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Description of the Fields of Vibration in 2D Latticed Structures with Triangular (Hexagonal) Cells

  • MECHANICS OF MACHINES
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Abstract

This article deals with the problem of describing the fields of vibration in string lattices with triangular (centered hexagonal) cells. The problems of this kind have not been adequately studied despite the fact that the required models find application in the dynamic analysis of various machines and structures as well as in crystallography and materials science. Equations of motion are provided. Problems of propagation of sinusoidal waves and induced oscillations under a random broadband force action are considered.

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REFERENCES

  1. Vibratsii v tekhnike. Spravochnik. T. 4. Vibratsionnye protsessy i mashiny (Vibrations in Technique. Reference Book, Vol. 4: Vibration Processes and Machines) Lavendel, E.E, Ed., Moscow: Mashinostroenie, 1981.

  2. Vaisberg, L.A, Kartavyi, A.N., and Korovikov, A.N., Proseivayushchie poverkhnosti grokhotov. Screening media: konstruktsii, materialy, opyt primeneniya (Screening Surfaces of Screens. Screening Media: Designs, Materials, Application Experience), St. Petersburg: VSEGEI, 2005.

  3. Nagaev, R.F. and Khodzhaev, K.Sh., Kolebaniya mekhanicheskikh sistem s periodicheskoi strukturoi (Oscillations of Mechanical Systems with a Periodic Structure), Tashkent: FAN, 1973.

  4. Burov, V.A., Voloshinov, V.G., Dmitriev, K.V., and Polikarpova, N.V., Acoustic waves in metamaterials, crystals, and anomalously refracting structures, Phys. Usp., 2011, vol. 54, no. 11, pp. 1165–1170.

    Article  Google Scholar 

  5. Bobrovnitskii, Yu.I., Special issue on acoustic metamaterials, J. Acoust. Soc. Am., 2012, vol. 132, no. 4, pp. 2783–2945.

    Article  Google Scholar 

  6. Bobrovnitskii, Yu.I., Models and general wave properties of two-dimensional acoustic metamaterials and media, Acoust. Phys., 2015, vol. 61, no. 3, pp. 255–264.

    Article  Google Scholar 

  7. Astashev, V.K. and Krupenin, V.L., Nelineinaya dinamika ul’trazvukovykh tekhnologicheskikh protsessov (Nonlinear Dynamics of Ultrasonic Technological Processes), Moscow: MGUP im. Ivana Fedorova, 2016.

  8. Krupenin, V.L., Vibrational and vibrational-impact processes in machines assembled from lattices, J. Mach. Manuf. Reliab., 2012, vol. 41, no. 6, pp. 441–456.

    Article  Google Scholar 

  9. Krupenin, V.L., Analysis of singularized motion equations of latticed vibroimpact 2D systems in renouncing Newton’s hypothesis, J. Mach. Manuf. Reliab., 2016, vol. 45, no. 2, pp. 104–112.

    Article  Google Scholar 

  10. Astashev, V.K., Krupenin, V.L., and Andrianov, N.A., Vibro-shock effects with limited oscillations of string grids with massive knots, Dokl. Akad. Nauk, 2018, vol. 480, no. 6, pp. 661–665.

    Google Scholar 

  11. Nikitenkova, S.P. and Potapov, A.I., Acoustic properties of two-dimensional phonon crystals with hexagonal symmetry, Vestn. Nauch.-Tekh. Razvit., 2010, no. 3 (31), pp. 25–30.

  12. Teoreticheskaya mekhanika. Uprugie i teplovye svoistva ideal’nykh kristallov. Uchebnoe posobie (Theoretical Mechanics. Elastic and Thermal Properties of Ideal Crystals, The School-Book), Krivtsov, A.M, Ed., St. Petersburg: Politekh. Univ., 2009.

  13. Aleksandrov, P.S., Vvedenie v obshchuyu teoriyu mnozhestv i funktsii (Introduction to the General Theory of Sets and Functions), Moscow: OGIZ, 1948.

  14. Krupenin, V.L., Calculation of mechanisms with threshold nonlinearities by singularization method, Mashinovedenie, 1984, no. 1, pp. 6–12.

  15. Babitsky, V.I. and Krupenin, V.L., Vibration of Strongly Nonlinear Discontinuous Systems, Berlin: Springer, 2001.

    Book  Google Scholar 

  16. Klyatskin, V.I., Stokhasticheskie uravneniya i volny v sluchaino-neodnorodnykh sredakh (Stochastic Equations and Waves in Randomly Inhomogeneous Media), Moscow: Nauka, 1980.

  17. Bolotin, V.V., Sluchainye kolebaniya uprugikh sistem (Random Oscillations of Elastic Systems), Moscow: Nauka, 1979.

  18. Dimentberg, M.F., Nelineinye stokhasticheskie zadachi mekhanicheskikh kolebanii (Nonlinear Stochastic Problems of Mechanical Oscillations), Moscow: Nauka, 1980.

  19. Krupenin, V.L., Investigation of one-dimensional and multidimensional vibroimpact processes during random broadband excitation, J. Mach. Manuf. Reliab., 2010, vol. 39, no. 6, pp. 530–538.

    Article  Google Scholar 

  20. Fedoryuk, M.V., Asimptotika: integraly i ryady (Asymptotics: Integrals and Series), Moscow: URSS, 2009.

  21. Gruber, P., Convex and Discrete Geometry, Berlin: Springer, 2007.

    MATH  Google Scholar 

  22. Erofeev, V.I., Pavlov, I.S., and Leontiev, N.V., A mathematical model for investigation of nonlinear wave processes in a 2d granular medium consisting of spherical particles, Composites: Mech.,Comput., Appl., 2013, vol. 4, no. 3, pp. 239–255.

    Google Scholar 

  23. Banakh, L.Ya., Oscillations of branched self-similar structures. Dichotomic lattice, Probl. Mashinostr. Avtomatiz., 2014, no. 1, pp. 110–114.

  24. Ganiev, R.F., Reviznikov, D.L., Sukharev, T.Yu., and Ukrainskii, L.E., Optimization of the spatial arrangement of working elements in oscillatory-type plants, J. Mach. Man. Reliab., 2018, vol. 47, no. 1, pp. 3–8.

    Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, project no. 19-1900065.

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Authors and Affiliations

  1. Blagonravov Institute of Machine Science, Russian Academy of Sciences, 101990, Moscow, Russia

    V. L. Krupenin

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  1. V. L. Krupenin
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Correspondence to V. L. Krupenin.

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Translated by O. Lotova

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Krupenin, V.L. Description of the Fields of Vibration in 2D Latticed Structures with Triangular (Hexagonal) Cells. J. Mach. Manuf. Reliab. 48, 525–534 (2019). https://doi.org/10.3103/S1052618819030087

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  • DOI: https://doi.org/10.3103/S1052618819030087

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