Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Periods of natural oscillations during iceberg towing
Petr A. Tarasov1, Konstantin A. Kornishin1, Yaroslav O. Efimov1, Mikhail L. Boldyrev1, Alexey V. Chernov2, Ivan A. Svistunov2,Dmitriy V. Nikushchenko3, Alexander A. Rodionov3, Nikita V. Tryaskin3
1Department of Marine Operations, Arctic Research Centre, Moscow, Russia
2Arctic and Antarctic Research Institute (AARI), St. Petersburg, Russia
3State Marine Technical University (SMTU), St. Petersburg, Russia

madd v xx – added mass of vessel under longitudinal oscillations of the“vessel-rope-iceberg” system, tons;
ρw – water density, tons/m3;b – half length of the iceberg, m;
Svert – sectional area of the iceberg in the vertical plane, m2;
Sw l – sectional area of the iceberg in the horizontal plane at thewaterline level, m2;
Vi – iceberg volume, m3;
Сw – hydrodynamic drag force coefficient of the iceberg;
Fo – water resistance force acting on iceberg during steady motion of
the “vessel-rope-iceberg” system, kN;
F – water resistance force acting on iceberg, kN;
T –rope tension force (towing force), kN;
M –moment of the restoring force, kN*m;
Ic – moment of inertia of the system “vessel-rope-iceberg” relative tothe center of mass in plane motion, tons*m2;
Ii – moment of inertia of the iceberg (cylinder) relative to the iceberg’s
center of mass in plane motion, tons*m2;
Iadd i – added moment of inertia of the iceberg (cylinder) relative to theiceberg’s center of mass in plane motion, tons*m2;
Iadd v – added moment of inertia of the vessel relative to the vessel’scenter of mass in plane motion, tons* m2;
g – gravity factor, m/s2;
k – stiffness of one of the rope branches, kN/m;
E* – Effective elasticity of the tow rope, kPa;
Sr – cross sectional area of the tow rope, m2;
t1 – period of long-period oscillations of the “vessel-rope-iceberg”
system, s;t2 – period of longitudinal oscillations of the “vessel-rope-iceberg”
system, s;t3 – period of torsional oscillations of the “vessel-rope-iceberg” system,s;t4 – the minimum period of iceberg’s oscillations (rolling, heaving,pitching), s;
th – heaving period of iceberg, s.

ABSTRACTThe article provides information on various types of oscillations thatarise during iceberg towing; both long-period and short-period
oscillatory processes are considered; simple formulas for calculating
the periods of oscillations are given. The results presented in the article
are based on experimental data obtained during iceberg towing trials in
the Barents and Kara seas in 2016-2017, as well as on the performed
numerical and analytical modeling. Oscillatory processes during steadyand unsteady movement of the “Vessel-Towing Rope-Iceberg” system
are considered; the gradation of these processes is given bycharacteristic periods, which vary from fractions and units of seconds
for heave motion of iceberg to several hours for oscillations of aniceberg and a vessel around a system center of mass. Frequency spectraof the experimental data from the dynamometer (records the towing
force with a discreteness of 0.125 seconds) records were analyzed forvarious stages of towing; the main modes of the vibration spectrum areidentified. For verification of analytical models describing long-term
oscillations of the “Vessel-Towing Rope-Iceberg”, authors used thevessel’s ice radar readings. The influence of the early forms of sea iceon the change of natural oscillations characteristics during iceberg
towing is also considered. The data presented in the article can be usedin planning and monitoring of the icebergs in order to minimize therisks of oscillatory processes development, and primarily resonancephenomena that can cause damage of towing system.

KEY WORDS: icebergs; towing; oscillations; resonance; water.
NOMENCLATURE
D – distance between vessel and iceberg, m;udrift – iceberg drift velocity, m/s;uо – “vessel-rope-iceberg” center-of-mass velocity, m/s;
ui – iceberg velocity, m/s;
uv – vessel speed in m/s;
mi – mass of iceberg, tons;
madd i – added mass of iceberg (cylinder), tons;
madd i xx – added mass of iceberg under longitudinal oscillations of the“vessel-rope-iceberg” system, tons;
madd i zz – added mass of iceberg under vertical oscillations, tons;
mv – mass of vessel, tons;

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