Multi flexible body analysis for application to wind turbine control design

Hodges, Dewey H.; Patil, Mayuresh

doi:10.2514/6.2000-30

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…A large portion of them were built on a displacement-based approach (Beheshti-Aval and Lezgy-Nazargah, 2012; Robbins and Reddy, 1991). An alternative approach is the intrinsic variable based mixed variational formulation (Hodges, 1990;Hodges and Patil, 2000;Yu and Blair, 2012), which treats force resultants and generalized strains as the primary unknowns rather than displacements or any other kinematic variables. The formulation renders a relatively more straightforward requirement for building a numerical solution scheme when geometrical nonlinearity is profound compared to the usual displacement-based approach (Yu and Blair, 2012).…”

Section: Introductionmentioning

confidence: 99%

Geometrically exact, intrinsic mixed variational formulation for smart, slender multilink composite structures

Asdaque

Roy

2021

Journal of Intelligent Material Systems and Structures

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Flexible links are often part of massive aerospace structures like helicopter or wind turbine blades, satellite bae, airplane wings, and space stations. In the present work, a mixed variational statement based on intrinsic variables is derived for multilinked smart slender structures. Equations involved in the derivation do not involve approximations of kinematical variables to describe the deformation of the reference line or the rotation of the deformed cross-section of the slender links resulting in a geometrically exact formulation. Finite element equations are derived from weak formulation, which can analyze large geometrically non-linear problems. The weakest possible variational statement provides greater flexibility in the choice of shape functions, therefore reducing the associated numerical complexities. The present work focuses on developing a single integrated computational platform which can study multibody, multilink, lightweight composite, structural system built with both embedded actuations, sensing, as well as passive links. Validation of static mechanical and electrical outputs from 3D FE simulation and literature proves the efficacy of the computational platform. Dynamic results will be communicated in future correspondence. The computational platform developed here can be applied for monitoring and active control applications of flexible smart multilink structures like swept wings, multi-bae space structures, and helicopter blades.

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Section: Introductionmentioning

confidence: 99%

Geometrically exact, intrinsic mixed variational formulation for smart, slender multilink composite structures

Asdaque

Roy

2021

Journal of Intelligent Material Systems and Structures

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“…[11][12][13] Lee et al 14 performed the structure dynamic analysis of horizontal wind turbine with both rigid-and flexiblebody subsystems and analyzed the natural characteristics of this rigid-flexible coupling model. 15 The wind turbine drivetrain is operated with varying loads excitation. As a consequence, it can cause the gearbox to be more prone to failure.…”

Section: Introductionmentioning

confidence: 99%

Natural characteristic analysis of wind turbine drivetrain considering flexible supporting

Zhang

Zhu

Song

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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The mechanical system of wind turbine is much complicated and can be divided into the drivetrain and supporting portions. The drivetrain consists of wheel, main shaft, gearbox, generator, etc. and the supporting portion mainly consists of a tower and a cabin. In order to reduce the unit cost of electricity, the capacity and size of wind turbine are increased gradually in the past years. Meanwhile, with the increase of the wind turbine height, the tower actually becomes more flexible as the supporting part. And the influence of the supporting tower flexibility becomes stronger due to the varying wind loads both in magnitude and direction. Using the rigid–flexible coupling multibody dynamic theory, the coupled dynamic model of the wind turbine drive train was developed considering the flexible supporting. Then the natural characteristics of the system were computed and investigated. For the dynamic modeling, the blades, the tower and main shaft were modeled as flexible bodies, while the other components, such as the hub and the gearbox, were modeled as rigid bodies. The potential resonance frequencies of the system were discussed through the Campbell diagram and the modal energy distribution analysis. The results show that the natural frequency of swing mode shapes for the tower was 0.399 Hz and 0.405 Hz. The first natural frequency of drivetrain, which represented a torsional vibration mode, was 1.64 Hz. From the Campbell diagram and the modal energy distribution analysis, resonances would not occur within the normal operating speed range for the drivetrain. And a comparison analysis indicated that the flexible supports would increase the bearing loads along axial direction and radial direction, especially in main shaft and torque arm, but that influence was not obvious at parallel stage. However, to some extent, the flexible supports can decrease the loads fluctuation of drivetrain. Finally, the online vibration experiments were carried out in the wind field. The vibration characteristics of the wind turbine drivetrain were analyzed and the experimental results also compared well with the theoretical dynamic results.

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“…The theoretical details were presented earlier in Ref. 12. Here we recapitulate the important steps in the derivation of the equations for the sake of completeness.…”

Section: Treatment Of Flexible Subsystemmentioning

confidence: 99%

“…12 As an intermediate step toward final realization of the methodology, here we propose a simplified analytical model, solution strategy, and numerical examples.…”

Section: Present Workmentioning

confidence: 99%

Multi‐flexible‐body Dynamic Analysis of Horizontal Axis Wind Turbines

2002

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A dynamic stability analysis is presented for a horizontal-axis wind turbine modeled as a multi-body system with both rigid-and flexible-body subsystems. The rigid-body subsystems are modeled as an interconnected set of rigid bodies using Kane's method, which can lead to equations of motion that are more compact than they would be using other methods. The flexible-body subsystems are modeled using nonlinear beam finite elements, derived from a mixed variational formulation for the dynamics of moving beams. The equations for the rigid and flexible subsystems are coupled to obtain a unified framework that models the dynamic behavior of the complete system. Linearization of the dynamic equations about the steady-state solution yields system equations with periodic coefficients that must be solved by Floquet theory to extract the dynamic characteristics. Numerical studies are presented to investigate the natural frequencies and mode shapes for a wind turbine with flexible blades. The presented results demonstrate the performance of the present methodology to aid in understanding of the dynamic characteristics of the wind turbine.

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Multi flexible body analysis for application to wind turbine control design

Cited by 11 publications

References 12 publications

Geometrically exact, intrinsic mixed variational formulation for smart, slender multilink composite structures

Geometrically exact, intrinsic mixed variational formulation for smart, slender multilink composite structures

Natural characteristic analysis of wind turbine drivetrain considering flexible supporting

Multi‐flexible‐body Dynamic Analysis of Horizontal Axis Wind Turbines

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