Advances in nonlinear acoustic/elastic metamaterials and metastructures

Acoustic/elastic metamaterials exhibit a wealth of unusual properties conducive to wave manipulation. This review outlines state-of-the-art developments from FPUT chains, granular crystals to nonlinear acoustic metamaterials (NAMs). It mainly discusses key advances made in the domain of NAMs for wave manipulation, vibration control and sound attenuation given the blooming interest in exploring how nonlinearity offers possibilities for discovering novel wave phenomena, principles and properties that potentially go well beyond linear metamaterials and the relevant linear theories. NAMs reveal intriguing wave phenomena, revolutionizing our understanding of wave behavior including the breakdown of reciprocity, stationary invariance and space–time invariance, and have the potential to promote superior engineering performance like ultra-low and ultra-broadband vibration reduction. An overview of present research and further challenges are provided in fields such as calculation methods, amplitude-dependent bandgaps, self-adaptive bands, nonreciprocal wave control, harmonic control, chaotic dynamics, vibration and sound attenuation, practical design, experimental implementation, and practical applications. © The Author(s) 2024.