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Статті в журналах з теми "Vibroimpact system"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Yu, B. S., and H. Wen. "Vibroimpact Dynamics of a Tethered Satellite System." Shock and Vibration 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/8748094.

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This paper presents the vibroimpact dynamics of an in-plane tethered subsatellite caused by sudden braking during deployment or retrieval. The full dynamics of the subsatellite are composed of its free-flight and the instantaneous impacts. At the moment of impact, the reflective angle of the subsatellite is envisioned to be equal to its incident angle such that the impact law is obtained. Then, the stability of the periodic vibroimpacts is analyzed using the composite Poincaré map. Further, the vibroimpact responses that do not exceed a specified region are numerically determined via the cell mapping method.

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2

Nguyen, V. D., and K. C. Woo. "New electro-vibroimpact system." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 4 (April 1, 2008): 629–42. http://dx.doi.org/10.1243/09544062jmes833.

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In this paper, a new vibro-impact mechanism based on a solenoid-actuated vibrator and its optimization are presented. The vibratory unit deploying electro-mechanical interactions of a conductor with oscillating magnetic field has been realized. The combination of resonance in an RLC circuit and a solenoid is found to create an oscillatory motion to the metal bar within the solenoid. This results in impacts of the metal bar on an obstacle block. Unanimously, the electromagnetic force generated within the solenoid acts as a non-linear electromagnetic spring. Hence, a vibro-impact mechanism gets created. This system is improved by adding a solid-state relay in series to the RLC circuit, which switches the power supply on and off periodically in accordance to a train of square waves produced by a function generator. This new control over the supplied harmonic voltage allows a small scale in the geometry of the vibratory unit but significantly increases the magnitude of impact forces and the progression rates obtained. This implies a very promising deployment of the mechanism in actual soil conditions.

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3

Yang, Guidong, Wei Xu, Dongmei Huang, and Mengli Hao. "Stochastic Responses of Lightly Nonlinear Vibroimpact System with Inelastic Impact Subjected to External Poisson White Noise Excitation." Mathematical Problems in Engineering 2018 (2018): 1–12. http://dx.doi.org/10.1155/2018/3627195.

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A procedure for analyzing stationary responses of lightly nonlinear vibroimpact system with inelastic impact subjected to external Poisson white noise excitation is proposed. First, the original vibroimpact system is transformed to a new system without velocity jump in terms of the Zhuravlev nonsmooth coordinate transformation and the Dirac delta function. Second, the averaged generalized Fokker-Planck-Kolmogorov (FPK) equation for transformed system under parametric excitation of Poisson white noise is derived by stochastic averaging method. Third, the averaged generalized FPK equation is solved by using the perturbation technique and inverse transformation of the Zhuravlev nonsmooth coordinate transformation to obtain the approximately stationary solutions for response probability density functions of original vibroimpact system. Last, analytical and numerical results for two typical lightly nonlinear vibroimpact systems are presented to assess the effectiveness of the proposed method. It is found that they are in good agreement and the proposed method is quite effective.

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4

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Comparison of Two Impact Simulation Methods Used for Nonlinear Vibroimpact Systems with Rigid and Soft Impacts." Journal of Nonlinear Dynamics 2013 (September 24, 2013): 1–12. http://dx.doi.org/10.1155/2013/485676.

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This paper compares the use of two impact simulation methods for two-degree-of-freedom nonlinear vibroimpact systems with rigid and soft impacts. These methods are (I) impact simulation by boundary conditions with the use of Newton's restitution coefficient based on stereomechanic shock theory and (II) impact simulation by contact interaction force based on quasistatic Hertz's contact theory. It is shown that both methods are applied and give the coinciding results for system with elastic rigid impact under periodic external loading. Loading curves built by parameter continuation method are confirming this result. Impact simulation by the second method is also fulfilled for vibroimpact system with rigid impact under random external loading. For vibroimpact system with soft impact, the simulation of impact by the second method gives a better result. The application of linear elastic force as contact one is possible too but the use of Hertz's contact force is more preferable. The authors consider that the impact simulation by Hertz contact interaction force gives good results for nonlinear vibroimpact systems with impacts of any kind if all limitations with Hertz's law used are observed.

