Synchronous stability and self‑balancing behavior of a three‑body vibrating system driven by four vibrators

• Autorzy: Chen Chen , Zhang Xueliang , Hu Wenchao , Li Ziqian , Cui Shiju , Wen Bangchun

Identyfikatory

DOI

10.1007/s43452-024-00865-1

• Języki publikacji: EN

Abstrakty

EN

Although many researchers have examined the synchronization characteristics of numerous dynamic models, equipment that utilizes synchronization phenomena with high yield, optimal isolation effect, and robust stability performance has not yet been completely into reality. In this paper, a novel model scheme with three bodies driven by four vibrators is presented, and the aim is to clarify the mechanism of synchronization and stability and find the self-balancing behavior of the system where the dynamic load transmitted to the foundation is zero. The motion differential equations of the system and the theoretical criteria for achieving stable synchronization behavior are provided. The kinetic and coupling dynamic characteristics of the system are discussed in detail through numerical analyses, including the stable states of four vibrators, phase relationships among three bodies, synchronization and stability ability coefficients, and a maximum of the coupling torque, etc. It shows that the self-balancing behavior of the system is occurring in Region 2, where the reverse relative motion of two rigid bodies exhibits stronger harmonic vibration, and the isolation body embodies no vibration, which probably leads to the minimum of transmitting the dynamic loads to the foundation. Additionally, it found the diversity of the nonlinear system, which is in all the other Regions except for Region 2. The characteristics analysis and simulation results verify the validity and feasibility of the theoretical investigation.

Słowa kluczowe

EN

synchronous stability; self balancing behavior; vibrating system

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2024
• Tom: Vol. 24, no. 2
• Strony: art. no. e64, 2024
• Opis fizyczny: Bibliogr. 31 poz., rys., tab., wykr.

Twórcy

autor

Chen Chen

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

autor

Zhang Xueliang

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China
• Key Laboratory of Vibration and Control of Aero‑Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

• https://orcid.org/0000-0002-5273-0764

autor

Hu Wenchao

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

autor

Li Ziqian

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

autor

Cui Shiju

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

autor

Wen Bangchun

• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning, People’s Republic of China

