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1.
Junguo Wang Jianzhong Zhou Dawei Dong Bin Yan Chunrong Huang 《Archive of Applied Mechanics (Ingenieur Archiv)》2013,83(3):413-430
A general model of a rub-impact rotor system is set up and supported by oil film journal bearings. The Jacobian matrix of the system response is used to calculate the Floquet multipliers, and the stability of periodic response is determined via the Floquet theory. The nonlinear dynamic characteristics of the system are investigated when the rotating speed and damping ratio is used as control parameter. The analysis methods are inclusive of bifurcation diagrams, Poincaré maps, phase plane portraits, power spectrums, and vibration responses of the rotor center and bearing center. The analysis reveals a complex dynamic behavior comprising periodic, multi-periodic, chaotic, and quasi-periodic response. The modeling results thus obtained by using the proposed method will contribute to understanding and controlling of the nonlinear dynamic behaviors of the rotor-bearing system. 相似文献
2.
Mergen H. Ghayesh Hossein A. Kafiabad Tyler Reid 《International Journal of Solids and Structures》2012,49(1):227-243
The sub- and super-critical dynamics of an axially moving beam subjected to a transverse harmonic excitation force is examined for the cases where the system is tuned to a three-to-one internal resonance as well as for the case where it is not. The governing equation of motion of this gyroscopic system is discretized by employing Galerkin’s technique which yields a set of coupled nonlinear differential equations. For the system in the sub-critical speed regime, the periodic solutions are studied using the pseudo-arclength continuation method, while the global dynamics is investigated numerically. In the latter case, bifurcation diagrams of Poincaré maps are obtained via direct time integration. Moreover, for a selected set of system parameters, the dynamics of the system is presented in the form of time histories, phase-plane portraits, and Poincaré maps. Finally, the effects of different system parameters on the amplitude-frequency responses as well as bifurcation diagrams are presented. 相似文献
3.
This paper investigates the steady-state periodic response and the chaos and bifurcation of an axially accelerating viscoelastic Timoshenko beam. For the first time, the nonlinear dynamic behaviors in the transverse parametric vibration of an axially moving Timoshenko beam are studied. The axial speed of the system is assumed as a harmonic variation over a constant mean speed. The transverse motion of the beam is governed by nonlinear integro-partial-differential equations, including the finite axial support rigidity and the longitudinally varying tension due to the axial acceleration. The Galerkin truncation is applied to discretize the governing equations into a set of nonlinear ordinary differential equations. Based on the solutions obtained by the fourth-order Runge–Kutta algorithm, the stable steady-state periodic response is examined. Besides, the bifurcation diagrams of different bifurcation parameters are presented in the subcritical and supercritical regime. Furthermore, the nonlinear dynamical behaviors are identified in the forms of time histories, phase portraits, Poincaré maps, amplitude spectra, and sensitivity to initial conditions. Moreover, numerical examples reveal the effects of various terms Galerkin truncation on the amplitude–frequency responses, as well as bifurcation diagrams. 相似文献
4.
In the present study, the geometrically non-linear dynamics of an axially moving plate is examined by constructing the bifurcation diagrams of Poincaré maps for the system in the sub and supercritical regimes. The von Kármán plate theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of this gyroscopic system are obtained based on an energy method by means of the Lagrange equations which yields a set of second-order non-linear ordinary differential equations with coupled terms. A change of variables is employed to transform this set into a set of first-order non-linear ordinary differential equations. The resulting equations are solved using direct time integration, yielding time-varying generalized coordinates for the in-plane and out-of-plane motions. From these time histories, the bifurcation diagrams of Poincaré maps, phase-plane portraits, and Poincaré sections are constructed at points of interest in the parameter space for both the axial speed regimes. 相似文献
5.
Mergen H. Ghayesh 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(9):1169-1181
Geometrically nonlinear dynamics of an axially accelerating beam is investigated numerically in this paper. Employing the Galerkin scheme, the equation of motion is reduced to a set of nonlinear ordinary differential equations with coupled terms. The linear part of this set of equations is then solved to determine the linear natural frequencies. The frequency of the axial acceleration is set to twice the first or second linear natural frequency (subharmonic resonance), and bifurcation diagrams of Poincaré maps are obtained via direct time integration and choosing the amplitude of the speed variations as a bifurcation parameter. The results are presented for four different values of the mean value of the axial speed, specifically in the form of time traces, phase-plane portraits, fast Fourier transforms (FFTs), and Poincaré maps. 相似文献
6.
