scholarly journals Nonlinear Dynamics of a Blade Rotor with Coupled Rubbing of Labyrinth Seal and Tip Seal

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Huabiao Zhang ◽  
Xinye Li ◽  
Dongai Wang ◽  
Tingting Liu
Keyword(s):  
Shooting Method ◽  
Rotation Velocity ◽  
Labyrinth Seal ◽  
Dynamic Equations ◽  
Almost Periodic ◽  
Contact Deformation ◽  
Periodic Motions ◽  
Bifurcation Diagrams ◽  
Hertz Contact ◽  
Chaotic Motions

The dynamic response and its stability of a blade rotor with coupled rubbing in the labyrinth seal and tip seal are investigated. The dynamic equations are established based on the Hertz contact rubbing force at the labyrinth seal and the tip rubbing force considering both the contact deformation of the tip seal and the bending deformation of the blade. Numerical simulations show that the coupled rubbing response includes periodic motions, almost periodic motions, and chaotic motions. Compared with the single rubbing fault, coupled rubbing increases the range of rotation velocity of contact. A new continuation shooting method is used in the solution and stability analysis of the periodic response to give the bifurcation diagrams. The paths of the system for entering and exiting chaos are analyzed.

scholarly journals Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

2011 ◽  
Vol 18 (1-2) ◽  
pp. 365-375 ◽  
Author(s):  
Qingkai Han ◽  
Xueyan Zhao ◽  
Xingxiu Li ◽  
Bangchun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Domain ◽  
Shooting Method ◽  
Viscous Friction ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Amplitude Spectra ◽  
Set Up ◽  
Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

scholarly journals Dynamics of Bohr almost periodic motions of topological abelian semigroups

2016 ◽  
Vol 95 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Xiongping Dai
Keyword(s):  
Almost Periodic ◽  
Periodic Motions

Nonlinear Vibrations and Chaotic Dynamics of the Laminated Composite Piezoelectric Beam

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang ◽  
Zhigang Yao
Keyword(s):  
Numerical Simulation ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Dynamical Behavior ◽  
Laminated Composite ◽  
Transverse Load ◽  
Nonlinear Phenomenon ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Piezoelectric Beam

This paper investigates the complicated dynamics behavior and the evolution law of the nonlinear vibrations of the simply supported laminated composite piezoelectric beam subjected to the axial load and the transverse load. Using the third-order shear deformation theory and the Hamilton's principle, the nonlinear governing equations of motion for the laminated composite piezoelectric beam are derived. Applying the method of multiple scales and Galerkin's approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of principal parametric resonance and 1:9 internal resonance. From the averaged equations obtained, numerical simulation is performed to study nonlinear vibrations of the laminated composite piezoelectric beam. The axial load, the transverse load, and the piezoelectric parameter are selected as the controlling parameters to analyze the law of complicated nonlinear dynamics of the laminated composite piezoelectric beam. Based on the results of numerical simulation, it is found that there exists the complex nonlinear phenomenon in motions of the laminated composite piezoelectric beam. In summary, numerical studies suggest that periodic motions and chaotic motions exist in nonlinear vibrations of the laminated composite piezoelectric beam. In addition, it is observed that the axial load, the transverse load and the piezoelectric parameter have significant influence on the nonlinear dynamical behavior of the beam. We can control the response of the system from chaotic motions to periodic motions by changing these parameters.

Internal Resonance of the Jeffcott Rotor With Nonlinear Spring Characteristics

2001 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Jeffcott Rotor ◽  
Two Degree Of Freedom

Abstract The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model executing lateral whirling motions has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward whirling mode pf and that of a backward whirling mode pb have the relation of internal resonance pf : pb = 1 : (−1). Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. While, in many cases of the practical rotating machinery, such a relationship holds apprximately due to small gyroscopic moment. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with small gyroscopic moment. Especially, the influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance, (b) almost-periodic motions occur, (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment, and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incrrect results.

Dynamics of a Simplified van der Pol Oscillator Revisited

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Bifurcation Analysis ◽  
Local Stability ◽  
Van Der Pol Oscillator ◽  
Nonsmooth Dynamics ◽  
Mapping Technique ◽  
Periodic Motions ◽  
Van Der Pol ◽  
Chaotic Motions ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, the dynamic characteristics of a simplified van der Pol oscillator are investigated. From the theory of nonsmooth dynamics, the structures of periodic and chaotic motions for such an oscillator are developed via the mapping technique. The periodic motions with a certain mapping structures are predicted analytically for m-cycles with n-periods. Local stability and bifurcation analysis for such motions are carried out. The (m:n)-periodic motions are illustrated. The further investigation of the stable and unstable periodic motions in such a system should be completed. The chaotic motion based on the Levinson donuts should be further discussed.

Bifurcation Analysis of a Fermi-Acceleration Oscillator Under Different Excitations

2011 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yu Guo
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Fermi Acceleration ◽  
Periodic Motions ◽  
Chaotic Motions

In this paper, switchability and bifurcation of motions in a double excited Fermi acceleration oscillator is discussed using the theory of discontinuous dynamical systems. The two oscillators are chosen to have different excitation and parameters. The analytical conditions for motion switching in such a Fermi-oscillator are presented. Bifurcation scenario for periodic and chaotic motions is presented, and the analytical predictions of periodic motions are presented. Finally, different motions in such an oscillator are illustrated.

Dynamic Mechanism of a Train Suspension System

2010 ◽  
Author(s):  
Albert C. J. Luo ◽  
Dennis O’Connor
Keyword(s):  
Numerical Simulations ◽  
System Parameter ◽  
Suspension System ◽  
Dynamic Mechanism ◽  
Impact Model ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Dynamical Behaviors ◽  
Mapping Structures

Nonlinear dynamical behaviors of a train suspension system with impacts are investigated. The suspension system is modelled through an impact model with possible stick between a bolster and two wedges. Based on the mapping structures, periodic motions of such a system are described. To understand the global dynamical behaviors of the train suspension system, system parameter maps are developed. Numerical simulations for periodic and chaotic motions are performed from the parameter maps.

Analytical Dynamics of a Ball Bouncing on a Vibrating Table

2012 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Theory Of Flow ◽  
Mapping Structures ◽  
Ball Bouncing ◽  
Vibrating Table

In this paper, the theory of flow switchability for discontinuous dynamical systems is applied. Domains and boundaries for such a discontinuous problem are defined and analytical conditions for motion switching are developed. The conditions explain the important role of switching phase on the motion switchability in such a system. To describe different motions, the generic mappings and mapping structures are introduced. Bifurcation scenarios for periodic and chaotic motions are presented for different motions and switchability. Numerical simulations are provided for periodic motions with impacts only and with impact chatter to stick in the system.

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