On the Effective Dynamic Mass of Mechanical Lattices with Microstructure
We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective dynamic mass. We first revisit a classical case of microstructure being modeled by a spring-interconnected mass-in-mass cell. The frequency-dependent effective dynamic mass of the cell is the sum of a static mass and of an added mass, in analogy to that of a swimmer in a fluid. The effective dynamic mass is derived using three different methods: momentum equivalence, dynamic condensation, and action equivalence.