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5

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Contact Impact Forces at Discontinuous 2-DOF Vibroimpact." Applied Mathematics and Nonlinear Sciences 1, no. 1 (March 14, 2016): 183–96. http://dx.doi.org/10.21042/amns.2016.1.00014.

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AbstractDynamic behaviour of contact impact forces in strongly nonlinear discontinuous vibroimpact system is studying. Contact impact force is one of the most significant vibroimpact system characteristics. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods. We simulate the impact by nonlinear contact interactive force according to Hertz’s contact law. This paper is the continuation of the previous works [1,2]. We have determined the instability zones and bifurcations points for loading curves [1] and frequency-amplitude response [2] under variation of excitation amplitude and frequency. In this paper we investigate the behaviour of contact forces at bifurcation points particularly at discontinuous bifurcation points where set-valued Floquet multipliers cross the unit circle by jump that is their moduli becoming more than unit by jump. It is phenomenon unique for nonsmooth systems with discontinuous right-hand side. We observe also the contact forces increase at nT -periodical multiple impacts regimes. We also learn the change of contact forces behaviour when the impact between system bodies became the soft one due the change of system parameters.

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6

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Intermittent transition to chaos in vibroimpact system." Applied Mathematics and Nonlinear Sciences 3, no. 2 (December 1, 2018): 475–86. http://dx.doi.org/10.2478/amns.2018.2.00037.

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AbstractChaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.

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7

Yurchenko, Daniil, Andrea Burlon, Mario Di Paola, Giuseppe Failla, and Antonina Pirrotta. "Stochastic response of a fractional vibroimpact system." Procedia Engineering 199 (2017): 1086–91. http://dx.doi.org/10.1016/j.proeng.2017.09.081.

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8

BAZHENOV, V. A., O. S. Pogorelova, and T. G. Postnikova. "Dangerous bifurcations in 2-dof vibroimpact system." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 26 (September 23, 2016): 109–13. http://dx.doi.org/10.20998/2078-9130.2016.26.82732.

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9

SHIMIZU, Yasuhiro, Hiroki MORI, Takahiro KONDOU, and Nobuyuki SOWA. "Low Frequency Vibration of a Vibroimpact System." Proceedings of Conference of Kyushu Branch 2017.70 (2017): 1113. http://dx.doi.org/10.1299/jsmekyushu.2017.70.1113.

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10

OGAWA, Ryo, Hiroki MORI, Takahiro KONDOU, Nobuyuki SOWA, and Tomohiro ABE. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2019 (2019): 122. http://dx.doi.org/10.1299/jsmedmc.2019.122.

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11

SHIMIZU, Yasuhiro, Hiroki MORI, Takahiro KONDOU, Nobuyuki SOWA, and Kazushi KAYAOKA. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2017 (2017): 353. http://dx.doi.org/10.1299/jsmedmc.2017.353.

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12

KAYAOKA, Kazushi, Hiroki MORI, Takahiro KONDOU, Nobuyuki SOWA, and Yasuhiro SHIMIZU. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2018 (2018): 106. http://dx.doi.org/10.1299/jsmedmc.2018.106.

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13

MORI, Hiroki, Tomohiro ABE, Takahiro KONDOU, Nobuyuki SOWA, and Kazushi KAYAOKA. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2018 (2018): 107. http://dx.doi.org/10.1299/jsmedmc.2018.107.

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14

SHIMIZU, Yasuhiro, Hiroki MORI, and Takahiro KONDOU. "Low Frequency Vibration of a Vibroimpact System." Proceedings of Mechanical Engineering Congress, Japan 2016 (2016): G1000703. http://dx.doi.org/10.1299/jsmemecj.2016.g1000703.

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15

ABE, Tomohiro, Hiroki MORI, Takahiro KONDOU, Nobuyuki SOWA, and Ryo OGAWA. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2020 (August 25, 2020): 138. http://dx.doi.org/10.1299/jsmedmc.2020.138.

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16

OTANI, Shinya, Hiroki MORI, Takahiro KONDOU, and Nobuyuki SOWA. "Low Frequency Vibration of a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2020 (August 25, 2020): 137. http://dx.doi.org/10.1299/jsmedmc.2020.137.

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17

Nguyen, V. D., and K. C. Woo. "Nonlinear dynamic responses of new electro-vibroimpact system." Journal of Sound and Vibration 310, no. 4-5 (March 2008): 769–75. http://dx.doi.org/10.1016/j.jsv.2007.10.032.

