In-Plane Nonlinear Dynamics of Wind Turbine Blades

Ramakrishnan, Venkatanarayanan; Feeny, Brian F.

doi:10.1115/detc2011-48219

Cited by 13 publications

(7 citation statements)

References 21 publications

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“…The dissipative energy of the blade E D is modelled using Eq. ( 21), where C is the structural damping coefficient [10].…”

Section: Structural Damping Forcesmentioning

confidence: 99%

“…They aimed to ascertain the non-linear behaviour caused by the large deformations of thin structures, such as wind turbine blades. Onedimensional blade models have a low computational cost and have been used to efficiently model nonlinear vibration analysis for a wind turbine blade, for both in-plane [10] and out-plane motion [11]. These models consider the geometric nonlinearity of blades, namely that large deformations cause a significant change in force, with a non-linear relationship between force and displacement.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Lopez-Lopez

Robles-Ocampo

Sevilla-Camacho

et al. 2020

SV-JME

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Wind turbine blades are designed to be thin and flexible elements. Because unstable dynamic behaviour can affect the life of the rotor, it is crucial to understand the instability of non-linear behaviour caused by large deflections. The present study undertakes both a stability analysis of the non-linear response and an experimental validation of a simplified model for a wind turbine blade based on a cantilever beam. The model is formulated taking into account large geometric deflections and assuming a Galerkin approach. The model is validated experimentally in a wind tunnel with aluminium beams of differing geometry. Analysis of the dynamic response using phase planes reveals that the degree of instability is related to the amplitude of the excitation and the stiffness characteristics.

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“…The dissipative energy of the blade E D is modelled using Eq. ( 21), where C is the structural damping coefficient [10].…”

Section: Structural Damping Forcesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Lopez-Lopez

Robles-Ocampo

Sevilla-Camacho

et al. 2020

SV-JME

View full text Add to dashboard Cite

show abstract

“…For example, the excavator cab is susceptible to impact with larger amplitude in working; thus analytical model of vibration isolation system of cab contains cubic stiffness term, and in addition cubic stiffness provides more elastic support [23]. Similarly, in the study of dynamics modeling of wind turbine blade, the calculation result of differential equation including cubic stiffness term appears more reliable [24]. Hence, based on the reasons above, the cubic spring stiffness is chosen…”

Section: Nonlinear Modeling Of Bolted Joint Beammentioning

confidence: 99%

Analytical Model of Bolted Joint Structure and Its Nonlinear Dynamic Characteristics in Transient Excitation

Liao

Zhang

2016

Shock and Vibration

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The dynamic response of crucial components often depends upon the dynamic behavior of bolted connections. As is usually the case, the accurate modeling of structures with many mechanical joints remains a challenge work. The nonlinear behavior included in assembled structures strongly depends on the interface properties. In this paper, an analytical model of the simple bolted joint beam in tangential direction is first proposed for transient excitation, based on phenomenological model. The fourth-order Runge-Kutta method is employed to calculate the transient response, where the dynamic response of the nonlinear stiffness on system is also investigated. The simulation results show that natural frequency has a certain dependence on cubic stiffness term and cubic stiffness is more suitable for modeling of nonlinear system of a wider frequency range. Thereby, a series Iwan model containing cubic stiffness term is established to describe nonlinear behaviors of bolted joint beams in shear vibration. The amplitude-frequency curves show that the influence of interaction between nonlinear stiffness and damping mechanism on dynamic response characteristics is more obvious. Finally, a new type of nonlinear model is applied into finite element analysis. The results of proposed transient excitation experiment are discussed qualitatively, indicating that nonlinear effects observed agree with the numerical simulation results.

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“…For practical reasons, the blade vibrations are usually investigated in flap‐ and edge‐wise directions separately. () These 2 directions are uncoupled only when the product moment of inertia is zero. Yet, for a general airfoil cross section, it is not zero, which introduces coupling between 2 bending directions.…”

Section: Introductionmentioning

confidence: 99%

Bend‐bend‐twist vibrations of a wind turbine blade

Acar

Feeny

2017

Wind Energy

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Dynamics of a wind turbine blade under bend-bend-twist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed mode method, and the equations of motion are found by applying Lagrange's formula.The bend-bend-twist equations are coupled with each other and have stiffness variations due to centrifugal effects and gravitational parametric terms, which vary cyclicly with the hub angle. To determine the natural frequencies and mode shapes of the system, a modal analysis is applied on the linearized coupled equations of constant angle snapshots of a blade with effects of constant speed rotation. Lower modes of the coupled bend-bend-twist model are dominantly in-plane or out-of-plane modes. To investigate the parametric effects, several blade models are analyzed at different angular positions. The stiffness terms involving centrifugal and gravitational effects can be significant for long blades. To further see the effect of blade length on relative parametric stiffness change, the blade models are scaled in size and analyzed at constant rotational speeds, at horizontal and vertical orientations. These studies show that the parametric stiffness effects should be taken into account when designing long blades. KEYWORDSblade vibrations, modal analysis, parametric excitation INTRODUCTIONVibrational analysis of a wind turbine blade plays an important role in turbine design. In horizontal-axis wind turbines, failure often takes place in the hub and gearbox, because of the cyclic loads applied by the blades. To prevent failure and make improvements in turbine design, dynamics of the blades must be investigated.Blades are under cyclic loading due to turbine rotation. A steady wind speed usually varies with altitude, so as the blade rotates with the hub, it is affected by a cyclicly varying amount of wind force. Also the tangential and radial components of gravity force vary cyclicly, changing the effective stiffness of the blade with hub angle. These effects introduce parametric terms into the equations of motion.For practical reasons, the blade vibrations are usually investigated in flap-and edge-wise directions separately. 1-3 These 2 directions are uncoupled only when the product moment of inertia is zero. Yet, for a general airfoil cross section, it is not zero, which introduces coupling between 2 bending directions. Dawson 4 studied bend-bend coupled vibrations in pretwisted beams and formulated natural frequencies using energy methods. Torsional vibrations are also coupled with bending vibrations for most blades. 5-7 Dokumaci 5 derived the torsion-bending coupled equations analytically, and Bishop et al 6 improved the theory by introducing warping. Cooley and Parker also worked on bend-twist coupled vibration of spinning beams, taking the centrifugal effects into account. 8 Hodges and Dowell found the equations of motion for a blade goi...

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In-Plane Nonlinear Dynamics of Wind Turbine Blades

Abstract: The INTRODUCTIONThis paper introduces a model of the lead-lag (in-plane) vibration motion of an operating wind turbine subjected to gravitational loading and aerodynamic loading, and provides initial analyses of resonances by using a simplification of the singlemode reduced-order model.

Cited by 13 publications

References 21 publications

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Dynamic Instability of a Wind Turbine Blade Due to Large Deflections: An Experimental Validation

Analytical Model of Bolted Joint Structure and Its Nonlinear Dynamic Characteristics in Transient Excitation

Bend‐bend‐twist vibrations of a wind turbine blade

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