Newton’s Third Law is not a Dogma but a Computational Hypothesis

Experimental modal analysis is an important stage in the development of a flying vehicle structure. In the experiment, the eigenfrequency of the structure is identified by a corresponding resonance peak of its amplitude-frequency response characteristic. Different sensors in the vibration machine provide different amplitude-frequency response characteristics. The resonance peaks obtained through different sensors for one and the same eigenfrequency of the structure are located with a frequency shift of approximately 1 Hz. This frequency-shift effect is an obstacle for the experimental modal analysis of structures with closely located oscillation modes. This paper explains the frequency-shift effect using the particle approach. A particle is a point mass, and a structure is a system of particles connected by springs, with each particle associated with its own structural model. Each particle has a “right” for its own resonance and “lives” in its own parallel reality. Each particle is associated with an acceleration sensor. The number of simultaneously considered models is equal to the number of sensors. The obtained modal-analysis results are related only to the corresponding particle. Newton’s third law of the particle interaction is not used in full when assessing the particles’ interaction. The action and reaction forces are still applied to different particles along the same line in the opposite directions, but these forces are different. Modal-analysis simulation is limited to the 2-DOF and the 3-DOF oscillation models.

References

[1] Churilin S.A. Finding the dynamic characteristics of self-deployable frame antennae using the results of its frequency tests. Reshetnevskiye chteniya–2009. Tr. konf. [Reshetnev readings–2009. Conference proceedings]. Krasnoyarsk, SibGU im. M.F. Reshetneva publ., 2009, vol. 1, pp. 92–93.

[2] Nikolayev S.M., Voronov S.A., Voronov P.S. Creating a software package for automating experimental modal analysis of complex mechanical structures. Applied Physics and Mathematics, 2015, no. 5, pp. 44–49 (in Russ.).

[3] Zimin V.N., Koloskov I.M., Meshkovskiy V.E., Tairova L.P., Churilin S.A. Experimental investigations of space structure elements. Engineering Journal: Science and Innovation, 2013, № 3(15) (in Russ.). Available at: http://engjournal.ru/catalog/machin/rocket/617.html

[4] Berns V.A., Dolgopolov A.V., Marinin D.A. Modal analysis of structures based on the test of their components. Proceedings of the Russian higher school Academy of sciences, 2014, no. 1(22), pp. 34–42 (in Russ.).

[5] Berns V.A., Levin V.E., Krasnorutskiy D.A., Marinin D.A., Zhukov E.P., Malenkova V.V., Lakiza P.A. Development of a calculation and experimental method for modal analysis of large transformable space structures. Spacecrafts & Technologies, 2018, vol. 2, no. 3(25), pp. 125–133 (in Russ.).

[6] Grigor’yev B.V. Analysis of the results of frequency tests in the case of close natural frequencies. TsAGI Science Journal, 1993, vol. 24, no. 4, pp. 124–127 (in Russ.).

[7] Derusova D.A., Vavilov V.P., Druzhinin N.V., Kazakova O.I., Nekhoroshev V.O., Fedorov V.V., Tarasov S.Yu., Shpil’noy V.Yu., Kolubayev V.A. Non-destructive testing of the cubsat satellite hull using laser vibrometry. Defektoskopiya, 2019, no. 5, pp. 57–64 (in Russ.), doi: 10.1134/S0130308219050075

[8] Bolotov B.P., Golovkin A.Yu., Solomonov D.G. Settlement and experimental modal analysis of a plate made of a polymer composite material. Aerokosmicheskaya tekhnika, vysokiye tekhnologii i innovatsii [Aerospace Engineering, High Technology and Innovation]. 2017, vol. 1, pp. 43–46.

[9] Ponomarev I.S., Makhnovich S.V., Pantileyev A.S. Peculiarities of experimental determination of frequencies and shapes of eigenmodes of cylindrical shells. Science bulletin of the Novosibirsk state technical university, 2016, no. 3(64), pp. 44–58 (in Russ.), doi: http://dx.doi.org/10.17212/1814-1196-2016-3-44-58

[10] Repin R.V., Zenkov S.G., Yashkin O.S. Verification of results of finite-element analysis of vibration parameters of the shell by the modal testing. Transactions of the Krylova state research centre, 2013, no. 75(359), pp. 69–78 (in Russ.).

[11] Dmitriyev S.N., Khamidullin R.K. Damping matrix correction using experimental modal damping coefficients. Engineering Journal: Science and Innovation, 2013, iss. 3, pp. 1–12 (in Russ.). Available at: http://engjournal.ru/catalog/machin/rocket/619.html, doi: 10.18698/2308-6033-2013-3-619

[12] Berns V.A., Zhukov E.P., Marinin D.A. Structural damping matrix of construction according to test results. Reshetnevskiye chteniya–2015. Tr. konf. [Reshetnev readings–2015. Conference proceedings]. Krasnoyarsk, SibGU im. M.F. Reshetneva publ., 2015, vol. 1, pp. 71–72.

[13] Berns V.A., Zhukov E.P., Marinin D.A. Identification of the Structures Dissipative Properties According to the Experimental Modal Analysis Results. Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, 2016, no. 4(109), pp. 4–23 (in Russ.), doi: 10.18698/0236-3941-2016-4-4-23

[14] Sistema upravleniya vibratsionnymi ispytaniyami SignalStar Vector2 [SignalStar Vector2 Vibration Test Management System. User

[15] Arinchev S.V. Simulation of reversed torsion of the AlMg6 aluminium bar using the macro-molecule approach. Proceedings of the XIII International Conference on Computational Plasticity. Fundamentals and Applications. COMPLAS 2015, Polytechnic University of Catalonia (UPC), Barcelona, Spain, 1–3 September 2015, Ebook_Complas_2015, pp. 429–439.

[16] Arinchev S.V. Back from the solid temperature to kinetic energy of its macro-molecules. Proceedings of the IV International Conference on Particle-Based Methods. Fundamentals and Applications. PARTICLES 2015, Polytechnic University of Catalonia (UPC), Barcelona, Spain, 28–30 September 2015, Ebook_Particles_2015, pp. 909–920.

[17] Arinchev S.V. Two-mass gyro-particle as the tool for supersonic aeroelasticity analysis. Proceedings of the VI International Conference on Particle-Based Methods. Fundamentals and Applications. PARTICLES 2019, Polytechnic University of Catalonia (UPC), Barcelona, Spain, 28–30 October 2019, Ebook_Particles_2019, pp. 644–655.

[18] Arinchev S.V. Teoriya kolebaniy nekonservativnykh system [Theory of oscillations of non-conservative systems]. Moscow, Bauman Press, 2002. 464 p.