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18

MORI, Hiroki, Takuo NAGAMINE, Tsubasa KOYAMA, and Yuichi SATO. "Self-Excited Vibration Generated in a Vibroimpact System." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C 77, no. 782 (2011): 3637–47. http://dx.doi.org/10.1299/kikaic.77.3637.

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19

Zhou, Jianxing, Wenlei Sun, and Liang Yuan. "Nonlinear Vibroimpact Characteristics of a Planetary Gear Transmission System." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/4304525.

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Анотація:

In order to research the vibroimpact characteristics of a planetary gear transmission system under high speed and lightly loaded conditions, a new modeling method is proposed. In the modeling process, linear spring was used to simulate gear mesh elasticity under heavy load cases, and Hertz contact theory was used to calculate the contact force of gear pair under light load cases. Then, effects of the working conditions on the system vibroimpact characteristics are analyzed. The results show that, with input speed growing, the mesh force produced obvious fluctuations on the resonance frequencies of the sun gear and carrier torsion vibration, ring gear’s transverse vibration under the heavy load. Under light load condition, the collision vibration occurs in the gear pair; the changing trend of the contact force shows strongly nonlinear characteristics. The time of mesh-apart in gears pair decreases gradually as the load is increased; until it reaches collision vibration threshold value, the gear pair is no longer mesh-apart. With increasing of the input speed, the time of mesh-apart is decreased gradually; the fluctuation amplitude of contact force shows a linearly increasing trend. The study provides useful theoretical guideline for planetary gear transmission low-noise design.

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20

Li, Qunhong, Limei Wei, Jieyan Tan, and Jiezhen Xi. "Double Grazing Periodic Motions and Bifurcations in a Vibroimpact System with Bilateral Stops." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/642589.

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The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system.

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21

Banakh, Liudmila, and Andrey Nikiforov. "Vibroimpact regimes and stability of system “Rotor—Sealing Ring”." Journal of Sound and Vibration 308, no. 3-5 (December 2007): 785–93. http://dx.doi.org/10.1016/j.jsv.2007.03.073.

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22

Bazhenov, Viktor, Olga Pogorelova, and Tatiana Postnikova. "Transitional regimes under route to chaos in vibroimpact system." Strength of Materials and Theory of Structures, no. 102 (July 12, 2019): 37–45. http://dx.doi.org/10.32347/2410-2547.2019.102.37-45.

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23

MORI, Hiroki, Takuo NAGAMINE, Takahiro KURATOMI, and Yuichi SATO. "11207 Low Frequency Vibration Generated in a Vibroimpact System." Proceedings of Conference of Kanto Branch 2013.19 (2013): 155–56. http://dx.doi.org/10.1299/jsmekanto.2013.19.155.

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24

Wang, Zihan, Jieqiong Xu, Shuai Wu, and Quan Yuan. "Control of Near-Grazing Dynamics in the Two-Degree-of-Freedom Vibroimpact System with Symmetrical Constraints." Complexity 2020 (April 10, 2020): 1–12. http://dx.doi.org/10.1155/2020/7893451.

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Анотація:

The stability of grazing bifurcation is lost in three ways through the local analysis of the near-grazing dynamics using the classical concept of discontinuity mappings in the two-degree-of-freedom vibroimpact system with symmetrical constraints. For this instability problem, a control strategy for the stability of grazing bifurcation is presented by controlling the persistence of local attractors near the grazing trajectory in this vibroimpact system with symmetrical constraints. Discrete-in-time feedback controllers designed on two Poincare sections are employed to retain the existence of an attractor near the grazing trajectory. The implementation relies on the stability criterion under which a local attractor persists near a grazing trajectory. Based on the stability criterion, the control region of the two parameters is obtained and the control strategy for the persistence of near-grazing attractors is designed accordingly. Especially, the chaos near codimension-two grazing bifurcation points was controlled by the control strategy. In the end, the results of numerical simulation are used to verify the feasibility of the control method.

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25

Blazejczyk-Okolewska, Barbara, and Wioleta Serweta. "A Method to Determine Structural Patterns of Mechanical Systems with Impacts." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/757980.

