# Free sinusoidal oscillations based on the mutual exchange of kinetic energy between three loads

DOI: 10.34759/trd-2023-129-02

### Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

### Abstract

It is noted that free sinusoidal oscillations in a classical mechanical oscillator are stipulated by the mutual transformation of kinetic energy into potential energy. The oscillator, in which free sinusoidal oscillations are being accompanied by the transformation of the kinetic energy of an inert element into the same kinetic energy of another inert element is well-known. The elements with another nature of reactivity are missing in such oscillator. Such oscillator is essentially mono-reactive. This oscillator disadvantage consists in its imbalance due to the asymmetry of the structure, which may require additional vibration protection measures. This drawback can be avoided by applying a symmetrical scheme with three weights. For the purposes of this work, it is convenient to employ a flat three-coordinate system similar to the three-phase coordinate system used in electrical engineering. For an arbitrary vector R, lying in the three-coordinate plane, which origin coincides with the origin, Theorem 1 is true. The coordinates x1, x2, x3 of the vector R form a regular triangle, which size does not change with an arbitrary rotation of the vector R. Theorem 2. The middle of the vector R is aligned with the center of the triangle x1x2x3. Half of the vector x1x2x3 plays the role of a crank, which in real devices is needed to develop the angular velocity ω and communicate the moment of force to compensate for dissipative losses. In a mono-reactive harmonic oscillator with three weights, free sinusoidal oscillations of any given frequency may occur, which is determined solely by the initial conditions.

### Keywords:

imbalance, asymmetry, vibration protection, symmetrical scheme, three-coordinate system, kinematics

### References

1. Aleroeva Kh.T., Aleroev T.S. Trudy MAI, 2017, no. 94. URL: http://trudymai.ru/eng/published.php?ID=80904
2. Dobryshkin A.Yu. Trudy MAI, 2020, no. 110. URL: http://trudymai.ru/eng/published.php?ID=112820. DOI: 10.34759/trd-2020-110-2
3. Bykova T.V., Mogilevich L.I., Popov V.S., Popova A.A., Chernenko A.V. Trudy MAI, 2020, no. 110. URL: http://trudymai.ru/eng/published.php?ID=112836. DOI: 10.34759/trd-2020-110-6
4. Aleroeva Kh.T. Trudy MAI, 2017, no. 92. URL: http://trudymai.ru/eng/published.php?ID=76821
5. Kholostova O.V., Safonov A.I. Trudy MAI, 2018, no. 100. URL: http://trudymai.ru/eng/published.php?ID=93297
6. Popov I.P. Trudy MAI, 2020, no. 115. URL: https://trudymai.ru/eng/published.php?ID=119888. DOI: 10.34759/trd-2020-115-01
7. Mukhametzyanova A.A. Trudy MAI, 2015, no. 84. URL: http://trudymai.ru/eng/published.php?ID=62975
8. Semenov M.E., Solov’ev A.M., Popov M.A. Trudy MAI, 2017, no. 93. URL: http://trudymai.ru/eng/published.php?ID=80231
9. Popov I.P. Trudy MAI, 2022, no. 122. URL: https://trudymai.ru/eng/published.php?ID=164101. DOI: 10.34759/trd-2022-122-03
10. Popov I.P. Trudy MAI, 2022, no. 126. URL: https://trudymai.ru/eng/published.php?ID=168987. DOI: 10.34759/trd-2022-126-01
11. Grushenkova E.D., Mogilevich L.I., Popov V.S., Popova A.A. Trudy MAI, 2019, no. 106. URL: http://trudymai.ru/eng/published.php?ID=105618
12. Dobryshkin A.Yu., Sysoev O.E., Sysoev E.O. Trudy MAI, 2019, no. 109. URL: http://trudymai.ru/eng/published.php?ID=111349. DOI: 10.34759/trd-2019-109-4
13. Petrukhin V.A., Mel’nikov V.E. Trudy MAI, 2017, no. 93. URL: http://trudymai.ru/eng/published.php?ID=80344
14. Dobryshkin A.Yu., Sysoev O.E., Sysoev E.O. Trudy MAI, 2020, no. 113. URL: http://trudymai.ru/eng/published.php?ID=117957. DOI: 10.34759/trd-2020-113-01
15. Sysoev O.E., Dobryshkin A.Yu., Nein S.N. Trudy MAI, 2018, no. 98. URL: http://trudymai.ru/eng/published.php?ID=90079
16. Bardin B.S., Savin A.A. Trudy MAI, 2016, no. 85. URL: http://trudymai.ru/eng/published.php?ID=65212
17. Blagodyreva O.V. Trudy MAI, 2017, no. 95. URL: http://trudymai.ru/eng/published.php?ID=84426
18. Zagordan A.A., Zagordan N.L. Trudy MAI, 2019, no. 108. URL: http://trudymai.ru/eng/published.php?ID=109383. DOI: 10.34759/trd-2019-108-4
19. Rybnikov S.I., Nguen T.Sh. Trudy MAI, 2017, no. 95. URL: http://trudymai.ru/eng/published.php?ID=84572
20. Animitsa V.A., Borisov E.A., Kritskii B.S., Mirgazov R.M. Trudy MAI, 2016, no. 87. URL: http://trudymai.ru/eng/published.php?ID=69626