However, due to the nature of nonlinear waves, developing a practical design to accomplish this control can be challenging. We recently designed and built an experimental nonlinear AMM and found it to be fundamentally flawed. In this paper we discuss the thought process that led to the flawed design and present the lessons learned from an unsuccessful experiment.