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Анотація:

A structural classification of vibroimpact systems based on the principles given by Blazejczyk-Okolewska et al. (2004) has been proposed for an arbitrary finite number of degrees-of-freedom. A new matrix representation to formulate the notation of the relations occurring in the system has been introduced. The developed identification and elimination procedures of equivalent systems and identification procedures of connected systems enable the determination of a set of structural patterns of systems with impacts.

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26

Ritto, T. G., F. S. Buezas, and Rubens Sampaio. "Proper orthogonal decomposition for model reduction of a vibroimpact system." Journal of the Brazilian Society of Mechanical Sciences and Engineering 34, no. 3 (September 2012): 330–40. http://dx.doi.org/10.1590/s1678-58782012000300013.

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27

Bazhenov, Viktor, Olga Pogorelova, Tatiana Postnikova, and Olga Lukianchenko. "Wavelet transform using for analysis of vibroimpact system chaotic behavior." Strength of Materials and Theory of Structures, no. 101 (December 30, 2018): 14–25. http://dx.doi.org/10.32347/2410-2547.2018.101.14-25.

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28

TAKATA, Souichiro, Shigeo KOTAKE, and Hiroaki HANAI. "459 Formulation of Grover Quantum Algorithm from multi vibroimpact system." Proceedings of Conference of Tokai Branch 2008.57 (2008): 309–10. http://dx.doi.org/10.1299/jsmetokai.2008.57.309.

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29

Avramov, K. V. "Application of nonsmooth transformations to analyze a vibroimpact duffing system." International Applied Mechanics 44, no. 10 (October 2008): 1173–79. http://dx.doi.org/10.1007/s10778-009-0135-5.

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30

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Breakup of Closed Curve - Quasiperiodic Route to Chaos in Vibroimpact System." Interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 8, no. 3 (September 2019): 299–311. http://dx.doi.org/10.5890/dnc.2019.09.006.

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31

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Change of impact kind in vibroimpact system due its parameters changing." MATEC Web of Conferences 16 (2014): 05007. http://dx.doi.org/10.1051/matecconf/20141605007.

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32

Xu Wei, Yang Gui-Dong, and Yue Xiao-Le. "P-bifurcations of a Duffing-Rayleigh vibroimpact system under stochastic parametric excitation." Acta Physica Sinica 65, no. 21 (2016): 210501. http://dx.doi.org/10.7498/aps.65.210501.

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33

MORI, Hiroki, Takuo NAGAMINE, Takahiro KURATOMI, and Yuichi SATO. "113 Study on Mechanism of Self-Excited Vibration of a Vibroimpact System." Proceedings of the Symposium on Evaluation and Diagnosis 2011.10 (2011): 53–56. http://dx.doi.org/10.1299/jsmesed.2011.10.53.

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34

Bazhenov, V. A., O. S. Pogorelova, and T. G. Postnikova. "Study of Routes to Chaos in Vibroimpact System with Continuous Wavelet Transform." Journal of Vibration Testing and System Dynamics 3, no. 3 (September 2019): 281–96. http://dx.doi.org/10.5890/jvtsd.2019.09.003.

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35

Wang, Jingyue, Haotian Wang, and Tie Wang. "External Periodic Force Control of a Single-Degree-of-Freedom Vibroimpact System." Journal of Control Science and Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/570137.

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Анотація:

A single-degree-of-freedom mechanical model of vibro-impact system is established. Bifurcation and chaos in the system are revealed with the time history diagram, phase trajectory map, and Poincaré map. According to the bifurcation and chaos of the actual vibro-impact system, the paper puts forward external periodic force control strategy. The method of controlling chaos by external periodic force feedback controller is developed to guide chaotic motions towards regular motions. The stability of the control system is also analyzed especially by theory. By selecting appropriate feedback coefficients, the unstable periodic orbits of the original chaotic orbit can be stabilized to the stable periodic orbits. The effectiveness of this control method is verified by numerical simulation.

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36

MORI, Hiroki, Takuo NAGAMINE, Tsubasa KOYAMA, and Yuichi SATO. "306 Analytical Study on Self-Excited Vibration Generated in a Vibroimpact System." Proceedings of the Dynamics & Design Conference 2011 (2011): _306–1_—_306–8_. http://dx.doi.org/10.1299/jsmedmc.2011._306-1_.

