Transverse motion instability of a submerged moored buoy

Jana Orszaghova, Hugh Wolgamot, Scott Draper, Rodney Eatock Taylor, Paul Taylor, Ashkan Rafiee

Research output: Contribution to journalArticle

Abstract

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.
Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalProceedings of the Royal Society A-Mathematical Physical and Engineering Sciences
Volume475
Issue number2221
DOIs
Publication statusPublished - 2 Jan 2019

Fingerprint

Transverse
direct power generators
Motion
Converter
Mathieu Equation
Mathieu function
pendulums
Pendulum
Pendulums
Natural Frequency
resonant frequencies
Irregular
Natural frequencies
Energy
Offshore Structures
Parametric Excitation
Period Doubling
Surge
period doubling
Subharmonics

Cite this

@article{349908d265914dd3ab6702480482ea6f,
title = "Transverse motion instability of a submerged moored buoy",
abstract = "Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.",
keywords = "wave energy converter, submerged buoy, Mathieu instability, damped elastic pendulum, mode coupling, parametric resonance",
author = "Jana Orszaghova and Hugh Wolgamot and Scott Draper and {Eatock Taylor}, Rodney and Paul Taylor and Ashkan Rafiee",
year = "2019",
month = "1",
day = "2",
doi = "10.1098/rspa.2018.0459",
language = "English",
volume = "475",
pages = "1--21",
journal = "Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences",
issn = "1364-5021",
publisher = "Royal Society of London",
number = "2221",

}

Transverse motion instability of a submerged moored buoy. / Orszaghova, Jana; Wolgamot, Hugh; Draper, Scott; Eatock Taylor, Rodney; Taylor, Paul; Rafiee, Ashkan.

In: Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, Vol. 475, No. 2221, 02.01.2019, p. 1-21.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Transverse motion instability of a submerged moored buoy

AU - Orszaghova, Jana

AU - Wolgamot, Hugh

AU - Draper, Scott

AU - Eatock Taylor, Rodney

AU - Taylor, Paul

AU - Rafiee, Ashkan

PY - 2019/1/2

Y1 - 2019/1/2

N2 - Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

AB - Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.

KW - wave energy converter

KW - submerged buoy

KW - Mathieu instability

KW - damped elastic pendulum

KW - mode coupling

KW - parametric resonance

U2 - 10.1098/rspa.2018.0459

DO - 10.1098/rspa.2018.0459

M3 - Article

VL - 475

SP - 1

EP - 21

JO - Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences

SN - 1364-5021

IS - 2221

ER -