This website uses local storage to ensure you get the best experience on our website.

Table of Contents

Flexibility Modelling

The structural formulation of Blades and Tower/Support Structure in Bladed are based on linear finite element bodies, enhanced by non-linear geometric stiffness models that account for the effect of small structural deflections on dynamics. For flexible structures, modal reduction via the Craig-Bampton method is applied to the tower and (optionally) to the blade.

The modal analysis calculates uncoupled blade and tower modes. In the subsequent simulations, the modes from different bodies are coupled together by the equations of motion, so that the actual eigenfrequencies of the coupled system are different from the uncoupled mode frequencies. The Linearisation calculations allows the coupled modal frequencies to be calculated and analysed.

The structural flexibility model for the blade and support structure is defined in the Flexibility Modeller screen, as described in the rest of this section.

Flexibility Model Inputs

In the Flexibility Model inputs section, the user can define inputs in order for Bladed to calculate uncoupled modes for the blades and support structure.

  • Tower: The support structure is modelled as a single finite element body. The user can specify the number of mode shapes to be calculated for the support structure to represent the structural deflection and dynamics. Enough modes should be included to capture the tower dynamics up to the frequencies of interest.

  • Blades: The blade can be sub-divided into many rigidly connected finite element bodies, in order to rigorously model large blade deflections. For maximum accuracy, enough blade parts should be specified to ensure that deflections remain small (less than approximately 5-7 degrees) within each blade part.

The structural deflection within each blade part can be accounted for either by calculating mode shapes, or by using the finite element degrees of freedom directly in the simulation. Modal reduction within the blade parts generally results in faster simulation than using the finite element model directly. If using modal reduction on the blade parts, careful attention should be paid to the number of modes on each part, to ensure that sufficient modes are included to capture the blade dynamic response.

Note that for blades with more than one part, it is recommended to use a fixed step integrator such as Newmark-β Implicit to improve simulation speed.

Running Modal Analysis

With the Flexibility Model inputs defined, a modal analysis calculation can be performed by clicking "Run modal analysis". This action will automatically close the screen; the screen can be re-opened to view the results once the modal analysis calculation is complete.

If modal reduction is selected for the blade, then mode shapes are calculated for each blade part. If modal reduction is not selected for the blade, then it is not necessary to calculate mode shapes on each part as the finite element model is used directly. In both cases, Bladed also performs a subsequent eigen analysis to calculate the coupled mode shapes and frequencies corresponding to the natural modes of the whole blade, based either on the blade part modes or the underlying finite element model. This is useful both for physical interpretation of the blade mode shapes and for applying damping, as explained in the next section.

Note that one way to ensure that you have specified sufficient modes on each blade part is to check that the whole blade mode frequencies are very similar when using modal reduction and the finite element model on the blade parts.

In the Modal analysis results and damping inputs section, the modal analysis results (such as modal frequencies and mode shape animations) can be reviewed. A damping ratio can then be specified for each mode.

  • Tower: The uncoupled tower modes frequencies are displayed and mode shape animations can be viewed. The damping ratio for each uncoupled tower mode can be specified as a percentage of critical damping.

  • Blade: The user can view the "whole blade mode shapes" and also assign damping ratios for each whole blade mode. Bladed will then automatically calculate the damping values to assign to each individual blade part.

The user can choose how many whole blade modes to specify damping ratios for using the "modes with damping defined" field. Any higher frequency modes will be assigned frequency proportional damping, based on the damping of the highest mode with damping defined. This approach applies high damping to high frequency modes and effectively excludes the higher whole blade modes from the blade dynamic response, so that they do not cause erroneous instability.

Geometric stiffness

For the blades there are two geometric stiffness settings available for the blades.

  • Axial loads only: The effect of internal forces along the element axis on dynamic response is included. This primarily accounts for "centrifugal stiffening" in the blade dynamic response. Geometric stiffness axial and shear forces are included when calculating the internal member loads.

  • Full model with orientation correction: The effect of internal axial and shear forces on dynamic response is included. This model can enhance prediction of torsion deflection in the blade. This model should be used with caution as it is only accurate when deflections within each blade part remain small (less than ~5-7 degrees). If several blade parts are used then this model can be activated to improve the accuracy of the solution, and will allow use of fewer blade parts than when using the "axial loads only" model.

A range of geometric stiffness options for the tower and support structure are also available.

Multi-part blade parameter selection

The best practice for determining the number of blade parts and modes per part, is to carry out a convergence test with respect to the blade loading and deflections. Not all configurations will lead to a converged blade model. One instance in which this can happen, is if one of the blade parts is significantly smaller than the others. The steady operational loads calculation can be used to determine whether the multi-part blade model has initialised to a suitable condition.

Last updated 13-12-2024