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37

Nazarenko, Ivan, Mykola Ruchynskyi, and Maksym Delembovskyi. "The Basic Parameters of Vibration Settings for Sealing Horizontal Surfaces." International Journal of Engineering & Technology 7, no. 3.2 (June 20, 2018): 255. http://dx.doi.org/10.14419/ijet.v7i3.2.14415.

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Анотація:

Are examined and defined pattern vibratory motion to form horizontal surfaces on the basis of the account of wave phenomena and bias voltages. Given numerical values screeds and rheological characteristics of sealing concrete.Based on the analysis of the energy balance, motion qualities limits are defined. Analytical dependences for the estimation of main parameters of the effective vibroimpact mode are suggested as well as the motion stability layout of the analyzed system is cited.

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38

Ding, Jie, Chao Wang, and Wangcai Ding. "Periodic Motion and Transition of a Vibro‐Impact System with Multilevel Elastic Constraints." Discrete Dynamics in Nature and Society 2021 (February 9, 2021): 1–13. http://dx.doi.org/10.1155/2021/6687887.

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Анотація:

In this paper, a single-degree-of-freedom vibroimpact system with multilevel elastic constraints is taken as the research object. By constructing the Poincaré map of the system and calculating the Lyapunov exponent spectrum of the system, the stability of the system is determined. Using the multiparameter collaborative numerical simulation method, the parameter domains of various periodic motions are determined, and the diversity and transition characteristics of periodic motions are revealed. At the same time, combined with the cell mapping method, the coexistence of attractors induced due to grazing bifurcation, saddle-node bifurcation, and boundary crisis is studied. Finally, the influence of system parameters on periodic motion distribution is analyzed, which provides a scientific basis for system parameter optimization.

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39

Liu, A. Q., B. Wang, Y. S. Choo, and K. S. Ong. "The Effective Design of Bean Bag as a Vibroimpact Damper." Shock and Vibration 7, no. 6 (2000): 343–54. http://dx.doi.org/10.1155/2000/351576.

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Анотація:

The technique of a bean bag damper has been effectively applied in many engineering fields to control the vibroimpact of a structural system. In this study, the basic parameters responsible for the design of an effective bean bag: the size of beans, the mass ratio of the bean bag to the structure to which it is attached, the clearance distance and the position of the bag, are studied by both theoretical and experimental analyses. These will provide a better understanding of the performance of the bean bag for optimisation of damper design. It was found that reducing the size of beans would increase the exchange of momentum in the system due to the increase in the effective contact areas. Within the range of mass ratios studied, the damping performance of the damper was found to improve with higher mass ratios. There was an optimum clearance for any specific damper whereby the maximum attenuation could be achieved. The position of the bag with respect to nodes and antipodes of the primary structure determined the magnitude of attenuation attainable. Furthermore, the limitations of bean bags have been identified and a general criteria for the design of a bean bag damper has been formulated based on the study undertaken. It was shown that an appropriately configured bean bag damper was capable of reducing the amplitude of vibration by 80% to 90%.

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40

Perret-Liaudet, Joël, and Emmanuel Rigaud. "Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments." Journal of Computational and Nonlinear Dynamics 2, no. 2 (December 21, 2006): 190–96. http://dx.doi.org/10.1115/1.2447549.

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Анотація:

The purpose of this paper is to investigate experimental responses of a preloaded vibroimpact Hertzian contact to an order 2 superharmonic excitation. A test rig is used, corresponding to a double sphere–plane contact preloaded by the weight of a moving body. Typical response curves are obtained under the superharmonic excitation. The Hertzian nonlinearity constitutes the precursor of vibroimpacts established over a wide frequency range. This behavior can be related to the existence of a transcritical bifurcation. In conjuction with the experiments, numerical results lead to the same conclusion. In particular, the threshold level of the excitation necessary to induce vibroimpact is confirmed.

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41

Ritto, T. G., F. S. Buezas, and Rubens Sampaio. "A new measure of efficiency for model reduction: Application to a vibroimpact system." Journal of Sound and Vibration 330, no. 9 (April 2011): 1977–84. http://dx.doi.org/10.1016/j.jsv.2010.11.004.

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42

Yang, Yongge, Wei Xu, Yahui Sun, and Yanwen Xiao. "Stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation." Communications in Nonlinear Science and Numerical Simulation 42 (January 2017): 62–72. http://dx.doi.org/10.1016/j.cnsns.2016.05.004.