Siavash Kazemirad Mergen H. Ghayesh Marco Amabili 《Archive of Applied Mechanics (Ingenieur Archiv)》2013,83(1):25-42
The thermo-mechanical nonlinear dynamics of a buckled axially moving beam is numerically investigated, with special consideration to the case with a three-to-one internal resonance between the first two modes. The equation of motion of the system traveling at a constant axial speed is obtained using Hamilton??s principle. A closed form solution is developed for the post-buckling configuration for the system with an axial speed beyond the first instability. The equation of motion over the buckled state is obtained for the forced system. The equation is reduced into a set of nonlinear ordinary differential equations via the Galerkin method. This set is solved using the pseudo-arclength continuation technique to examine the frequency response curves and direct-time integration to construct bifurcation diagrams of Poincaré maps. The vibration characteristics of the system at points of interest in the parameter space are presented in the form of time histories, phase-plane portraits, and Poincaré sections. 相似文献
7.
Vibration characteristics of a hydraulic generator unit rotor system with parallel misalignment and rub-impact 总被引:1,自引:0,他引:1
Zhiwei Huang Jianzhong Zhou Mengqi Yang Yongchuan Zhang 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(7):829-838
The object of this research aims at the hydraulic generator unit rotor system. According to fault problems of the generator
rotor local rubbing caused by the parallel misalignment and mass eccentricity, a dynamic model for the rotor system coupled
with misalignment and rub-impact is established. The dynamic behaviors of this system are investigated using numerical integral
method, as the parallel misalignment, mass eccentricity and bearing stiffness vary. The nonlinear dynamic responses of the
generator rotor and turbine rotor with coupling faults are analyzed by means of bifurcation diagrams, Poincaré maps, axis
orbits, time histories and amplitude spectrum diagrams. Various nonlinear phenomena in the system, such as periodic, three-periodic
and quasi-periodic motions, are studied with the change of the parallel misalignment. The results reveal that vibration characteristics
of the rotor system with coupling faults are extremely complex and there are some low frequencies with large amplitude in
the 0.3–0.4× components. As the increase in mass eccentricity, the interval of nonperiodic motions will be continuously moved
forward. It suggests that the reduction in mass eccentricity or increase in bearing stiffness could preclude nonlinear vibration.
These might provide some important theory references for safety operating and exact identification of the faults in rotating
machinery. 相似文献
8.
This paper investigates the nonlinear forced dynamics of an axially moving Timoshenko beam. Taking into account rotary inertia and shear deformation, the equations of motion are obtained through use of constitutive relations and Hamilton’s principle. The two coupled nonlinear partial differential equations are discretized into a set of nonlinear ordinary differential equations via Galerkin’s scheme. The set is solved by means of the pseudo-arclength continuation technique and direct time integration. Specifically, the frequency-response curves of the system in the subcritical regime are obtained via the pseudo-arclength continuation technique; the bifurcation diagrams of Poincaré maps are obtained by means of direct time integration of the discretized equations. The resonant response is examined, for the cases when the system possesses a three-to-one internal resonance and when not. Results are shown through time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The results indicate that the system displays a wide variety of rich dynamics. 相似文献
9.
Mei Cheng Guang Meng Jianping Jing 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,76(3-4):215-227
The non-linear dynamic behaviors of a rotor-bearing-seal coupled system are investigated by using Muszynska’s non-linear seal fluid dynamic force model and non-linear oil film force, and the result from the numerical analysis is in agreement with the one from the experiment. The bifurcation of the coupled system is analyzed under different operating conditions. It is indicated that the dynamic behavior of the rotor-bearing-seal system depends on the rotation speed, seal clearance and seal pressure of the rotor-bearing-seal system. The system state trajectory, Poincaré maps, frequency spectra and bifurcation diagrams are constructed to analyze the dynamic behavior of the rotor center. Various non-linear phenomena in the coupled system, such as periodic motion and quasi-periodic motion are investigated. The results show that the system has the potential for chaotic motion. The study may contribute to a further understanding of the non-linear dynamics of such a rotor-bearing-seal coupled system. 相似文献
10.
The chaos of nonholonomic systems with two external nonlinear nonholonomic constraints where the magnitude of velocity is
a constant and the magnitude of the velocity is a constant with a periodic disturbance, respectively, is completely identified
for the first time. The scope of the chaos study is extended to nonlinear nonholonomic systems. By applying the nonlinear
nonholonomic form of Lagrange’s equations, the dynamic equation is expressed. The existence of chaos in these two nonlinear
nonholonomic systems is first wholly proved by all numerical criteria of chaos, i.e., the most reliable Lyapunov exponents,
phase portraits, Poincaré maps, and bifurcation diagrams. Furthermore, it is found that the Feigenbaum number still holds
for nonlinear nonholonomic systems. 相似文献
11.
Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow 总被引:1,自引:0,他引:1
Xiaoyao Shen Jiuhong Jia Mei Zhao 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(3):225-240
A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing
motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory.
The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through
numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction
and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing
system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated
motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent
bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can
be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding
of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow. 相似文献
12.
13.
