Dear Friends,

For a column design, natural frequency calculated by “Freeze” method in empty condition is 2.15428 Hz, however when I changed mode to “Eigen solver” method then it is coming 6.11444 Hz.

I didn’t understood why the difference is so big?

This is affecting directly on the wind deflection. See the results below,

By “Eigen solver”: -
Compute the maximum dynamic deflection [Z]:
= L^(5) * Vc² * 0.00243 / ( W * Dl * Dr ) * ( 1E-6)
= 839^(5)*78.1²*0.00243/(1655*0.030*71.136)*(1E-6)
= 9.038 mm

Allowable Deflection : 42.000 Actual Deflection : 9.038 mm

The Natural Frequency for the Vessel (Ope...) is 6.11444 Hz

By “Freeze”: -
Compute the maximum dynamic deflection [Z]:
= L^(5) * Vc² * 0.00243 / ( W * Dl * Dr ) * ( 1E-6)
= 839^(5)*27.5²*0.00243/(1655*0.030*71.136)*(1E-6)
= 1.122 mm

Allowable Deflection : 42.000 Actual Deflection : 1.122 mm

The Natural Frequency for the Vessel (Ope...) is 2.15428 Hz

Little bit confused about which method shall we use?

The difference is large and can have an opinion only knowing more details.

As I understand, in eigensolver the natural frequency is determined by the solution of a mass/stiffness matrix so the method should be accurate.

Freese method has assumptions and some restrictions. I attach a copy (anyway it's an old document available on internet) so you can understand more details by studying it.

Thanks for feeze pdf mariog.

What I understood from PVElite manual is, for skirt supported vessels, Eigen solver is the good approach. For other supports freeze method gives approximate answers.
But still, PVElite calculates deflection in two ways. One is by kanti Mahajan method as shown in above post which is very much little than calculated under “wind deflection calculations” where the deflection value is 46.611 mm!!!! see below the output extract...


Wind Deflection Calculations:


The following table is for the Operating Case.

Wind Deflection

| | Cumulative | Centroid | Elem. End | Elem. Ang. |
From| To | Wind Shear | Deflection |Deflection | Rotation |
| | kgf | mm | mm | |
--------------------------------------------------------------
10| 20| ... | 44.7444 | 44.7444 | 0.022351 |
20|Legs| 58.2430 | 44.7451 | 44.7472 | 0.022374 |
Legs| 30| 1650.00 | 44.9236 | 45.2827 | 0.022572 |
30| 40| 733.476 | 45.3162 | 45.3501 | 0.022579 |
40| 50| 674.797 | 45.9219 | 46.5944 | 0.022692 |
50| 60| 31.6190 | 46.6030 | 46.6115 | 0.022692 |

Critical Wind Velocity for Tower Vibration

| | 1st Crit. | 2nd Crit. |
From| To | Wind Speed | Wind Speed |
| | km/hr | km/hr |
-------------------------------------
10| 20| 38.2475 | 239.047 |
20| 30| 38.2775 | 239.234 |
30| 40| 32.7119 | 204.449 |
40| 50| 26.8916 | 168.073 |
50| 60| 27.0115 | 168.822 |

Allowable deflection at the Tower Top (Ope)( 6.000"/100ft. Criteria)
Allowable deflection : 42.000 Actual Deflection : 46.611 mm

** Warning: Allowable Deflection Criteria Exceeded **