Experimental Study of Nonlinear MooredBuoy Responses

1
Experimental Study of Nonlinear Moored-Buoy
Responses

• Objectives
• To Identify and Classify Highly Nonlinear
  Experimental Structural Responses Under Combined
  Deterministic and Random Waves
• To Validate Analytical Model Predictions and
  Investigate Fluid-Structure Interactions

Experimental Configuration (SDOF)

• Principal Investigator
• Prof. Solomon C.S. Yim Civil
  Engineering Department Oregon State
  University

• Approach
• Modifying Existing ID Techniques and/or
  Developing New Tools to Classify Degree of
  Nonlinearity
• Comparing Overall Behaviors of Experimental Data
  and Simulations to Validate Analytical Model
• Conducting Sensitivity Study to examine
  Hydrodynamic Properties

2
Highly Nonlinear Experimental Structural
Responses
Possible Chaos (Poincare Map)

• Observations
• Primary and Secondary Resonances in Frequency
  Response Diagram
• Harmonic, Subharmonic, Superharmonic, and
  Possibly Chaotic Responses
• Transition Behavior of Multiple Coexisting
  Response Attractors

Possible Chaos (Poincare Time History)
Coexisting Harmonics and Subharmonics
3
Poincare Analysis of Multiple Coexisting
Responses
Sections I V
Sections III VII
Sections II VI
Sections IV VIII
4
Comparisons of Experimental Results and
Analytical Predictions
Numerical Model
Time-Averaged PDF
where
Frequency Response Diagram
Distributions of Large Excursions
5
On-Going/Future Research
Cd versus Reynolds Number

• On-Going Research
• Identifying Best-Fit Fluid-Structure Models
• Investigating Hydrodynamic Properties
• Predicting Occurrence of (Noisy) Chaos
• Verifying Inter-Domain Transitions as
  Analytically Predicted

Cm versus Reynolds Number

• Future Research
• Formulating Models Based on Large Body Theory
• Extending Analysis Procedure to MODF Experimental
  Results
• Comparing SDOF and MDOF Results

6
Stochastic Analysis of Nonlinear System under
Narrowband Excitation

• Objectives
• Improve accuracy of prediction using
  semi-analytical method
• Apply semi-analytical method to
  nonlinear-structure nonlinearly-damped (NSND)
  model
• Compare prediction with experimental data

• Principal Investigator
• Prof. Solomon C.S. Yim
• Civil Engineering Department
• Oregon State University

• Approach
• Identify typical nonlinear response behavior
  under deterministic excitation
• Employ semi-analytical method to predict system
  response
• Validate prediction method through comparison
  with experimental data

7
Stochastic Analysis of Nonlinear System under
Narrowband Excitation
Response under Deterministic Excitation Typical
Nonlinear Response Behavior
Progress System Configuration
(a) Plan view (b)
Profile view Fig.1 Experimental model of
nonlinear system
Fig.2 Four different response behavior under
same excitation
Coexisting Attraction Domain
Response Amplitude Curve
Fig 3. Small amplitude harmonic, 1/3 subharmonic,
1/2 subharmonic and large amplitude harmonic
Fig 4. Response amplitude curve of system in
subharmonic region
8
Stochastic Analysis of Nonlinear System under
Narrowband Excitation
Jump Phenomena
Inter-Domain Transition
Fig 5. Amplitude jump from large amplitude to
small amplitude harmonic domain
Fig 6. Schematic diagram of inter-domain
transitions
Intra-Domain Transition
Response under Narrowband Excitation Stochastic
behavior of the excitation parameter
Where, A(1),A(2) excitation amplitude of
current and next cycles, ? phase angle
difference, ?(1)-?(2)
Fig 7. Intra-domain transitions within four
different attraction domains
9
Stochastic Analysis of Nonlinear System under
Narrowband Excitation
Numerical simulation
Large amplitude harmonic response
1/2 subharmonic response
1/3 subharmonic response
small amplitude harmonic response
Fig 8. Time series of narrowband excitation
amplitude (top) and corresponding response
amplitude (bottom)
Fig 9. Amplitude response map correspond to time
series shown in Fig 8.
Result Overall Response Amplitude Probability
Distribution

• Future study
• Apply semi-analytical method to NSND model
• Predict response of NSND model with coefficient
  determined by system identification technique
• Verify prediction using experimental data

Fig 10. Overall response amplitude probability
distributions (compared with simulation result)
10
Modeling and Validation of Nonlinear Stochastic
Barge Motions
Modeling and Validation of Nonlinear Stochastic
Barge Motions
Objectives - To examine predictive capability
of coupled Roll-Heave-Sway models to
estimate stochastic properties of nonlinear
barge response behavior - To develop
probability-based analysis and design
methodology
FIG. 1. Roll-Heave-Sway Model
Approach - Develop Roll-Heave-Sway
barge-motion models (and lower order ones)
- Identify system coefficients - Examine and
compare numerical predictions with measured
data - Develop nonlinear extreme-value
prediction techniques
Principal Investigator - Prof. Solomon C.S. Yim
Civil Engineering Department Oregon State
University
11
Modeling and Validation of Nonlinear Stochastic
Barge Motions
Identification of System Coefficients for
Roll-Heave Model - Regular Waves
Comparison of Model Predictions with Measured
Data - Measured Random Waves -
Simulated Random Waves
measured
predicted
FIG. 1. Roll vs Roll Velocity
(Regular Waves, Case SB27)
measured
predicted
Future Research - Examine complex nonlinear
behavior including resonance and possible
chaos - Perform and compare simulations - Use
model to verify proposed theories on capsize
FIG. 2. Roll vs Heave (Regular
Waves, Case SB27)
12
Modeling and Validation of Nonlinear Stochastic
Barge Motions
measured
predicted
FIG.3. Roll Distribution (measured
random waves)
FIG.5. Roll vs Wave (measured random
waves)
measured
predicted
FIG.4. Heave Distribution (measured
random waves)
FIG.6. Roll vs Heave (measured
random waves)
13
Modeling and Validation of Nonlinear Stochastic
Barge Motions
measured
predicted
FIG.7. Roll Distribution (simulated
random waves)
FIG.9. Roll vs Wave (simulated
random waves)
measured
measured
FIG.8. Heave Distribution
(simulated random waves)
FIG.10. Roll vs Heave (simulated
random waves)