This paper presents a new four-dimensional (4-D) smooth quadratic autonomous chaotic system, which can present periodic orbit,
chaos, and hyper-chaos under the conditions on different parameters. Importantly, the system can generate a four-wing hyper-chaotic
attractor and a pair of coexistent double-wing hyper-chaotic attractors with two symmetrical initial conditions. Furthermore,
a four-wing transient chaos occurs in the system. The dynamic analysis approach- in the paper involves time series, phase
portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents, to investigate some basic dynamical behaviors of the
proposed 4-D system. 相似文献
14.
Yong-Gang Wang Hui-Fang Song Dan Li Jing Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2010,80(7):815-828
The chaotic vibrations of a bimetallic shallow shell of revolution under time-varying temperature excitation are investigated
in the present study. The governing equations are established in forms similar to those of classical single-layered shell
theory by re-determination of reference surface. The nonlinear differential equation in time-mode is derived by variational
method following an assumed spatial-mode. The Melnikov function is established theoretically to estimate regions of the chaos,
and the Poincaré map, phase portrait, Lyapunov exponent, and Lyapunov dimension are used to determine if a chaotic motion
really appears. Further investigations are developed by means of detailed numerical simulation, and both the bifurcation diagrams
and corresponding maximum Lyapunov exponent are illustrated. The influence of static and time-dependent temperature parameters,
height parameter of the shell, and damping parameter on the dynamic characteristics is examined. Interesting phenomena such
as the onset of chaos, transient chaotic motion, chaos with interior crisis and period window, period-doubling scenario and
reversed period-doubling bifurcation leading to chaos, jump phenomena, and chaos suddenly converting to period orbit have
been observed from these figures. 相似文献
15.
Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system 总被引:2,自引:0,他引:2
This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular
contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system.
The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without
considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic
solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results
show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable
periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation
margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance
speed. 相似文献
16.
This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow
model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may
be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the
rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories
of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent
analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the
design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly
nonlinear regimes. 相似文献
17.
Nonlinear dynamics and stability of the rotor–bearing–seal system are investigated both theoretically and experimentally. An experimental rotor–bearing–seal device is designed and corresponding tests are carried out. The experimental rotor system is simplified as the Jeffcott rotor. The nonlinear oil–film forces are obtained under the short bearing theory and Muszynska nonlinear seal force model is used. Numerical method is utilized to solve the nonlinear governing equations. Bifurcation diagrams, waterfall plots, Poincaré maps, spectrum plots and rotor orbits are drawn to analyze various nonlinear phenomena and system unstable processes. Theoretical results from numerical analysis are in good agreement with results from experiments. Conclusions are drawn and prove that this study will contribute to the further understanding of nonlinear dynamics and stability of the rotor system with the fluid-induced forces from oil–film bearings and the seals. 相似文献
18.
The three-dimensional nonlinear planar dynamics of an axially moving Timoshenko beam is investigated in this paper by means of two numerical techniques. The equations of motion for the longitudinal, transverse, and rotational motions are derived using constitutive relations and via Hamilton’s principle. The Galerkin method is employed to discretize the three partial differential equations of motion, yielding a set of nonlinear ordinary differential equations with coupled terms. This set is solved using the pseudo-arclength continuation technique so as to plot frequency-response curves of the system for different cases. Bifurcation diagrams of Poincaré maps for the system near the first instability are obtained via direct time integration of the discretized equations. Time histories, phase-plane portraits, and fast Fourier transforms are presented for some system parameters. 相似文献
19.
The nonlinear global forced dynamics of an axially moving viscoelastic beam, while both longitudinal and transverse displacements are taken into account, is examined employing a numerical technique. The equations of motion are derived using Newton′s second law of motion, resulting in two partial differential equations for the longitudinal and transverse motions. A two-parameter rheological Kelvin–Voigt energy dissipation mechanism is employed for the viscoelastic structural model, in which the material, not partial, time derivative is used in the viscoelastic constitutive relations; this gives additional terms due to the simultaneous presence of the material damping and the axial speed. The equations of motion for both longitudinal and transverse motions are then discretized via Galerkin’s method, in which the eigenfunctions for the transverse motion of a hinged-hinged linear stationary beam are chosen as the basis functions. The subsequent set of nonlinear ordinary equations is solved numerically by means of the direct time integration via modified Rosenbrock method, resulting in the bifurcation diagrams of Poincaré maps. The results are also presented in the form of time histories, phase-plane portraits, and fast Fourier transform (FFTs) for specific sets of parameters. 相似文献
20.
This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze micropolar fluid-film journal bearings with nonlinear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor–bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various nondimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The methods of analysis employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the dynamic system varies with the nondimensional speed ratios, the nondimensional parameter, and permeability. The modeling results obtained by using the method proposed in this paper can be employed to predict the dynamics of the rotor–bearing system, and the undesirable behavior of the rotor and bearing centers can be avoided. 相似文献