Modal sensitivity analysis of acoustic metamaterials for structural damage detection

Abstract

Metamaterials have garnered significant research interest over the past few decades, primarily due to their unique properties not found in naturally occurring materials. However, when integrated into operational engineering structures, metamaterials can sustain damage, compromising their extraordinary attributes and potentially leading to structural failure. This work marks a novel advancement in the field of metamaterials research, providing an in-depth analysis into the impact of damage on the structural dynamic properties of finite acoustic metamaterials (AMMs) consisting of periodic locally resonant mass-in-mass units. A modal sensitivity analysis is formulated based on equations of motion of a damaged AMM, along side with associated eigenvalue problem and frequency response functions. The critical role of the internal spring is analytically revealed in determining the effective mass of a damaged unit. To evaluate the effects of damage on AMMs, an extensive numerical investigation is conducted on a finite AMM; an damage index is proposed for measuring the modal deformation of each spring. It is unequivocally demonstrated that frequency response functions, eigenvalues, and mode shapes of damaged AMMs undergo substantial changes at frequencies near bandgaps and these changes diminish as frequencies move away from the bandgaps. This behavior directly corresponds to the frequency-dependent changes in the effective mass of a mass-in-mass unit due to damage. Hence, this work constitutes a leap forward in our understanding of the structural dynamics of damaged metamaterials and offers valuable insights that could facilitate the development of more effective damage identification techniques and the realization of resilient metamaterial-based structures.