# Plotting tower shapes with Modes v.2.2

Dear Jason,

I’m currently doing a modal analysis of a 63m tower. I used the program Modes v.2.2 to calculate the modes. Below the input for Modes.

0.0 Steady state angular velocity of rotor (rpm) [Ignored for towers]
0.0 Pitch angle for blades (degrees) [Ignored for towers]
63.0 Total beam length (m)
0.0 Rigid beam length (m)
28850.0 End mass (kg)
5 Number of modes shapes or coefficients
2 Order of first coefficient
10 Number of input stations for distributed parameters
1.0 Factor to adjust tower stiffness
1.0 Factor to adjust in-plane stiffness [Ignored for towers]
0.00E+00 1.8797984E+03 6.4919605E+10
1.11E-01 1.7732607E+03 5.4495781E+10
2.22E-01 1.3267888E+03 3.2870718E+10
3.33E-01 1.1738875E+03 2.2766165E+10
4.44E-01 1.0259185E+03 1.5197022E+10
5.56E-01 8.8288178E+02 9.6859372E+09
6.67E-01 8.5328798E+02 8.7442928E+09
7.78E-01 7.0137313E+02 5.9951282E+09
8.89E-01 5.0270006E+02 2.7937987E+09
1.00E+00 6.4997856E+02 3.1947576E+09

For the lines of distributed parameters, the first column is the fractional
distance along the flexible portion of the tower. It must go from 0 to 1.
The second column is the mass/length in kg/m, and the third column is the
stiffness in N m^2.[/code]

Output of Modes:

[code] Shape 1 Shape 2 Shape 3 Shape 4 Shape 5
------- ------- ------- ------- -------
Freq (hz) 0.4459 2.8752 8.0611 19.6116 26.3147

``````x^2         0.5963    -15.8018     48.2225   -621.2538    631.6574
x^3        -0.1676      8.9338    327.6914   3204.8274  -4760.0376
x^4         1.7325    -32.1423  -1542.1295  -5478.7134  12354.1416
x^5        -1.4457     82.9072   1838.8284   3606.8958 -13313.1475
x^6         0.2845    -42.8969   -671.6127   -710.7558   5088.3857[/code]
``````

I’m trying now to compare now the shapes 1&2 with a simple MATLAB script that I wrote. The first and second frequencies look very plausibel and the discrepancy between both models are very low.

My problem occurs when I want to plott them. I’m plotting with Matlab the shapes with the polynomial functions:

```Shape_1=-0.5963*x.^2+0.1676*x.^3-1.7325*x.^4+1.4457*x.^5-0.2845*x.^6 Shape_2=-15.8018*x.^2+8.9338*x.^3-32.1423*x.^4+82.9072*x.^5-42.8969*x.^6```

And I get the following functions:

For comparison I scaled the x-axis with my model but still the shapes don’t look right.

I already looked up to BModes but I didn’t find something that could help me to plot them right. Am I missing some correction factor or something similar?

Best regards,

Natalia

Dear Natalia,

In your polynomial equation, x must be between 0 (at the tower base) and 1 (at the tower top). Thus, the value of polynomial at the top (x=1) should be 1. Is this what you’ve done?

As suggested many times on this forum, I suggest using BModes in combination with the ModeShapePolyFitting.xls spreadsheet to compute tower modes for ElastoDyn. This spreadsheet will plot the mode shape polynomial for you.

Best regards,

Dear Jason,

first, thank you so much for the quick response. With the correction you mention of tower base (=0) and tower top (=1) the graphics work very well!

Best regards,

Natalia