Melnikov's method for chaos of a two-dimensional thin panel in subsonic flow with external excitation

Li, Peng; Yang, Yiren; Zhang, Minglu

doi:10.1016/j.mechrescom.2011.07.008

Cited by 38 publications

(21 citation statements)

References 7 publications

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“…Equation 10 implies that the coefficient " k only depends on k, n r . On letting the numerator and denominator of Eq.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

“…It is well known that the general streamlined design of highspeed trains is adopted for the purpose of optimization of aerodynamic performance, as a consequence, a large quantity of plate structures such as train-body skins and windows are widely used [8,9]. These external plates with one side exposed to airflow can be severely excited by aerodynamic pressure, which has been confirmed by the test of the Wuhan-Guangzhou railway passengers dedicated line of China when the testing train CRH-3 moves at almost 400 km/h [10]. Although the amplitude of these vibrations is general the order of the plate thickness and may not lead these structures to break immediately, they can inflict longterm fatigue damage and influence their considerable service.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear flutter behavior of a plate with motion constraints in subsonic flow

Yang

2014

Meccanica

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This paper is aimed at presenting the nonlinear flutter peculiarities of a cantilevered plate with motion-limiting constraints in subsonic flow. A non-smooth free-play structural nonlinearity is considered to model the motion constraints. The governing nonlinear partial differential equation is discretized in space and time domains by using the Galerkin method. The equilibrium points and their stabilities are presented based on qualitative analysis and numerical studies. The system loses its stability by flutter and undergoes the limit cycle oscillations (LCOs) due to the nonlinearity. A heuristic analysis scheme based on the equivalent linearization method is applied to theoretical analysis of the LCOs. The Hopf and two-multiple semi-stable limit cycle bifurcation bifurcations are supercritical or subcritical, which is dependent on the location of the motion constraints. For some special cases the bifurcations are, interestingly, both supercritical and subcritical. The influence of varying parameters on the dynamics is discussed in detail. The results predicted by the analysis scheme are in good agreement with the numerical ones.

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“…Equation 10 implies that the coefficient " k only depends on k, n r . On letting the numerator and denominator of Eq.…”

Section: Equilibrium Pointsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear flutter behavior of a plate with motion constraints in subsonic flow

Yang

2014

Meccanica

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“…In this section, the chaotic thresholds of Equation (2.5) can be characterized by Melnikov theory [14] [15]. The complex dynamics of stable oscillators can be easily depicted.…”

Section: Melnikov Analysis For the Perturbed Systemmentioning

confidence: 99%

“…In Section 2, we study the chaotic behavior of system of Equation (1.2) and the chaos can be controlled by finding an appropriate controller. In Section 3, we study the chaos control in controlled system by Melnikov method [11]- [15]. In Section 4, the bifurcation diagrams and the maximum Lyapunov exponents are given to support the theoretical analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Xing¹,

Yin

Li³

2014

OALib

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Chaos appears in the whole process of fiber-optic signal propagation with one external perturbation due to the absence of damping. Via adding a proper controller, chaos cannot be suppressed when the controller's strength is weak. With the increase of the controller strength, the fiber-optic signal can stay in a stable state. However, unstable phenomenon occurs in the propagation of the fiber-optic signal when the strength exceeds a certain degree. Moreover, we discuss the parameters' sensitivity to be controlled. Numerical results show that vibration, oscillation and escape can occur during the transmission of optic signals with different parametric regions.

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“…Thin panel structures such as the train-body skins have been widely used in the streamlined design of high-speed trains for the optimization of aerodynamic performance [1,2]; however, typical problems of flow-induced vibrations of such panels accompanied by the speedup of high-speed trains are, as expected, emerging and receiving more and more attention as a practical issue that requires urgent resolution [3].…”

Section: Introductionmentioning

confidence: 99%

On double stable limit cycle flutter of a plate with motion constraints in subsonic flow

Yang

2015

Meccanica

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This paper revisits the nonlinear flutter model of a cantilevered plate with motion-limiting constraints in subsonic flow. The nonlinear flutter behavior of this model was firstly explored in an earlier paper. Recently, it has become clear that the results of nonlinear limit cycle flutter reported in that earlier paper are incomplete. A further reevaluation of this problem is undertaken here to reveal some new and fresh results. The flutter regions are evaluated and summarized in different two-parameter planes and a heuristic analysis scheme based on the equivalent linearized method is utilized to analyze the limit cycle flutter in these regions. Results show that flutter regions vary with the spring stiffness and location; the system exhibits both the single and the double stable limit cycle flutter; the occurrences of these two types of limit cycle flutter are closely associated with bifurcations of a different nature.

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Melnikov's method for chaos of a two-dimensional thin panel in subsonic flow with external excitation

Cited by 38 publications

References 7 publications

Nonlinear flutter behavior of a plate with motion constraints in subsonic flow

Nonlinear flutter behavior of a plate with motion constraints in subsonic flow

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

On double stable limit cycle flutter of a plate with motion constraints in subsonic flow

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