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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
For the details on the bend radius of the helical channel and the hydraulic diameter of the channel, see  and references therein.
As a matter of fact, Newton’s original law of motion is represented in terms of momentum and velocity.
Biolek, D., Biolek, Z., Biolkova, V.: Memristors and other higher-order elements in generalized through-across domain. In: 2016 IEEE International Conference on Electronics, Circuits and Systems (ICECS), pp. 604–607. IEEE (2016)
Brzeski, P., Pavlovskaia, E., Kapitaniak, T., Perlikowski, P.: The application of inerter in tuned mass absorber. Int. J. Non-Linear Mech. 70, 20–29 (2015)
Chen, M.Z., Hu, Y.L., Huang, L.X., Chen, G.R.: Influence of inerter on natural frequencies of vibration systems. J. Sound Vib. 333(7), 1874–1887 (2014)
Chen, M.Z., Papageorgiou, C., Scheibe, F., Wang, F.C., Smith, M.C.: The missing mechanical circuit element. IEEE Circuits Syst. Mag. 9(1), 10–26 (2009)
Chua, L.: Resistance switching memories are memristors. Appl. Phys. A 102(4), 765–783 (2011)
Chua, L.: If it’s pinched it’s a memristor. In: Memristors and Memristive Systems, pp. 17–90. Springer (2014)
Chua, L.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24(2), 319–368 (2015)
Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)
Chua, L.O.: Nonlinear circuit foundations for nanodevices, Part I: the four-element torus. Proc. IEEE 91(11), 1830–1859 (2003)
Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)
Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97(10), 1717–1724 (2009)
Gonzalez-Buelga, A., Lazar, I.F., Jiang, J.Z., Neild, S.A., Inman, D.J.: Assessing the effect of non-linearities on the performance of a tuned inerter damper. Struct. Control Health Monit. 24(3), e1879 (2017)
Hu, Y.L., Chen, M.Z.: Performance evaluation for inerter-based dynamic vibration absorbers. Int. J. Mech. Sci. 99, 297–307 (2015)
Jeltsema, D., Doria-Cerezo, A.: Port-hamiltonian formulation of systems with memory. Proc. IEEE 100(6), 1928–1937 (2011)
Lewis, T.D., Jiang, J.Z., Neild, S.A., Gong, C., Iwnicki, S.D.: Using an inerter-based suspension to improve both passenger comfort and track wear in railway vehicles. Veh. Syst. Dyn. 10, 1–22 (2019)
Li, Y., Lombardi, L., De Luca, F., Farbiarz, Y., Blandon, J.J., Lara, L.A., Rendon, J.F., Jiang, J.Z., Neild, S.: Optimal design of inerter-integrated vibration absorbers for seismic retrofitting of a high-rise building in Colombia. In: Journal of Physics: Conference Series, vol. 1264, p. 012031. IOP Publishing (2019)
Liu, X.F., Jiang, J.Z., Titurus, B., Harrison, A.J.L., McBryde, D.: Testing and modelling of the damping effects for fluid-based inerters. Proc. Eng. 199, 435–440 (2017)
Luo, J.N., Macdonald, J., Jiang, J.Z.: Identification of optimum cable vibration absorbers using fixed-sized-inerter layouts. Mech. Mach. Theory 140, 292–304 (2019)
Marian, L., Giaralis, A.: Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems. Probab. Eng. Mech. 38, 156–164 (2014)
Oster, G.F., Auslander, D.M.: The memristor: a new bond graph element. J. Dyn. Syst. Meas. Contr. 94(3), 249–252 (1972)
Pei, J.S., Wright, J.P., Todd, M.D., Masri, S.F., Gay-Balmaz, F.: Understanding memristors and memcapacitors in engineering mechanics applications. Nonlinear Dyn. 80(1–2), 457–489 (2015)
Pershin, Y.V., Di Ventra, M.: Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23(7), 881–886 (2010)
Pershin, Y.V., La Fontaine, S., Di Ventra, M.: Memristive model of amoeba learning. Phys. Rev. E 80(2), 021926 (2009)
Sah, M.P., Yang, C.J., Kim, H., Muthuswamy, B., Jevtic, J., Chua, L.: A generic model of memristors with parasitic components. IEEE Trans. Circuits Syst. I Regul. Pap. 62(3), 891–898 (2015)
Shen, Y.J., Chen, L., Liu, Y.L., Zhang, X.L., Yang, X.F.: Optimized modeling and experiment test of a fluid inerter. J. VibroEng. 18(5), 2789–2800 (2016)
Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002)
Smith, M.C., Wang, F.C.: Performance benefits in passive vehicle suspensions employing inerters. Veh. Syst. Dyn. 42(4), 235–257 (2004)
Stulov, A.: Hysteretic model of the grand piano hammer felt. J. Acoust. Soc. Am. 97, 2577–2585 (1995)
Swift, S.J., Smith, M.C., Glover, A.R., Papageorgiou, C., Gartner, B., Houghton, N.E.: Design and modelling of a fluid inerter. Int. J. Control 86(11), 2035–2051 (2013)
Wang, F.C., Hong, M.F., Chen, C.W.: Building suspensions with inerters. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 224, 1605–1616 (2010)
Wang, F.C., Liao, M.K.: The lateral stability of train suspension systems employing inerters. Veh. Syst. Dyn. 48(5), 619–643 (2010)
Wang, F.C., Liao, M.K., Liao, B.H., Su, W.J., Chan, H.A.: The performance improvements of train suspension systems with mechanical networks employing inerters. Veh. Syst. Dyn. 47(7), 805–830 (2009)
Wang, F.Z.: A triangular periodic table of elementary circuit elements. IEEE Trans. Circuits Syst. I Regul. Pap. 60(3), 616–623 (2013)
Wang, F.Z., Chua, L.O., Yang, X., Helian, N., Tetzlaff, R., Schmidt, T., Li, C., Carrasco, J.M.G., Chen, W.L., Chu, D.: Adaptive neuromorphic architecture (ANA). Neural Netw. 45, 111–116 (2013)
Wang, F.Z., Li, L., Shi, L.P., Wu, H.Q., Chua, L.O.: \(\phi \) memristor: real memristor found. J. Appl. Phys. 125(5), 054504 (2019)
Zhang, S.Y., Jiang, J.Z., Neild, S.: Optimal configurations for a linear vibration suppression device in a multi-storey building. Struct. Control Health Monit. 24(3), e1887 (2017)
Zhang, X.L., Gao, Q., Nie, J.M.: The mem-inerter: a new mechanical element with memory. Adv. Mech. Eng. 10(6), 1–13 (2018)
Zhang, X.L., He, H., Nie, J.M., Chen, L.: A semi-active skyhook-inertance control strategy based on continuously adjustable inerter. Shock Vib. 2018, 1–8 (2018)
Zhang, X.L., Nie, J.M., Huang, Z.X., He, H., Chen, L.: Hydraulic mem-inerter device and its application (2019). US Patent App. 16/158,857
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)
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Zhang, X., Geng, C., Nie, J. 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
- Nonlinear element
- Extended mem-dashpot
- Memory effect
- Displacement-dependent Mechanism
- Pinched hysteresis loop