Center for Mechanics and Materials, Department of Civil Engineering

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Free Vibrations of Marine Risers Conveying Fluid
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• Center for Mechanics and Materials, Department
  of Civil Engineering
• King Mongkuts University of Technology Thonburi

23 - 25 October 2002 The 8th National Convention
on Civil Engineering hosted by Khon Kaen
University
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INTRODUCTION

• Growing of Energy Industry and Marine Exploration
  signifies the study of off-shore in-shore
  structures.

• Marine riser is used as a fluid-transported
  curved pipe drilling the undersea economical
  resources i.e. oil, gas, mud, etc.

• Marine riser serves the off-shore structural
  system as the link between the platform and the
  well head on the sea base.

Express Platform, North Sea
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INTRODUCTION-cont

• The riser structure is modeled as a beam-column
  like structure conveying fluid.

• The both ends are pinned supports having small
  static offset.

• After installing the drilling system, the riser
  experienced the current and wave forces in
  addition to its own weight, fluid pressures, and
  vessel offsets.

Example of a marine riser
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INTRODUCTION-cont

• Delicate design and construction must be done
  otherwise the severe accident would occur and
  affect among workmen, sea environments, and
  assets.

• This research numerically investigates the free
  vibrations of marine risers transporting internal
  fluid.

• These tasks benefit the structural/offshore
  engineers.

Fire hazard of an offshore platform
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LITERATURE REVIEWS

• Irani et al. (1987) studied dynamic analysis of
  3D riser with internal steady flow and nutation
  dampers.

• Moe and Chucheepsakul (1988) applied asymptotic
  approach and FEM to natural vibration analysis
  with zero-flexural stiffness.

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LITERATURE REVIEWS

• Wu and Lou (1991) studied effect of bending
  rigidity on riser dynamics using perturbation
  method.

• Chucheepsakul et al. (1994, 1999, 2002) studied
  riser statics and dynamics neglecting flexural
  stiffness.

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ASSUMPTIONS

• Material is homogeneous.

• Material is linear elastic obeying Hookes Law.

• Torsion is not considered.

• Poissons effect is neglected.

Steel pipe/riser
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STATIC ANALYSIS
Equilibrium Equations
The static solution can be generally obtained by
using the finite element method.
Drilling System
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FREE VIBRATION ANALYSIS

• Applying Hamiltons Principle yields the
  nonlinear equations of motion.

• Through Galerkin FE procedure, the linearized
  equations of motion become the following matrix
  free vibration equation.

Typical Riser Configurations
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FREE VIBRATION-cont
From,
where the mass and gyroscopic matrices are
Riser Motion
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FREE VIBRATION-cont
The stiffness matrix is
Riser Motion
With some manipulations, the matrix equation can
be formed into eigenproblem and then solved
numerically by QZ-Algorithm.
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EXAMPLES AND RESULTS

• The next table table 2 shows aspects of
  flexural rigidity and internal flow speed on
  natural frequencies of marine risers.

• Effect of top tensions on the natural frequencies
  of marine risers is depicted in the next figure
  figure 1.

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• Aspects of flexural rigidity and internal flow
  speed on natural frequencies of marine risers.
  table 2

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EXAMPLES AND RESULTS

• Effect of top tensions on the natural frequencies
  of marine risers. figure 1

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CONCLUSIONS

• By considering the bending effect, the natural
  frequencies increase with increment of flexural
  stiffness.

• The steady high velocity internal flow with
  uniform top tension significantly effects the
  riser behaviors by reducing the natural
  frequencies.

• The top tension has obvious influence on the
  increase in natural frequencies.

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ACKNOWNLEDGEMENT
The authors would like to thank these
organizations

• Thailand Research Fund (TRF)

• Center for Mechanics and Materials (MecMat),
  Department of Civil Engineering, KMUTT
  URL http//www.kmutt.ac.th/mecmat/