Abstract
Acoustic metamaterials are synthetic architected media featured by a periodic microstructured cell hosting one or more resonant oscillators. The cellular microstructure can be parametrically design to functionalize the dispersion properties of elastic waves. A one–dimensional crystal lattice, characterized by a diatomic periodic cell, is considered to prototypically simulate the essential undamped dynamics of weakly nonlinear acoustic waveguides. A cubic nonlinearity affects the intracellular elastic coupling between the primary atom and the secondary atom (resonator). In the small-amplitude oscillation range, the dispersion relations for the linear wavefrequencies ω(β) and linear waveforms ϕ(β) are determined as analytical functions of the wavenumber β. A general asymptotic approach, based on the multiple scale method, is employed to determine the amplitude-dependent dispersion relations for the nonlinear wavefrequencies ϖ(β) and nonlinear waveforms ψ(β). The actual existence of stable periodic oscillations orbits, confined on the invariant manifolds in the space of the two principal coordinates corresponding to the nonlinear waveforms, is successfully verified by numerical simulations.
Published Version
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