Petronas Deepwater Seminar

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Floating Production Systems - Houston

Petronas Deepwater SeminarSession 1AIntroduction to Dynamics


John ChianisFPS Houston

Vice President, Deepwater Technology and Engineering

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Introduction to DynamicsAgenda:

SDF System

Demonstration

Response Amplitude Operator (RAO)

Sensitivity to K, C and M

6 DOF Motion Definition

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SDF System

SDF System = Single Degree of Freedom System

If the response of a system can be described by a single coordinate, it

can be classified a SDF system

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SDF System

Mathematical Representation of a SDF System

M

K CM = Mass

K = Stiffness

C = DampingTime

Osc

illat

ion

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SDF System

Definition of a Oscillation

Length

Amplitude

Period is the time for one complete oscillation

A Regular Oscillation is Characterized by a Constant

Amplitude and Period

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SDF System

Time-Related Parameters of a Regular Oscillation

Time for one complete oscillation

Number of oscillations in a given time period

No. of oscillations (in radians) in a given time

Period, T

Frequency, f

Circular Frequency,

sec

sec-1

rad/sec

f = 1 / T

= 2 f

= 2 / T

DefinitionParameter Units Relationship

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DemonstrationPurpose:

Demonstrate the response of a Single Degree of Freedom (SDF) system subjected to base excitation.

Procedure:Measure the vertical displacement of a mass while the suspended spring/mass system is oscillated up and down with a unit amplitude motion. Repeat for different periods of oscillation.

Demonstration

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Demonstration

Mass

Rubber Bands

1) Hold the spring-mass system as shown

2) Oscillate hand up and down with a unit amplitude motion keeping the period of the oscillation constant

3) Measure the resulting vertical displacement of the mass and plot

4) Repeat steps 1 thru 3 for different periods of oscillation

Datum

Datum

Resulting Vertical Displacement of Mass

Unit Amplitude Oscillations of Hand

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Demonstration

Time

Hand

Mass

Datum

Datum

For a unit amplitude motion at a constant period of oscillation . . .

What is the resulting vertical displacement of the mass?

Data Measurement

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Demonstration Results:

Point 1Very small motion for low period excitation

Point 2Motion follows

excitation at high period

Point 3Motion/excitation

resonance

1.0

Vert

ical

Dis

plac

emen

t of

Mas

s (ft

)

Period of Excitation (sec)

Increasing

Pt. 1

Pt. 2

Pt. 3

Demonstration

Above plot shows vertical displacement of mass for constant amplitude excitation at three periods of oscillation

Resonance

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Believe it or not . . .

Demonstration

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Notes:1 Response can be motion (displacement, velocity &

acceleration), load (force & moment), stress, etc.

2 Amplitude is 1/2 crest-to-trough height

3 Theoretical wave with a sinusoidal form

4 Typical ocean waves have a range of periods from 4 sec to 25 sec

Response Amplitude OperatorRAO =The response1 of a floating system to a series of unit amplitude2regular3 waves of varying period4

=


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SDF System

m

k c

X(t)

BaseExcitation

T1

T2

T3

Tn

Unit Amplitude Regular Excitation

Waves Floating Platform


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Types

Units of Typical RAOs are as Follows:


Displacement

Velocity

Acceleration

Load

Stress

Translation

ft / ftRotation

rad / ftTranslation

ft / sec / ftRotation

rad / sec / ftTranslation

ft / sec2 / ftRotation

rad / sec2 / ftForce

kips / ftMoment

kip ft / ft

ksi / ft

RAO Units

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0

Period (sec)

Mot

ion

(ft/f

t)

K=600 K=150 K=50

Sensitivity of RAO to K (stiffness)


Increasing the stiffness of a system shifts its peak RAO response to the left, i.e. higher frequency

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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0

Period (sec)

Mot

ion

(ft/f

t)

C=30 C=50 C=100

Sensitivity of RAOs to C (damping)


Increasing the damping of a system reduces its peak RAO response

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Sensitivity of RAOs to M (mass)



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 10.0 20.0 30.0

Period (sec)

Mot

ion

(ft/ft

)

M=50 M=100 M=200

Increasing the mass of a system shifts its peak RAO response to the right, i.e. lower frequency

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6 DOF Motion Definition

6 DOF Motion Definition (Rigid Body)Z (up)

Heave

YawX (to bow)

Surge

Roll

Y (to port)Sway

Pitch

Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20

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Petronas Deepwater Seminar