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43

Shokhin, A. E., K. V. Krestnikovskii, and A. N. Nikiforov. "On self-synchronization of inertial vibration exciters in a vibroimpact three-mass system." IOP Conference Series: Materials Science and Engineering 1129, no. 1 (April 1, 2021): 012041. http://dx.doi.org/10.1088/1757-899x/1129/1/012041.

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44

MORI, Hiroki, Takuo NAGAMINE, Takanori KOBAYASHI, and Yuichi SATO. "10906 Suppression of Low Frequency Vibration of a Vibroimpact System by a Dynamic Absorber." Proceedings of Conference of Kanto Branch 2014.20 (2014): _10906–1_—_10906–2_. http://dx.doi.org/10.1299/jsmekanto.2014.20._10906-1_.

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45

Bazhenov, V. A., P. P. Lizunov, O. S. Pogorelova, and T. G. Postnikova. "Numerical Bifurcation Analysis of Discontinuous 2-DOF Vibroimpact System. Part 2: Frequency-Amplitude Response." Journal of Applied Nonlinear Dynamics 5, no. 3 (September 2016): 269–81. http://dx.doi.org/10.5890/jand.2016.09.002.

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46

Rong, Hai-wu, Xiang-dong Wang, Qi-zhi Luo, Wei Xu, and Tong Fang. "Subharmonic response of single-degree-of-freedom linear vibroimpact system to narrow-band random excitation." Applied Mathematics and Mechanics 32, no. 9 (August 10, 2011): 1159–68. http://dx.doi.org/10.1007/s10483-011-1489-x.

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47

Ganiev, M. M., and I. M. Ganiev. "Dynamic Model of Ultrasonic Microforging in a Rod Vibroimpact System with a Rigidly Adjusted Gap." Journal of Machinery Manufacture and Reliability 49, no. 7 (December 2020): 584–90. http://dx.doi.org/10.3103/s1052618820070079.

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48

Rong, Haiwu, and Xiangdong Wang. "Subharmonic Response of Linear Vibroimpact System with Fractional Derivative Damping to a Randomly Disrobed Periodic Excitation." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/208096.

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Анотація:

The subharmonic response of single-degree-of-freedom vibroimpact oscillator with fractional derivative damping and one-sided barrier under narrow-band random excitation is investigated. With the help of a special Zhuravlev transformation, the system is reduced to one without impacts, thereby permitting the applications of asymptotic averaging over the period for slowly varying random process. The analytical expression of the response amplitude is obtained in the case without random disorder, while only the approximate analytical expressions for the steady-state moments of the response amplitude are obtained in the case with random disorder. The effects of the fractional order derivative term, damping term, random disorder, and the coefficient of restitution and other system parameters on the system response are discussed. Theoretical analyses and numerical simulations show that fractional derivative makes both the system damping and stiffness coefficients increase, such that it changes the system parameters region at which the response amplitude reaches the maximum. The system energy loss in collision is equivalent to increasing the damping coefficient of the system. System response amplitude will increase when the excitation frequency is close to the resonant frequency and will decay rapidly when the excitation frequency gradually deviates from the resonance frequency.

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49

Li, Qunhong, Pu Chen, and Jieqiong Xu. "Codimension-Two Grazing Bifurcations in Three-Degree-of-Freedom Impact Oscillator with Symmetrical Constraints." Discrete Dynamics in Nature and Society 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/353581.

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This paper investigates the codimension-two grazing bifurcations of a three-degree-of-freedom vibroimpact system with symmetrical rigid stops since little research can be found on this important issue. The criterion for existence of double grazing periodic motion is presented. Using the classical discontinuity mapping method, the Poincaré mapping of double grazing periodic motion is obtained. Based on it, the sufficient condition of codimension-two bifurcation of double grazing periodic motion is formulated, which is simplified further using the Jacobian matrix of smooth Poincaré mapping. At the end, the existence regions of different types of periodic-impact motions in the vicinity of the codimension-two grazing bifurcation point are displayed numerically by unfolding diagram and phase diagrams.

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50

Haiwu, Rong, Wang Xiangdong, Luo Qizhi, Xu Wei, and Fang Tong. "Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/967395.

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Анотація:

The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.

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