This document summarizes a student's study of flow induced vibration of a circular cylindrical structure. It includes calculations of the cylinder's properties and natural frequencies. It then discusses practical applications of vortex induced vibration including failures of structures like bridges. It notes multibody effects are important in applications like heat exchangers where multiple tubes can vibrate together. Methods for suppressing vortex induced vibration on cylinders are also listed.

1. Study of Flow Induced Vibration of a
Circular Cylindrical Structure
NAME : Dilshan K.M.G.L.
COURSE : BSc. Engineering
INDEX NO. : 150131A
DATE OF PER. : 11.05.2018
DATE OF SUB. : 25.05.2018

2. Calculation
Mass of the cylinder (M) = 358.28𝑔
Length of the cylinder (L) = 0.57𝑚
Circumference of the cylinder (C) = 0.29𝑚
Diameter of the cylinder (D) =
𝐶
𝜋
=
0.29
𝜋
= 0.0923𝑚
Spring stiffness =
𝑊
∆𝑙
=
0.089565 ×9.81 𝑁
(95−75) 𝑚𝑚
= 0.044 𝑁/𝑚𝑚
Spring
Initial length
(mm)
Final length
(mm)
Applied weight
(g)
Spring stiffness
(N/mm)
1 75 95 89.565 0.043931633
2 77 110 89.565 0.026625232
3 77 104 89.565 0.03254195
4 76 112 89.565 0.024406463
Spring stiffness =
∑ 𝐾
4
=
0.044 +0.027+0.033+0.024
4
= 0.030 𝑁/𝑚𝑚
Moment of inertia of the cylinder
𝐼 =
1
4
𝑀𝑅2
+
1
12
𝑀𝐿2
𝐼 =
1
4
× 0.358 × 0.04622
+
1
12
× 0.358 × 0.572
= 0.009891𝑘𝑔𝑚2
First natural frequency
𝑓1 =
1
2𝜋
√
𝐾
𝑀
𝑓1 =
1
2𝜋
√0.03 ×106
358 .28
= 1.446 𝑠−1
Second natural frequency
𝑓1 =
𝑙
4𝜋
√
𝐾
𝐼
𝑓1 =
0.57
4𝜋
√
0.03×106
9.89
= 2.481 𝑠−1

3. Discussion
Practical applications of vortex induced vibration
Vortex induced vibration can be simply demonstrated using this experiment, flow around cylinder.
Here because of the excessive curvature, at some point on the cylinder, flow will separate from the
surface on the cylinder and then vortices will have generated. That will be caused by the pressure
difference between upstream and downstream flow. Since vortices are not symmetric around the axis
of the cylinder, lift force generated by the vortices are not symmetric, thus there will be resultant
force always to one side, either up or down. So that cylinder tends to vibrate at a frequency.
Vortex induced vibration (VIV) is affected to different branch of engineering fields, from cables to
exhaust pipe arrays. That is very important when structures near to costal areas because of the tide
and high wind speed directly entangle with the structure.
VIV is important to buildings structures as well as moving solid bodes. There are plenty of examples
in the vicinity that was designed and build considering the VIV effect. Basically, VIV strongly
important to slender structural components like towers that had lower cross-sectional areas relative to
the height of that. Offshore platforms, bridges, heat exchangers, marine cables, towed cables,
pipelines, and also many hydrodynamic and hydrodynamic based applications is affected with the
VIV.
Most of the times the structure gets failed because of the fatigue failure, that is happened due to
cyclic loads. VIV produced unsymmetrical forces along the vibrating axis caused for the fatigue
failure.
There are some engineering applications that collapsed due to VIV effect such as Tacoma Narrows
Bridge. That failure is occurred due to the fatigue failure, due to oscillating forces. Another structure
is John Hancock Building in Boston. That building covered using black glasses and most of the
glasses were broken without no reason. And also, after completing the construction, most of the
window glasses in other offices near that building were shattered. Engineers thought that was due to
high speed wind. But finally discovered that is happened due to VIV. Another thing is that building is
not bend along the vertical axis but tends to twist along the central axis. Because of the structural
components were unbearable torsion and there was threat to deform. So, engineers had to add counter
masses on the bottom floor to reduce the twisting moment. That twisting also happened due to VIV
effect.
And also, structural platforms in the drilling and production risers in petroleum production is affected
by the VIV from two ways. Hydrodynamic forces and aerodynamic forces. Structures under the sea is
affected by the hydrodynamic forces and thin tubes on the platform is affected by the aerodynamic
forces. There are several types of platforms in petroleum production. Most of the platforms can be
categorized under fixed rigs, tension leg, spar platforms. In fixed rigs platforms, structure is
connected to the bottom of the sea permanently. The thin structure connected each other. That
structure has higher resistance to vibration than other kind of platforms. So that hydrodynamic effect
is not much affected. In tension leg platforms, structed is anchored using several counter masses.
That cables must be arranged considering VIV effect due to solid body interaction. In spar platform,
there is only one beam that connected the structure to the ground. So that tidal waves can be affected
on the body.

4. Importance of multibody effect in practice
In the heat exchangers, the arrangement of the tubes in the space must be planed considering VIV
effect. Steam, vaporized water is passing through the tubes so that tubes will get vibrate because
steam particles collapse with the wall of the tube. When there are several tubes along each other,
resonance can be induced. The tubes are not vibrating in same frequency because the velocities of the
steam can be varying. So that vibration of a tube can be affected to another tube and also situation
can be benefitted or can get disaster. If the arrangement is in the way that reduce the VIV effect, the
possibility fatigue failure is reduced and fatigue life is increased. But the positions are in the way the
increase the frequency of vibration, the fatigue life can be decreased and final result will be
catastrophic. Here the frequencies of the vibration are varying along the cable and also frequency
shedding can be changed. So that nodes can be generated on the cable but the nodes are not stable.
That also caused to increase the fatigue failure.
Another example can be explained using tension leg
platform in the petroleum production in the middle
of the sea. Previous example is due to aerodynamics
and this one is based on the hydrodynamics. Here
the platform is anchored to the bottom of the sea
and for one anchor has several cables. The
arrangement of the cable must be designed using
within single anchor and among other anchors.
VIV increases the effective drag coefficient due to
increment of pressure forces. Also, that introduced
another drag coefficient called fluctuating drag
coefficient. The large towers such as chimneys in
coal power plants, are affected by there drag forces
and also that will tend to bend the structure and
twist. The flexibility of the structure must be
slightly increased due to that effect, otherwise that
will tend to collapse.
There are several methods that can used to suppression of the VIV on cylindrical objects.
1. Helical strake
2. Shroud
3. Axial slats
4. Streamline fairing
5. Splitter plate
6. Ribboned cable
7. Pivoted guiding vane
8. Spoiler plates

5. Reference
FUNDAMENTALS OF VORTEX-INDUCED VIBRATION. (2015). Retrieved from Bureau of
Safety and Environmental Enforcement: https://www.bsee.gov/sites/bsee.gov/files/tap-technical-
assessment-program//485ab.pdf
Kim, K.‐ P. Y.‐ M. (2017, July 27). The evaluation of wind‐ induced vibration responses to a
tapered tall building. Retrieved from Wiley online library:
https://onlinelibrary.wiley.com/doi/pdf/10.1002/tal.371
Techet, A. (2005). Vortex Induced Vibatiob. Retrieved from MIT:
http://web.mit.edu/13.42/www/handouts/reading-VIV.pdf

6. y = 0.0538x - 2.2751
0
2
4
6
8
10
12
50 70 90 110 130 150 170 190 210 230
Velocity(m/s)
Counter value
Velocity vs Counter Value