Bibliografia

• 1. Senator M. Synchronization of two coupled escapement-driven pendulum clocks. J Sound Vib. 2006;291:566-603.
• 2. Kapitaniak M, Czolczynski K, Perlikowski P, Stefanski A, Kapitaniak T. Synchronous states of slowly rotating pendula. Phys Rep Rev Sect Phys Lett. 2014;541:1-44.
• 3. Teufel A, Steindl A, Troger H. Synchronization of two flow excited pendula. Commun Nonlinear Sci Numer Simul. 2006;11:577-94.
• 4. Czolczynski K, Perlikowski P, Stefanski A, Kapitaniak T. Synchronization of slowly rotating pendulums. Int J Bifurc Chaos. 2012;22:1250128.
• 5. Perlikowski P, Stefański A, Kapitaniak T. 1:1 Model locking and generalized synchronization in mechanical oscillators. J Sound Vib. 2008;318:329-40.
• 6. Wang PY, Zhang M. Passive synchronization in optomechanical resonators coupled through an optical field. Chaos Solitons Fractals. 2021;144: 110717.
• 7. Pecora LM, Carroll TL, Johnson GA, Mar DJ, Heagy JF. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos. 1997;7:520-43.
• 8. Blekhman II. Synchronization in science and technology. New York: ASME Press; 1988.
• 9. Blekhman II, Sorokin VS. On the separation of fast and slow motions in mechanical systems with high-frequency modulation of the dissipation coefficient. J Sound Vib. 2010;329:4936-49.
• 10. Wen BC, Zhang H, Liu SY, He Q, Zhao CY. Theory and techniques of vibrating machinery and their applications. Beijing: Science Press; 2010.
• 11. Wen BC, Fan J, Zhao CY, Xiong WL. Vibratory synchronization and controlled synchronization in engineering. Beijing: Science Press; 2009.
• 12. Zhang XL, Li ZM, Li M, Wen BC. Stability and sommerfeld effect of a vibrating system with two vibrators driven separately by induction motors. IEEE ASME Trans Mechatron. 2021;26:807-17.
• 13. Zhang XL, Gu DW, Yue HL, Li M, Wen BC. Synchronization and stability of a far-resonant vibrating system with three rollers driven by two vibrators. Appl Math Model. 2021;91:261-79.
• 14. Peng H, Hou YJ, Fang P, Zou M, Zhang ZL. Synchronization analysis of the anti-resonance system with three exciters. Appl Math Model. 2021;97:96-112.
• 15. Zou M, Fang P, Hou YJ, Chai GD, Chen JS. Self-synchronization theory of tri-motor excitation with double-frequency in far resonance system. Proc Inst Mech Eng C J Mech Eng Sci. 2020;234:3166-84.
• 16. Balthazar JM, Felix JLP, Brasil RMLRF. Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure. J Vib Control. 2004;10:1739-48.
• 17. Balthazar JM, Felix JLP, Brasil RMLRF. Some comments on the numerical simulation of self-synchronization of four non-ideal exciters. Appl Math Comput. 2005;164:615-25.
• 18. Kong XX, Jiang J, Zhou C, Xu Q, Chen CZ. Sommerfeld effect and synchronization analysis in a simply supported beam system excited by two non-ideal induction motors. Nonlinear Dyn. 2020;100:2047-70.
• 19. Kong XX, Li WJ, Jiang J, Dong ZX, Wang ZZ. Dynamic characteristics of a simply supported elastic beam with three induction motors. J Sound Vib. 2021;520: 116603.
• 20. Yu XX, Mao KM, Lei S, Zhu YM. A new adaptive proportional-integral control strategy for rotor active balancing systems during acceleration. Mech Mach Theory. 2019;136:105-21.
• 21. Sperling L, Merten F, Duckstein H. Self-synchronization and automatic balancing in rotor dynamics. Int J Rotating Mach. 2000;6:275-85.
• 22. Liu SH, Jiang LZ, Zhou WB, Yu J, Liu X. Study on the influence of damage characteristics of longitudinal ballastless track on the dynamic performance of train-track-bridge coupled systems. Arch Civ Mech Eng. 2022;23:23.
• 23. Cui PL, Du L, Zhou XX, Li JL, Li YB, Wu Y. Synchronous vibration moment suppression for ambs rotor system in control moment gyros considering rotor dynamic unbalance. IEEE ASME Trans Mechatron. 2022;27:3210-8.
• 24. Heindel S, Mueller PC, Rinderknecht S. Unbalance and resonance elimination with active bearings on general rotors. J Sound Vib. 2017;431:422-40.
• 25. Zhang XL, Wen BC, Zhao CY. Theoretical study on synchronization of two exciters in a nonlinear vibrating system with multiple resonant types. Nonlinear Dyn. 2016;85(1):141-54.
• 26. Sun XT, Jing XJ, Cheng L, Xu J. A 3-D Quasi-zero-stiffness-based sensor system for absolute motion measurement and application in active vibration control. IEEE ASME Trans Mechatron. 2015;20(1):254-62.
• 27. Wu J, Wang K, Gao L, Xiao S. Study on longitudinal vibration of a pile with variable sectional acoustic impedance by integral transformation. Acta Geotech. 2019;14(6):1857-70.
• 28. Zhang XL, Wen BC, Zhao CY. Vibratory synchronization transmission of a cylindrical roller in a vibrating mechanical system excited by two exciters. Mech Syst Signal Proc. 2017;96:88-103.
• 29. Blekhman II, Yaroshevich NP. Extension of the domain of applicability of the integral stability criterion (extremum property) in synchronization problems. J Appl Math Mech. 2004;68:839-46.
• 30. Cieplok G, Wójcik K. Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion. J Theor Appl Mech. 2020;58(2):513-24.
• 31. Yang Y, Fu R, Huang L. Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria. Syst Control Lett. 2004;53:89-105.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).