Wind induced vibrations on tall vessels are a concern and AutoPIPE Vessel currently has two methods to address this design consideration.

1. Obtain first the natural frequency ‘f’ of your vessel
2. Check for vibration possibility

If W/LDr² <=20, issue message in report “Vibration analysis necessary to be performed as W/LDr² <=20”

vibration analysis must be performed and proceed to step 3

where

W= corroded wt. in lb,

L=length in ft.,

Dr=average internal diameter of top half of the structure in ft.

If 25 > W/LDr² >20, issue message in report “Vibration analysis not necessary to be performed as W/LDr² >20”

If 25 > W/LDr², issue message in report “Vibration analysis not necessary to be performed as W/LDr² >20”

3. Perform stability investigation,

Calculate damping factor D_F=Wδ/LDr²

Default value of δ = 0.03 (Table 3)

If D_F <= 0.75, issue message in report “system is unstable and vortex shedding vibration analysis is required as D_F <= 0.75”, proceed to step 4

If D_F > 0.75, issue message in report “Vortex shedding vibration analysis not necessary to be performed as D_F > 0.75”

4. Calculate critical wind velocity being where S = 0.226 (Strouhal number)

Justification: In the book this formula appears as   in mph, but Dr is introduced in feet, f in Hz, so the number of Strouhal is affected by a conversion factor from feet to miles and hours to seconds. To reverse this change and work in consistent units we have to divide by 1.466 (1mph = 5280/3600 = 1.466 ft/s). And to place S in the denominator, we inverse the coefficient:

5. Calculate maximum wind velocity at top of the structure (H = 10m or 30ft)

V_w =V_b(L/H)^0.143

Where V_b = wind velocity at H

6. Apply gust factor, 1.3 to obtain maximum gust velocity = 1.3V_w
7. If V_c <=maximum gust velocity, perform amplitude calculations go to step 8.

If V_c > maximum gust velocity, issue message in report “Vibration amplitude no need to be calculated as V_c > maximum gust velocity”.

8. Calculate amplitude of maximum dynamic deflection, Z=L⁵V_C²/W δ D_r (10)^-6 (0.00243) in.
9. Check if Z < Maximum Deflection input by user, issue message in report “structure is safe:amplitude of maximum dynamic deflection < maximum allowable deflection”

If Z> Maximum Deflection input by user, issue message in report “structure is unsafe:amplitude of maximum dynamic deflection exceeds maximum allowable deflection, please modify design”

Reference: Kanti Mahajan, PE. (1979). Design of Process Equipment. Tulsa, OK: Pressure Vessel Handbook Publishing.