Modified mass-in-mass chain
https://doi.org/10.17073/1609-3577j.met202411.627
Abstract
Mathematical models of acoustic metamaterials based on classical and modified (with additional harmonic interaction between neighboring internal masses) one-dimensional infinite mass-in-mass chain are considered. Equations are obtained for the acoustic and optical branches of the dispersion relation, for the band gap width, and for the effective mass. Using the derived equations, the classical and modified mass-in-mass chains are modeled at different ratios of masses and spring stiffness. A qualitative analysis of an interesting special case ωm = ωM was performed, on the basis of which a formal generalization of the equations of relativistic quantum mechanics was obtained using the long-wave approximation.
Keywords
classical and modified mass-in-mass chains,
acoustic and optical branches of dispersion,
band gap,
effective mass,
acoustic metamaterials
Supporting agencies: The work was carried out within the framework of the program "Sirius. Summer: start your project", project task "Propagation of waves in an acoustic metamaterial based on a classical and modified one-dimensional mass-in-mass chain". The authors express their gratitude for the discussion to Oleg I. Markov and Evgeny A. Belkin.
About the Authors
V. O. Turin
Orel State University named after I.S. Turgenev
Russian Federation
Russian Federation
95 Komsomolskaya Str., Orel 302026
Valentin O. Turin — Cand. Sci. (Phys.-Math.), IEEE Senior Member, Associate Professor of the Department of Experimental and Theoretical Physics
I. V. Nazritsky
Orel State University named after I.S. Turgenev
Russian Federation
Russian Federation
95 Komsomolskaya Str., Orel 302026
Ilya V. Nazritsky — Master's Student
D. D. Kireev
Orel State University named after I.S. Turgenev
Russian Federation
Russian Federation
95 Komsomolskaya Str., Orel 302026
Daniil D. Kireev — Master's Student
P. A. Andreev
Orel State University named after I.S. Turgenev
Russian Federation
Russian Federation
95 Komsomolskaya Str., Orel 302026
Pavel A. Andreev — Postgraduate Student
Yu. V. Ilyushina
Moscow Aviation Institute
Russian Federation
Russian Federation
4 Volokolamskoe Highway, Moscow 125993
Yulia V. Ilyushina — Assistant
References
1. Veselago V.G. The electrodynamics of substances with simultaneously negative values of ε and μ. Soviet Physics Uspekhi. 1967; 10(4): 509. https://doi.org//10.1070/PU1968v010n04ABEH003699
2. Brillouin L. Wave propagation in periodic structures: Electric filters and crystal lattices. New York: McGraw-Hill; 1946. 247 p.
3. Zegrya G.G., Perel' V.I. Fundamentals of semiconductor physics. Moscow: Fizmatlit; 2009. 335 p.
4. Crawford F.S. Waves. Berkeley physics course. New York: McGraw-Hill; 1968. Vol. 3. 625 p.
5. Vincent J. H. On the construction of a mechanical model to illustrate Helmholtz’s theory of dispersion. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1898; 46(283): 557—563.
6. Chan C.T., Jensen L.I., Fung K.H. On extending the concept of double negativity to acoustic waves. Journal of Zhejiang University – Science A: Applied Physics & Engineering. 2006; 7(1): 24—28. https://doi.org//10.1631/jzus.2006.A0024
7. Huang H.H., Sun C.T., Huang G.L. On the negative effective mass density in acoustic metamaterials. International Journal of Engineering Science. 2009; 47(4): 610—617. https://doi.org//10.1016/j.ijengsci.2008.12.007
8. Erofeev V.I., Kolesov D.A., Malkhanov A.O. Nonlinear localized longitudinal waves in a metamaterial designed as a “mass-in-mass” chain. Acoustical Physics. 2022; 68(5): 423—426. https://doi.org//10.31857/S0320791922040049
9. Turin V.O., Ilyushina Y.V., Andreev P.A., Cherepkova A.Yu., Kireev D.D., Nazritsky I.V. A mass-in-mass chain and the generalization of the Dirac equation with an eight-component wave function and with optical and acoustic branches of the dispersion relation. Russian Microelectronics. 2023; 52(suppl. 1): S299—S305. https://doi.org//10.13140/RG.2.2.34830.74566
Review
For citations:
Turin V.O., Nazritsky I.V., Kireev D.D., Andreev P.A., Ilyushina Yu.V. Modified mass-in-mass chain. Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering. 2024;27(4):330-340. (In Russ.) https://doi.org/10.17073/1609-3577j.met202411.627
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