This paper investigates the equivalence relationship between the mem-inerter and semi-active inerter. First of all, an equivalent inertance theorem is established that gives a necessary and sufficient condition for the equivalence of the mem-inerter and inerter in energy concept and the fact that the mem-inerter with initial-position-inertance mechanism is equivalent to the semi-active inerter performing initial-position-dependent inertance control strategy is demonstrated. Then, to further investigate the equivalence relationship mentioned above, an internal-helix fluid inerter device with displacement-dependent inertance mechanism is considered and confirmed as a physical embodiment of the mem-inerter via analyses of algebraic and dynamic relationships of the device model variables as well as pinched hysteresis loops. Finally, a vehicle suspension is taken as an example to present the inherent semi-active property of this passive memory element and its performance benefits. As a non-conservative motion system, the suspension equipped with the mem-inerter is modeled by using integrated Lagrange method. A comparison analysis between the suspensions with the mem-inerter and semi-active is performed to demonstrate that they have similar transfer characteristics and load adaptivity. The inherent semi-active property and the resulting load adaptivity of the mem-inerter are verified by the fact that the suspension with the mem-inerter has a more smooth and constant ride quality than the one with the inerter. This work is very helpful in establishing a standard equivalence between semi-active and memory mechanical elements, and offering a theoretical reference for substituting linear elements of existing systems with memory elements directly for performance improvement.

本文研究了mem-inerter和半主动inerter的等价关系。首先，建立了等效惯性定理，给出了能量概念上mem-inerter和inerter等价的充分必要条件，以及具有初始位置惯性机制的mem-inerter等价于半展示了执行依赖于初始位置的惯性控制策略的主动惯性器。然后，为了进一步研究上述等价关系，通过分析装置模型变量的代数和动力学关系，考虑并确认具有位移依赖惯性机制的内螺旋流体惰性装置是 mem-inerter 的物理体现以及收缩的磁滞回线。最后，以车辆悬架为例，展示了这种被动存储元件的固有半主动特性及其性能优势。作为一个非保守运动系统，装有记忆惯性器的悬架采用集成拉格朗日方法建模。对具有记忆惰性和半主动悬架的悬架进行了比较分析，以证明它们具有相似的传递特性和负载适应性。mem-inerter 的固有半主动特性和由此产生的负载适应性通过以下事实得到验证：带有 mem-inerter 的悬架比带有 inerter 的悬架具有更平稳和稳定的乘坐质量。这项工作非常有助于建立半主动和记忆机械元件之间的标准等效，