Calculation of Vibroshock Processes with Repeated Collisions (Bouncing)


In this paper, we consider the problem of calculating the parameters of damped oscillations under the collision of two systems with one degree of freedom. Such oscillations can be accompanied by vibroshock processes with repeated collisions (modes with bounce). The nature of these processes depends on the accepted models of energy dissipation and the design features of the colliding objects. The corresponding equations of motion are given. A method for constructing the laws of motion based on the method of averaging vibroshock systems is presented. Examples are given. Considerations can be used, for example, in the calculation and analysis of specific phenomena that occur in the elements of switching devices, as well as in other systems, in particular, those associated with the description of vibration fields generated by shocks.

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  1. 1

    Revich, Yu.V., Azbuka elektroniki. Izuchaem Arduino (The alphabet of electronics. Learning Arduino), Moscow: ACT Kladez, 2017.

  2. 2

    Mandel’shtam, L.I., Lektsii po teorii kolebanii (Lectures on the Theory of Oscillations), Moscow: Nauka, 1972.

  3. 3

    Nagaev, R.F., Mekhanicheskie protsessy s povtornymi zatukhayushchimi soudareniyami (Mechanical Processes with Repeated Decaying Collisions), Moscow: Nauka, 1985.

  4. 4

    Kobrinskii, A.A., Mekhanizmy s uprugimi svyazyami (Mechanisms with Elastic Bonds), Moscow: Nauka, 1964.

  5. 5

    Babitskii, V.I. and Krupenin, V.L., Kolebaniya v sil’no nelineinykh sistemakh (Oscillations in Strongly Nonlinear Systems), Moscow: Nauka, 1972.

  6. 6

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

    Google Scholar 

  7. 7

    Babitskii, V.I., Kovaleva, A.S., and Krupenin, V.L., The study of quasiconservative vibro-shock systems by averaging, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1982, no. 1, p. 41.

  8. 8

    Burd, V.Sh. and Krupenin, V.L., Usrednenie v kvazikonservativnykh sistemakh (Averaging in Quasiconservative Systems), Moscow: Belyi Veter, 2016.

  9. 9

    Rabotnov, Yu.N., Elementy nasledstvennoi mekhaniki tverdykh tel (Elements of Hereditary Mechanics of Solids), Moscow: Nauka, 1977.

  10. 10

    Ilyushin, A.A. and Pobedrya, B.E., Osnovy matematicheskoi teorii termovyazkouprugosti (Fundamentals of the Mathematical Theory of Thermoviscoelasticity), Moscow: Nauka, 1970.

  11. 11

    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, Compos.: Mech.,Comput., Appl., 2013, vol. 4, no. 3, p. 239.

    Google Scholar 

  12. 12

    Krupenin, V.L., On the description of strongly nonlinear vibroconducting and vibrogenerating media, J. Mach. Manuf. Reliab., 2016, vol. 45, no. 4, pp. 297–306.

    Article  Google Scholar 

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This work was supported by the Russian Foundation for Basic Research, project no. 18-08-00168.

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Correspondence to V. L. Krupenin.

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Translated by A. Ivanov

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Krupenin, V.L. Calculation of Vibroshock Processes with Repeated Collisions (Bouncing). J. Mach. Manuf. Reliab. 49, 177–183 (2020).

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  • collisions
  • vibroshock system
  • bounce
  • bounce time
  • contact system
  • “impulse-phase” variables
  • dissipation models
  • systems with relaxation.