Breather Propagation and Arrest in a Strongly Nonlinear Locally Resonant Lattice

Locally resonant metamaterials have recently drawn the attention of many researchers due to their capability in controlling low-frequency waves by forming a bandgap resulting from mode hybridization. Although linear acoustics of these metamaterials have been extensively explored, only a little is known about their nonlinear acoustics. This work investigates the nonlinear acoustics of a 1D discrete strongly nonlinear locally resonant metamaterial under impulsive force excitation. The metamaterial is modeled as a chain of linearly grounded masses connected by essential strong nonlinearity (purely cubic nonlinearity), and embedded by linear local resonators. Numerical investigations demonstrate the existence of different families of traveling breathers that depend on the coupling coefficient between the local resonator and its holding cell. One of these families is reported for the first time in the current work due to the existence of multiple fast frequencies in its profile. Although the investigated system is undamped, numerical simulations demonstrate that the breather arrest is controlled by certain parameters of the system. In the limit of small energy levels, the complexification averaging method (CX-A) is utilized with the help of numerical observations to demonstrate some aspects of the nonlinear acoustics of the system. Particularly, analytical analysis is used to determine the nonlinear band structure of the system. The outcome indicates the presence of two energy-dependent nonlinear propagation zones (PZs) (i.e., acoustics and optical) and three complementary attenuation zones (AZs) for the infinite lattice case. In addition, the different families of traveling breathers in the semi-infinite lattice are investigated analytically and compared to their corresponding numerical results.