Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method

S. Chucheepsakul, N. Srinil

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.
LanguageEnglish
Pages1067-1097
Number of pages30
JournalOcean Engineering
Volume29
Issue number9
DOIs
Publication statusPublished - 2002

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Cables
Euler equations
Stiffness matrix
Strain energy
Stretching
Equations of motion
Natural frequencies

Keywords

  • marine cables
  • free vibrations
  • coupled transverse modes
  • variational method
  • dynamic tension
  • frequency avoidance phenomenon

Cite this

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abstract = "This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.",
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Free vibrations of three-dimensional extensible marine cables with specified top tension via a variational method. / Chucheepsakul, S.; Srinil, N.

In: Ocean Engineering, Vol. 29, No. 9, 2002, p. 1067-1097.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Chucheepsakul, S.

AU - Srinil, N.

PY - 2002

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N2 - This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.

AB - This paper presents a model formulation that can be used for analyzing the three-dimensional vibration behaviours of an inclined extensible marine cable. The virtual work-energy functional, which involves strain energy due to axial stretching of the cable and virtual work done by external hydrostatic forces is formulated. The coupled equations of motion in the Cartesian coordinates of global systems are obtained by taking into account the difference between Euler's equations and equilibrium equations. The method of Galerkin finite element is used to obtain the mass and stiffness matrices which are transformed into the local coordinate systems. Then the eigenvalue problem is solved to determine its natural frequencies and corresponding mode shapes. The model formulation developed herein is conveniently applied for the cases of specified top tension. The numerical investigations are carried out to demonstrate the validity of the model and to explore in details the influence of various parameters on the behaviours of marine cables. Results for the frequency avoidance phenomenon, maximum dynamic tension and coupled transverse mode shapes are presented and discussed.

KW - marine cables

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KW - dynamic tension

KW - frequency avoidance phenomenon

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