Vibration analysis of nonlinear and linear elastic systems

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.

Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.

Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.

Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

1. Pat. № 2706770 Rossiyskaya Federatsiya, MPK B 60G 11/10. Uprugiy mekhanizm s regressivno-progressivnoy kharakteristikoy / S.A. Kuznetsov, A.S. Lichkovakha, B. A. Shemshura . Zayavl. 09.01.2019; opubl. 20.11.2019, Byul. № 32. [Pat. No. 2706770 Russian Federation, IPC B 60G 11/10. Elastic mechanism with a regressiveprogressive characteristic / S.А. Kuznetsov, A.S. Lichkovakha, B.A. Shemshura. Applied. 01/09/2019; publ. 20.11.2019, Bul. No. 32.

2. Pat. № 2486065 Rossiyskaya Federatsiya, MPK B 60G 11/04. Uprugaya podveska s regressivno-progressivnoy kharakteristikoy / S.A. Kuznetsov, V.N. Semenov, YA.A. Lysenko, YU.YU. Oleynicheva. – Zayavl. 15.02.2012; opubl. 27.06.2013, Byul. № 18. [Pat. No. 2486065 Russian Federation, IPC B 60G 11/04. Elastic suspension with a regressive-progressive characteristic / S.A. Kuznetsov, V.N. Semenov, Ya.A. Lysenko, Yu. Yu. Oleinicheva. Applied. 02/15/2012; publ. 06/27/2013, Bul. No. 18.

3. Pat. № 2521879 Rossiyskaya Federatsiya, MPK B 60G 3/16. Uprugaya podveska s regressivno-progressivnoy kharakteristikoy / V.N. Semenov, S.A. Kuznetsov, A.A. Galushkin. Zayavl. 13.12.2012; opubl. 10.07.2014, Byul. № 19. [Pat. No. 2521879 Russian Federation, IPC B 60G 3/16. Elastic suspension with a regressive-progressive characteristic / V.N. Semenov, S.A. Kuznetsov, A.A. Galushkin. Applied. 12/13/2012; publ. 07/10/2014, Bul. No. 19.

4. Popov, Ye.P. Teoriya i raschet gibkikh uprugikh sterzhney / Ye.P. Popov. M.: Nauka. Gl. red. fiz.-mat. lit., 1986. 296s. [Popov, E.P. Theory and calculation of flexible elastic rods / E.P. Popov. M .: Science. Ch. ed. physical-mat. lit., 1986. 296s.

5. Ponomarov, S.D. Raschoty na prochnost' v mashinostroyenii /S.D. Ponomarev, V.L. Biderman, V.I. Feodos'yev. M.: Mashgiz, 1956. T.1. 886 s. [Ponomarev S. D. Strength calculations in mechanical engineering / S.D. Ponomarev, V.L. Biderman and V.I. Feodosiev. M .: Mashgiz, 1956 . Vol. 1. 886p.

6. Anfilof'yev A. V. Geometricheskoye predstavleniye ellipticheskikh integralov / A. V. Anfilof'yev, V. M. Zamyatin // Izvestiya Tomskogo politekhnicheskogo universiteta [Izvestiya TPU]. 2005. T. 308, № 5. S. 11-14. [Anfilofiev AV Geometric representation of elliptic integrals / AV Anfilofiev, VM Zamyatin // Bulletin of the Tomsk Polytechnic University [Bulletin of TPU]. 2005. T. 308, No. 5. pp. 11-14.

7. Lichkovakha, A.S. Issledovaniye deformatsii sterzhnya bol'shoy gibkosti pri osevom nagruzhenii /A.S. Lichkovakha, B.A. Shemshura, S.A. Kuznetsov // Izvestiya vysshikh uchebnykh zavedeniy. Severo-kavkazskiy region. Tekhnicheskiye nauki. 2016. №3. S. 71-76. [Lichkovakha, A.S. Investigation of the deformation of a rod of great flexibility under axial loading / A.S. Lichkovakha, B.A. Shemshura, S.A. Kuznetsov // News of higher educational institutions. North Caucasian region. Technical science. 2016. No. 3. рр. 71-76.

8. Lichkovakha A.S., Issledovaniye napryazhonno-deformirovannogo sostoyaniya vnetsentrenno szhatogo sterzhnya bol'shoy gibkosti: / A.S. Kuznetsov, B.A.Shemshura, A.S. Lichkovakha. Elektronnyy nauchnyy zhurnal Inzhenernyy vestnik Dona №1, 2018 ivdon.ru/ru/magazine/archive/nly2018/4773-0,9p.l. [Lichkovakha AS, Investigation of the stress-strain state of an eccentrically compressed rod of great flexibility: / A.S. Kuznetsov, B.A. Shemshura, A.S. Lichkovakha. Electronic scientific journal Engineering Bulletin of Don No. 1, 2018 ivdon.ru/ru/magazine/archive/nly2018/4773-0.9 pp.

9. A.S. Lichkovakha, B. A. Shemshura, S.A. Kuznetsov K opredeleniyu energeticheskogo balansa nelineynoy uprugoy sistemy// A.S. Lichkovakha, B.A. Shemshura, S.A. Kuznetsov// Vestnik Rostovskogo gosudarstvennogo universiteta putey soobshcheniya , 2018. №2. S.137-143. [A.S. Lichkovakha, B.A. Shemshura, S.A. Kuznetsov On the determination of the energy balance of a nonlinear elastic system. Lichkovakha, B.A. Shemshura, S.A. Kuznetsov // Bulletin of Rostov State University of Railways, 2018. No. 2. pp. 137-143.

10. Basov K. A. ANSYS dlya konstruktorov / K. A. Basov. M. : DMK Press, 2009. 248 c. [Basov, K. A. ANSYS for designers / K. A. Basov M.: DMK Press, 2009. 248 p.

11. Okhorzin, V. A. Prikladnaya matematika v sisteme Mathcad / V. A. Okhorzin. M. :, Lan', 2009. 352 c. Bibliographic list [Okhorzin, V. A. Applied mathematics in the Mathcad system / V. A. Okhorzin. M., Lan, 2009. 352 p.