Stability and Periodic Motions for a System Coupled with an Encapsulated Nonsmooth Dynamic Vibration Absorber
Source abstract
Abstract
The dynamic vibration absorber (DVA) is widely used in engineering models with complex vibration modes. The research on the stability and periodic motions of the DVA model plays an important role in revealing its complex vibration modes and energy transfer. The aim of this paper is to study the stability and periodic motions of a two-degrees-of-freedom system coupled with an encapsulated nonsmooth dynamic vibration absorber under low-frequency forced excitation. Based on the slow–fast method, the model is transformed into a six-dimensional piecewise smooth system coupling two time scales. The existence and stability of the admissible equilibrium points for the model are discussed under different parameter conditions. Based on the first integrals, the Melnikov vector function of the nonsmooth dynamic vibration absorber model is calculated. The existence and number of periodic orbits bifurcated from a family of periodic orbits under different parameters are discussed. The phase diagram configuration of periodic orbits is given based on numerical simulation. The results obtained in this paper offer a new perspective for vibration analysis and parameter control for nonsmooth dynamic vibration absorbers.
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Research context
OpenAlex topics: Vibration Control and Rheological Fluids · Magnetic Bearings and Levitation Dynamics · Brake Systems and Friction Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing 100124, China
Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China
Funding
National Natural Science Foundation of China · National Key R&D Program of China
References (34)
Show source-provided references
1. Research developments in vibration control of structures using passive tuned mass dampers10.1016/j.arcontrol.2017.09.015 ↗
2. Influence of temperature on the passive control of a rotating machine using wires of shape memory alloy in the suspension10.1088/1361-665X/ab7112 ↗
3. The theory of the dynamic vibration absorber
4. Frahm, H. (1909). Device for Damping Vibrations of Bodies. (0,989,958), U.S. Patent.
5. Synthesis of a nonlinear dynamic vibration absorber10.1016/0016-0032(52)90457-2 ↗
6. Theory of the dynamic vibration neutralizer with motion limiting stops10.1115/1.3422718 ↗
7. Dynamics of multiple-degree-of-freedom oscillators with colliding components10.1006/jsvi.1993.1269 ↗
8. On the design of the piecewise linear vibration absorber10.1023/A:1008309409223 ↗
9. Shock isolation through passive energy pumping caused by nonsmooth nonlinearities10.1142/S0218127405013101 ↗
10. Targeted energy transfer in systems with non-polynomial nonlinearity10.1016/j.jsv.2007.12.024 ↗
11. Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink10.1007/s00707-011-0492-0 ↗
12. Control of vertical oscillations of a cable by a piecewise linear absorber10.1016/j.jsv.2018.07.033 ↗
13. A novel energy sink with piecewise linear stiffness10.1007/s11071-018-4488-3 ↗
14. Performance of non-smooth nonlinear energy sink with descending stiffness10.1007/s11071-020-05528-3 ↗
15. Development and validation of a piecewise linear nonlinear energy sink for vibration suppression and energy harvesting10.1016/j.jsv.2021.116104 ↗
16. Theoretical and experimental study of an enhanced nonlinear energy sink10.1007/s11071-021-06553-6 ↗
17. Two-modal resonance control with an encapsulated nonlinear energy sink10.1016/j.jsv.2021.116667 ↗
18. Vibration suppression and modal energy transfers in a linear beam with attached vibro-impact nonlinear energy sinks10.1016/j.cnsns.2020.105415 ↗
19. Study of mixed-mode oscillations in a parametrically excited van der Pol system10.1007/s11071-014-1377-2 ↗
20. Amer, T.S., Starosta, R., Almahalawy, A., and Elameer, A.S. (2022). The stability analysis of a vibrating auto-parametric dynamical system near resonance. Appl. Sci., 12.10.3390/app12031737 ↗
21. Stability of three degrees-of-freedom auto-parametric system10.1016/j.aej.2022.01.064 ↗
22. Modeling and analysis of a piezoelectric transducer embedded in a nonlinear damped dynamical system10.1007/s11071-023-08283-3 ↗
23. Modeling and analyzing the motion of a 2DOF dynamical tuned absorber system close to resonance10.1007/s00419-022-02299-8 ↗
24. Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber10.1007/s11071-020-05725-0 ↗
25. Vibration reduction mechanism of Van der Pol oscillator under low-frequency forced excitation by means of nonlinear energy sink10.1016/j.ijnonlinmec.2023.104389 ↗
26. Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments10.1016/j.physd.2009.06.013 ↗
27. Vibration absorption in systems with a nonlinear energy sink: Nonlinear damping10.1016/j.jsv.2009.02.052 ↗
28. Dynamics of coupled DAHL type and nonsmooth systems at different scales of time10.1142/S0218127413501149 ↗
29. Periodic motion and frequency energy plots of dynamical systems coupled with piecewise nonlinear energy sink10.1115/1.4053509 ↗
30. A ground-limited nonlinear energy sink10.1007/s10409-022-09027-x ↗
31. Hong, J., Jiang, L.M., Wang, Y.F., Su, Z.M., and Ma, Y.H. (2022). Nonlinear dynamics of an elastic stop system and its application in a rotor system. Appl. Sci., 12.10.3390/app12105103 ↗
32. Unique normal form of a class of 3 dimensional vector fields with symmetries10.1016/j.jde.2014.05.039 ↗
33. di Bernardo, M., Budd, C.J., Champneys, A.R., and Kowalczyk, P. (2008). Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer.
34. Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds10.1016/j.cnsns.2022.106840 ↗