Bladed versions affected: all Bladed versions supporting model linearisation calculations.
Date of last article update: 14 September 2023
The uncoupled contributions to coupled modes in the $01 file are obtained from normalising entries in the rows of the calculated A matrix. These contributions represent displacement magnitudes of each uncoupled mode that contributes to the coupled mode shape. Contributions below a specified tolerance will be set to zero. In version 4.15, the tolerance is set to 1e-6 and the values are presented in scientific notation, while in all previous versions, it is set to 1e-3 using standard notation. The change makes it easier to evaluate whether specific modes remain influential when dynamic stall or wake models are active.
The energy contribution is derived by normalising the magnitudes of uncoupled mode shapes to coupled modes. The meaning of the energy contributions are ill-defined for a system which includes servo systems anyway (as explained below) and so we would not recommend using it to compare against other tools. These results are saved to the $CM file.
The stiffness and mass (and damping) matrices make sense for a system which just represents a physical structure, whose degrees of freedom are all second-order modes representing movement of parts of the structure. Then everything is straightforward, and the percentages should be expressed as energy in the sense of ½kx2 terms where k is stiffness and x is displacement. The problem is that the system dynamics include non-structural modes, which affect the dynamic response but can’t be represented in the same way. This could include pitch actuator dynamics, generator/power converter dynamics, perhaps with internal control loops, measurement sensors, etc. The dynamics of these components partly come from electronic circuits (including digital controls) rather than masses and stiffnesses, so it’s not possible to define the energy in those modes, and indeed the concept of mass and stiffness matrices is no longer strictly useful. If any of these additional dynamics can be represented as second-order modes then one can ‘pretend’ that they represent masses and stiffnesses with modes containing a certain energy, although this is quite artificial; and in practice there is no need for them to be second-order, and often they are not. Because of this, the concept of % contributions becomes ill-defined. Bladed uses an algorithm to come up with these contributions in order to give the user some idea of what a given coupled mode represents physically, but the algorithm is not theoretically rigorous – it can’t be, because the problem is not rigorously posed. It’s just trying to be a bit helpful, and the algorithm seems to produce helpful results at least most of the time. It would be possible to generate a Campbell diagram including only the structural dynamics, and then everything would be easy, and mass and stiffness matrices could be calculated. However, ignoring the non-structural dynamics is not correct, because they do have an influence on the frequencies and damping of the coupled modes.