Abstract <p>Locally resonant metamaterials (LRMs) exhibit exceptional wave attenuation capabilities. However, we show that unavoidable physical clearances resulting from fabrication tolerances, material wear, or corrosion introduce dead-zone nonlinearities that can significantly degrade their performance. Using a one-dimensional (1D) mass-in-mass LRM model incorporating dead zones in each unit cell’s local resonator, we combine analytical and numerical methods to characterize the dynamics. Analytically, a novel approach based on the describing function (DF) extracts the band structure. It shows a characteristic softening effect and a narrowing of the bandgap caused by the dead-zone. A hybrid DF–Harmonic Balance Method (HBM) and full HBM analyses further predict the emergence of higher-order odd harmonics. Using a monatomic (mass-mass) model, critical boundaries and key operational regions are identified. Through numerical simulations, key metrics such as frequency spectra, phase portraits, bifurcation diagrams, and Poincaré sections highlight chaotic behavior. Quantitative chaos detection via sample entropy and the 0-1 test confirms these states. Contrary to studies linking chaos to enhanced performance, we show that the broadband frequency injection inherent to chaotic and highly nonlinear dynamics significantly reduces LRM attenuation through (1) rapid collapse of attenuation within highly nonlinear (HN) bandgap regions and (2) gradual reduction in bandgap intensity, accompanied by narrowing and a red shift, occurring away from the HN region. This degradation, or decrease in performance, is consistently observed across three transmission perspectives: kinetic energy, harmonic excitation, and chirp excitation. It yields a performance loss of approximately 6.8–8.5% per order-of-magnitude increase in non-dimensional dead-zone length. These findings offer quantitative guidelines for robust LRM design and quality control.</p> Graphical abstract <p></p>

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Performance degradation in locally resonant metamaterials due to dead-zone nonlinearity

  • Ali Heidari Shirazi,
  • Reza Abedi

摘要

Abstract

Locally resonant metamaterials (LRMs) exhibit exceptional wave attenuation capabilities. However, we show that unavoidable physical clearances resulting from fabrication tolerances, material wear, or corrosion introduce dead-zone nonlinearities that can significantly degrade their performance. Using a one-dimensional (1D) mass-in-mass LRM model incorporating dead zones in each unit cell’s local resonator, we combine analytical and numerical methods to characterize the dynamics. Analytically, a novel approach based on the describing function (DF) extracts the band structure. It shows a characteristic softening effect and a narrowing of the bandgap caused by the dead-zone. A hybrid DF–Harmonic Balance Method (HBM) and full HBM analyses further predict the emergence of higher-order odd harmonics. Using a monatomic (mass-mass) model, critical boundaries and key operational regions are identified. Through numerical simulations, key metrics such as frequency spectra, phase portraits, bifurcation diagrams, and Poincaré sections highlight chaotic behavior. Quantitative chaos detection via sample entropy and the 0-1 test confirms these states. Contrary to studies linking chaos to enhanced performance, we show that the broadband frequency injection inherent to chaotic and highly nonlinear dynamics significantly reduces LRM attenuation through (1) rapid collapse of attenuation within highly nonlinear (HN) bandgap regions and (2) gradual reduction in bandgap intensity, accompanied by narrowing and a red shift, occurring away from the HN region. This degradation, or decrease in performance, is consistently observed across three transmission perspectives: kinetic energy, harmonic excitation, and chirp excitation. It yields a performance loss of approximately 6.8–8.5% per order-of-magnitude increase in non-dimensional dead-zone length. These findings offer quantitative guidelines for robust LRM design and quality control.

Graphical abstract