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      Discrete breathers in a mechanical metamaterial

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          Abstract

          We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.

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          Author and article information

          Journal
          28 July 2022
          Article
          2207.13968
          af6fd5d9-0a44-4343-8898-2fca7d0fdb16

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          nlin.PS

          Nonlinear & Complex systems
          Nonlinear & Complex systems

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