Extension of the domain of applicability of the integral stability criterion (extremum property) in synchronization problems

Blekhman, I. I.; Yaroshevich, Nikolay

doi:10.1016/j.jappmathmech.2004.11.005

Cited by 38 publications

(21 citation statements)

References 5 publications

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“…4 Using the method of direct separation of motions and the Poincare-Lyapunov small-parameter method, Blekhman proposed the synchronization theory of vibrating machines with two or more URs and has successfully solved a number of self-synchronization, such as self-synchronization of the unbalanced and planetary URs on a flatly oscillating solid body, self-synchronization of the URs on the spatially oscillating softly vibrato-isolated solid body, selfsynchronization of the URs in the carrying vibrating systems with collisions of the bodies, and so on. [4][5][6][7][8] In view of engineering applications, Chinese Scholar Wen applied such methods to develop the theories of selfsynchronization of two URs in vibrating systems of circular motion, linear motion, centroid rotation motion, and spatial motion and established a branch of vibration utilization engineering. [9][10][11][12] The key to develop vibrating machines with multiple URs lies in the fact that the coupling characteristics of the system and its internal law of the distribution of energy must be understood perfectly.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of synchronization for four hydraulic motors in a vibrating pile driver system

Bin

Zhao

Wang

et al. 2016

Advances in Mechanical Engineering

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This article proposes a self-synchronous vibrating mechanism with four unbalanced rotors driven by four hydraulic motors mounted symmetrically on two coaxial rotating beams. Analytical expressions of the steady-state response for the multi-body vibrating system are deduced. The dimensionless coupling equations of the four unbalanced rotors are derived by virtue of the averaging method of modified small parameters. The synchronization and stability criteria are deduced using the existence and stability of the zero solution for the dimensionless coupling equations of the four unbalanced rotors. The coefficients of synchronization ability are defined. By numeric analysis, effect of the dynamic parameters on the characteristics of coupling dynamics for the unbalanced rotors is discussed to determine dynamic parameter intervals of synchronization stability. Computer simulations are carried out to verify the correctness of the theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

Dynamics of synchronization for four hydraulic motors in a vibrating pile driver system

Bin

Zhao

Wang

et al. 2016

Advances in Mechanical Engineering

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“…Blekhman et al [1] and Blekhman and Yaroshevich [2] proposed the self-synchronization theory of vibration system driven by two induction motors. When the structure parameters of the two motors meet the requirements, the system can be operated as synchronously.…”

Section: Introductionmentioning

confidence: 99%

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

Liú

Jiang

et al. 2015

Appl. Math. Mech.-Engl. Ed.

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This paper studies self-synchronization and stability of a dual-motor driven vibration system with a two-stage vibration isolation frame. Oscillation amplitude of the material box large enough can be ensured on the vibration system in order to screen materials. Reduction of the dynamic load transmitted to the foundation can also be achieved for the vibration system. A Lagrange equation is used to set up the motion differential equations of the system, and a dimensionless coupled equation of the eccentric rotors is obtained using a method of modified average small parameter. According to the existence condition of zero solution in the dimensionless coupled equation of the eccentric rotors, the precondition for commencing self-synchronization motion is achieved. The stability condition of self-synchronization is obtained based on the Routh-Hurwitz criterion. The theoretical analysis is validated by simulations and experiments.

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“…Synchronization has been also investigated in nonlinear circuits by many researchers, such as Rayleigh, Vincent, Moler, etc [2]. In the 1960s, Blekhman [3][4][5][6][7][8][9] proposed the selfsynchronization theory of vibration mechanism driven by two induction motors, which was that two induction motors installed in a vibration mechanism could operate synchronously when their structure parameters met certain requirements. Sperling [10,11] described a well suited method for the derivation of the conditions for the existence and the stability of synchronous motion by applying harmonic influence coefficients.…”

Section: Introductionmentioning

confidence: 99%

The self-synchronous theory of a dual-motor driven vibration mechanism without shimmy

Liú

et al. 2015

Arch Appl Mech

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The paper focuses on the self-synchronous motion and stabilizing conditions of a vibration mechanism driven by dual-motor, which can eliminate the shimmy. The differential equations of motion of the vibration mechanism are derived by applying Lagrange's equation and the dimensionless coupled equations of the exciters with a modified average small parameter method are obtained. The condition of existence for zero solution of the dimensionless coupled equation is used to derive the condition for the self-synchronous motion of the vibration mechanism. The stability condition of self-synchronous motion is obtained according to the Routh-Hurwitz criterion. Afterward, the numerical simulations are carried out to verify the results of the theoretical analysis. The results are concluded that increasing the mass ratio of the two exciters and decreasing the frequency ratio along the vertical direction, the angle of the resonant excitation and the mass ratio of the inner rigid body against the vibration system are all able to enhance the ability of self-synchronization of the vibration mechanism. The simulation results are finally validated by experiments.

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Extension of the domain of applicability of the integral stability criterion (extremum property) in synchronization problems

Cited by 38 publications

References 5 publications

Dynamics of synchronization for four hydraulic motors in a vibrating pile driver system

Dynamics of synchronization for four hydraulic motors in a vibrating pile driver system

Self-synchronization theory of dual motor driven vibration system with two-stage vibration isolation frame

The self-synchronous theory of a dual-motor driven vibration mechanism without shimmy

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