Abstract
With the aim of developing high-performance locally resonant metamaterials, the effect of nonlinear hyperelastic interactions between a rubberlike elastomeric local resonator and the host matrix is investigated. The results reveal a new emergent physical phenomenon not previously reported within the framework of elastoacoustic metamaterials: The appearance of a half subharmonic attenuation zone complementing the local resonance band gap around the fundamental frequency. Evidence of the emergent attenuation zone is provided by direct numerical simulations as well as semianalytical developments via the method of multiple scales. The analyses demonstrate that, in the considered nonlinear locally resonant metamaterial, the combined effects of autoparametric and local resonance induce saturation of the primary wave at certain conditions and, subsequently, promote energy exchange from a primary propagating wave to an evanescent subharmonic wave, giving rise to an additional attenuation zone. This opens new possibilities for the design of passive filtering devices for elastoacoustic waves.
Highlights
The interest in metamaterials originates from the challenge for designing a new generation of materials with superior properties, not found in nature
The aim was to explore the effect of material nonlinearities of rubberlike materials, described by the neo-Hookean material model, on the dynamical behavior of metamaterials
In order to unravel the formation mechanism of the subharmonic attenuation zone, the dynamics of an approximate nonlinear model system involving only quadratic nonlinearity has been investigated using the method of multiple scales
Summary
The interest in metamaterials originates from the challenge for designing a new generation of materials with superior properties, not found in nature. Within the framework of acoustic metamaterials, Lazarov and Jensen [26] have used the harmonic balance method to investigate the amplitude dependence of the locally resonant band gap in a discrete lattice system including cubic interaction between the local resonators and the main chain atoms The effect of both softening and stiffening ( known as hardening) cubic nonlinearity on the amplitude-dependent dispersion behavior of the nonlinear locally resonant lattice metamaterial has been addressed by Manimala and Sun [27]. It should be pointed out that the present work is fundamentally different from other publications [40,41,42] on soft elastomeric metamaterials, where wave tailoring is achieved by induced geometrical modifications during wave propagation, e.g., as a result of buckling [42], or from the recent work by Konarski et al [43] in which a frequency-dependent effective medium theory for locally resonant metamaterials with hyperelastic inclusions and embedded mechanical instabilities has been derived. IV, the analytical expressions for the quadratic metamaterial model are used to unravel the underlying physical phenomenon explaining the emergent subharmonic attenuation zone
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