Dynamical Properties of a Periodic Mass-Spring Nonlinear Seismic Metamaterial

Nonlinear seismic metamaterials are a challenging class of acoustic metamaterials that are receiving growing attention. Here, it is shown that, in the presence of third-order forces, in a periodic arrangement of an anharmonic mass-spring system, the rectangular bipolar pulse distribution, ansatz solution of the equation of motion, can be projected onto the exact solution. This latter is derived casting the equation of motion in the form of a cubic Duffing differential equation and describes the wave propagating inside the system. Simple expressions for the amplitude and the period of the rectangular distribution are derived from the matching of the first-order contributions of the two solutions. These results could be employed to further tailoring the properties of nonlinear seismic metamaterials for engineering applications.