Abstract
Anyone who ever gave attention to advances in circuit elements will be familiar with the three elementary two-terminal passive elements: resistor, inductor, capacitor and their memory counterparts: memristor, meminductor and memcapacitor, respectively. Similarly, it is reported that the mem-dashpot and the mem-spring were viewed as the memory counterparts of the damper and the spring in the field of mechanical engineering. However, what is the memory counterpart of the inerter as a new two-terminal element? In 2018, Zhang predicted the existence of such a mechanical element, which he called a mem-inerter. Although he postulated this element, until now no one offered either a useful physical realization or an example of a mem-inerter. Here, a displacement-dependent fluid inerter device is found to be a physical realization of a mem-inerter, though with a parasitic element called the extended mem-dashpot, which is viewed as the mechanical counterpart of an extended memristor. Experimental results confirm this finding and the existence of the mem-inerter and the extended mem-dashpot in the real world. This work is very helpful in finding and designing mem-inerter and extended mem-dashpot devices, and modeling some important nonlinear hysteretic devices and systems, which is a fundamental branch of research in nonlinear dynamics.
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Notes
For the details on the bend radius of the helical channel and the hydraulic diameter of the channel, see [29] and references therein.
As a matter of fact, Newton’s original law of motion is represented in terms of momentum and velocity.
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Funding
This study was funded by the National Natural Science Foundation of China (Grant Nos. 51875257 and 51805223), the Jiangsu Government Scholarship for Overseas Studies (Grant No. JS-2019-192) and the Six Talent Peaks Program of Jiangsu Province of China (Grant No. 2016-GDZB-097)
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Zhang, XL., Geng, C., Nie, JM. et al. The missing mem-inerter and extended mem-dashpot found. Nonlinear Dyn 101, 835–856 (2020). https://doi.org/10.1007/s11071-020-05837-7
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DOI: https://doi.org/10.1007/s11071-020-05837-7