The mem-inerter: A new mechanical element with memory

Abstract

A new two-terminal mechanical element named the mem-inerter described by a relation between integrated momentum and displacement is introduced as the memory counterpart of an inerter. It exhibits an individual ''fingermark'' featured by a pinched hysteresis loop located within the momentum-velocity plane. The mem-inerter is attached to a simple mass-spring-damper system. The system equipped with a mem-inerter is mathematically modeled, and its nonlinear vibration equation is derived. To ensure a fair performance comparison between the systems equipped with the meminerter and the inerter, the nonlinear mem-inerter with an appropriate helix pitch can be proved to be equivalent to the linear inerter with a fixed inertance by the fact that the systems have the same displacement transmissibility for forced response. Under such a premise, it is found that the system with the mem-inerter having positive initial displacement has better performance for free response than the system with the inerter. Furthermore, the application scenario that both systems are arranged on an inclined plane is taken as an example of the positive initial displacement. The example demonstrates that the system with the mem-inerter has significantly better transient performance than the system with the inerter.

Modeling a helical fluid inerter system with time‐invariant mem‐models

“…meaning that indeed, the behavior is better modeled by a mem-inerter, not a nonlinear inerter. In addition, this meminerter is more complicated than the definition in Zhang et al 40 This mem-inerter is a system-level model as proposed previously in Equation (19). Similar to the system-level mem-models studied in Pei et al, 31 _…”

“…Capturing both variable inertance and variable damping follows well with the physics observed in the experiments. If the definition for the mem-inerter in Zhang et al 40 is inadequate, then it would show up in the term of B(x). We treat this as a model selection problem: based on our identification, we choose the model that fits the data better.…”

“…Zhang et al 40 propose the concept of a mem-inerter and contrast it with definitions of a linear and nonlinear inerter. The physical motivation seems to compare well with this study.…”

“…The physical motivation seems to compare well with this study. However, the definition for the mem-inerter in Zhang et al 40 is not as comprehensive as those for memristive and memcapacitive system models, such as those defined here.…”

“…Initially, we pose the problem by assuming that we are unsure of the exact type of elements in the model and want to use the experimental data to identify this. We also investigate whether the definition for the meminerter in Zhang et al 40 is adequate in this context.…”