What is the simplest mathematical model of a mechanical metamaterial that contains rigidity and an external vibration disturbance?

In my mind, there are mechanical oscillatory systems with concentrated parameters. These oscillatory systems are design schemes (may be quite crude, but that's another question) for technical objects whose properties can be represented by a spring, mass, or damper. If an external harmonic effect is applied to the system, then the linear oscillatory system may be in a state of resonance or a mode of dynamic vibration damping. In principle, the concepts of negative rigidity, etc. can be considered within the framework of structural methods. Recently, they have begun to consider metamaterials, the elementary cell of which has some structure similar to some conventional mechanism. The question is, can these mechanisms be modeled using linear oscillatory systems, just as mechanical oscillatory systems are modeled? Are there any such materials? And what does a closed mathematical model of the simplest metamaterial look like?

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