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We report on the existence of discrete breathers in a one-dimensional,mass-in-mass chain with linear intersite coupling and nonlinear Hertzian localresonators, which is motivated by recent studies of the dynamics ofmicrospheres adhered to elastic substrates. After predicting theoretically theexistence of the discrete breathers in the continuum and anticontinuum limitsof intersite coupling, we use numerical continuation to compute a family ofbreathers interpolating between the two regimes in a finite chain, where thedisplacement profiles of the breathers are localized around one or two latticesites. We then analyze the frequency-amplitude dependence of the breathers byperforming numerical continuation on a linear eigenmode (vanishing amplitude)solution of the system near the upper band gap edge. Finally, we use directnumerical integration of the equations of motion to demonstrate the formationand evolution of the identified localized modes, including within settings thatmay be relevant to future experimental studies.

Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators