Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

Abstract

Abstract. To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).