I am currently interested in programming the dynamic flap-wise motion of a"simplified" blade/beam under external forcing. My interest lies in controlling the vibrations in order to reduce fatigue. I have
seen that “Modes” give an approximation of the different mode-shapes and natural frequencies. For what I have understood, a lumped-mass/spring method has been used for modelling the
blade and the homogeneous form of this system of equations leads to an eigenvalue problem from which you extracted frequencies and mode-shapes, is that correct?
If yes, I believe that it is possible to use a “generalised” force vector (neglecting damping for now) for a dynamic simulation right? If this is the case, I guess this must be quite easy
to modify “Modes” for this purpose, however I am not familiar with FORTRAN. In addition, the information about “Modes” calculations don’t allow me to re-write (and fully understand) a similar
code in another language.
I was wondering If you could refer me to some references/guides about the theory behind “Modes”. I guess that most people are now using Bmodes and Fast for a much more accurate coupling of the dynamics. However, I would like to start with a system of smaller size.
There is no theory manual for the old Modes program, but I wrote a similar program in one of my courses in graduate school, and summarized the theoretical basis in the class report. Please find this attached. While not identical, it should give you the basic understanding of the theory behind Modes.
Modes is only set up to solve the Eigenvalue problem – with no external loading; my guess is that it would not be easy to modify Modes so that its suitable for transient time-domain simulation with external forcing.
RotatingBeamFinalReport.pdf (638 KB)
I’m going to have a look at it, thank you Jason.
Concerning the structural modelling of the wind turbine blades, I chose to developed a finite element code for rotating tapered beam. I now would like to apply it to approximate the blade given in the pdf “Definition of a 5-MW Reference Wind Turbine for Offshore System Development”.
This pdf gives me access to the structural properties of the blade, however when I’m using them for calculating the natural frequencies of the blades my results are far off. My code only takes into account the flap-wise vibrations and considers other vibrations uncoupled.
My main questions are:
Is it possible to model flap-wise blade vibrations only and get results close to the Blade Collective Flap = 0.69930 Hz ? or do I need other significant inputs ?
I used the old Modes code with flap and edge uncoupled to predict the mode shapes/frequencies of the NREL 5-MW turbine blade when the this turbine was first created. With Modes used in this way, I was able to get very close to 0.7 Hz.
Thanks for your quick answer. I have managed to obtain very close natural frequencies, however I’m not sure that my method is right.
My finite element code is assembling beam elements, each of 6 DOFs ( 2 translations and 1 rotation per node) . The inputs required for each section of the tapered beam are the
1- Area (A)
2- Elastic modulus (E)
3- Area moment of inertia (I)
Based on the following information given in the pdf
Radius BMassDen FlpStff FlpIner
Which I interpret as:
BMassDen (kg/m) : Linear density
FlpStff (N.m^2) : Flap-wise stiffness ∫∫ E(x,y)x^2dx*dy ( according to one of your previous post)
FlpIner (kg.m) : Flap-wise mass moment of inertia per unit length
Using those I calculate the
Average section Area : A= BMassDen /density (unit: m^2)
Area moment of inertia of the section : I = FlpIner/ density (unit: m^4)
And assuming a constant elastic modulus per section
E= FlpStff / I (unit: N/m^2)
Could you please let me know if this looks correct to you, Thanks.
It’s ok, I figured it out. Thanks for your help.