Acoustics of locally bilinear periodic metamaterials

Abstract

The scope of traditional metamaterials is expanded by analyzing bilinear discontinuities in an otherwise continuous medium. This amplitude independent nonlinearity is sought for its practicality and utility. Wave propagation has to be solved for in the time domain due to the difference in energy transfer from compression to rarefaction across an interface. Various sizes, orientations and shapes of the discontinuities are analyzed on a unit cell level. Periodic chains with the same type of material discontinuity have recently been shown to exhibit a rich dispersion behavior, such as negatively sloped dispersion branches [Titovich (2017), J. Acoust. Soc. Am. 141(5), 3698]. These waves are now investigated in a continuum, where the discontinuity is modelled as displacement-dependent complex impedance relating the interface tractions. The onset of chaotic behavior as well as its effect on absorption is discussed. Also, the ability of such periodic discontinuities to produce nonlinear non-reciprocity is invest...