A three-degree-of-freedom model for vortex-induced vibrations of turbine blades

Wang, Dan; Chen, Yushu; Wiercigroch, Marian; Cao, Qingjie

doi:10.1007/s11012-016-0381-7

Cited by 19 publications

(9 citation statements)

References 42 publications

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“…Interactions among different vibration types can occur in various engineering systems. Classical examples are vortex-induced vibrations occurring owing to fluid flow [1], which may interact with other vibrations generated by different mechanisms, such as parametric excitation or external loading. Under specific conditions, different vibration interactions may lead to dangerous resonant states.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Warmiński

2019

Nonlinear Dyn

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The regular and chaotic vibrations of a nonlinear structure subjected to self-, parametric, and external excitations acting simultaneously are analysed in this study. Moreover, a time delay input is added to the model to control the system response. The frequencylocking phenomenon and transition to quasi-periodic oscillations via Hopf bifurcation of the second kind (Neimark-Sacker bifurcation) are determined analytically by the multiple time scales method up to the second-order perturbation. Approximate solutions of the quasi-periodic motion are determined by a second application of the multiple time scales method for the slow flow, and then, slow-slow motion is obtained. The similarities and differences between the van der Pol and Rayleigh models are demonstrated for regular, periodic, and quasi-periodic oscillations, as well as for chaotic oscillations. The control of the structural response, and modifications of the resonance curves and bifurcation points by the time delay signal are presented for selected cases.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Warmiński

2019

Nonlinear Dyn

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“…, where C L is the lift coefficient. In order to simulate the interactions between the structure and vortices, the time-varying variable 33,34,[57][58][59], where C L0 is the reference lift coefficient. The lift force then can be written as…”

Section: Model Of Structural Vibrationmentioning

confidence: 99%

“…The van der Pol oscillator is widely used to simulate the lift force acting on the structure [30,[59][60][61][62], and the corresponding equation of the wake oscillator can be written as…”

Section: Wake Oscillator Modelmentioning

confidence: 99%

Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

et al. 2021

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A low dimensional model of a top tensioned riser (TTR) under excitations from vortices and timevarying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid-structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as 'lock-in' phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass-damping parameters are investigated and the results of multiple scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass-damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-

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“…Substitute (28) and (29) into Eqs (26) and (27) and consider the internal resonance condition, yielding…”

Section: The Reduced Model With Galerkin Discretizationmentioning

confidence: 99%

“…A van der Pol oscillation was used to model an aeroelastic system possessing limit cycle oscillations [22] . The vortex-induced vibrations for a cylinder [25] , an offshore riser [26] and a turbine blade [27] were analyzed, where the time-varying characteristic of the vortices was modeled by the van der Pol oscillation and effects of the structural motion on the fluid were also studied. A van der Pol damping term was added to the equations of four coupled elastic beams to represent the self-excitation and fluid-structure interaction of the system [15] .…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

Chen

Wang

Wiercigroch

et al. 2016

Appl. Math. Mech.-Engl. Ed.

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A reduced model simulating vortex-induced vibrations (VIVs) for turbine blades is proposed and analyzed. The rotating blade is modeled as a uniform cantilever beam while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with equations of motion for a blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. Nonlinear characteristics for the dynamic responses are investigated with the multiple scale method and the modulation equations are derived. The transition set consisting of the bifurcation and hysteresis sets is constructed by using the singularity theory and the effects of system parameters including the van der Pol damping and the coupling parameter on the equilibrium solutions are analyzed. Frequency-response curves are obtained and the stabilities are determined by using the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the validity of the multiple scale method. The results indicate that the new coupled model can be useful to explain the rich dynamic response characteristics including possible bifurcation phenomena in the VIVs.

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A three-degree-of-freedom model for vortex-induced vibrations of turbine blades

Cited by 19 publications

References 42 publications

Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Nonlinear dynamics of self-, parametric, and externally excited oscillator with time delay: van der Pol versus Rayleigh models

Bifurcation analysis of vortex-induced vibration of low-dimensional models of marine risers

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

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