1 challenge the future impulse based substructuring theory, improvement and implementation on real...
Post on 19-Dec-2015
214 views
TRANSCRIPT
1Challenge the future
Impulse Based Substructuring Theory, Improvement and Implementation on real problems
Nazgol HaghighatSupervisor: Prof. Dr. Ir. Daniel J. Rixen
2Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
3Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
4Challenge the future
What is IBS?
• IBS is one of the Dynamic Substructuring methods
• IBS can be applied to study performance of a system with time (Dynamic Analysis)
• IBS is working in time domain and can be used instead of numerical time integration (Newmark)
• IBS can be applied only on linear systems
5Challenge the future
Dynamic substructuring
Simpler substructures:
Large and complex structures:
Analysing a structure by studying its subparts
Assembling the substructures: By considering interface forces (λ)
• They must be in equilibrium • They must satisfy compatibility condition at interface
6Challenge the future
Dynamic substructuring techniques
By using impulse responses and applying convolution product
Analysing each subsystem individually:• Physical domain• Modal domain• Frequency domain• Time domain
7Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
8Challenge the future
Why IBS is important?
• Can provide dynamic response of large and complex structures
• Offers advantages in shock analysis compared to frequency based substructuring
• Can be implemented easily• Provides the possibility of analysing a system in the
basic design steps
9Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
10Challenge the future
IBS general frame work
Obtaining Impulse Response Functions (IRFs):
Decomposing the structure into some subsystems:
Assembling substructures: (Assembly Equation)
11Challenge the future
Obtaining Impulse Response Functions (IRFs)
1. Applying impact at the input or interface forces positions; Unit Impact
Can be interpreted as a short vary high accelerationCan be modelled: - Experimentally
Hammer impact
- Numerically Defining special initial conditions in time integration of motion equation
2. Measuring or computing dynamic response of the system under a unit impact
12Challenge the future
Numerical time integration (Newmark)
Linearized motion equation:
M linearized mass matrix C linearized damping matrixK linearized stiffness matrixu array of degrees of freedomf external applied forces
Newmark time integration scheme:using finite time difference concept
β , γ Newmark parametersu array of DoFsdt size of the time step
13Challenge the future
Numerical models of unit impact
IF impact model:
3 different impact models can be defined:
1. Initial applied velocity (IV) 2. Initial applied force (IF) 3. Applied force at second time step (SF)
14Challenge the future
Discretizing the input force using IF impact model
Discretizing the input force with IF impact model at each time step
IBS assembly equation (using IF impact model)
Convolution product :
Compatibility condition :
15Challenge the future
Computed IRFs under IF impact model(Applying Newmark time integration)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10
-4
t(s)
H(1
)LL
(t)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.0160
0.002
0.004
0.006
0.008
0.01
0.012
0.014
t(s)
H(2
)00
(t)
16Challenge the future
Does IBS really work?
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-2
0
2
4
6
8
10
12
14
16x 10
-9
time(s)
Ux (
t)
IBSIF
NI
Dynamic response of the bar system under an excitation described by unit step
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-8
-6
-4
-2
0
2
4
6
8x 10
-8
time(s)
Ux (
t)
IBSIF
NI
Dynamic response of the bar system under a periodic excitation
Results of IBS (IF impact model) are exactly equal to results of Newmark time integration (constant average
acceleration)
17Challenge the future
Advantage and disadvantage of IBS
The IRFs (of substructure) can be computed once and being used several times in different analysis
Convolution product can be applied only for the same length of time of IRFs
18Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
19Challenge the future
Is IBS efficient for long time simulations?
1. Costs in computing IRFs2. Costs in computing convolution product
Suggested solution : Truncating Impulse Response Functions
20Challenge the future
Applying Truncation on Different types of IRFs
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1x 10
-4
t(s)
H(1
)LL
(t)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.0160
0.002
0.004
0.006
0.008
0.01
0.012
0.014
t(s)
H(2
)0
0(t
)
• Boundary DoFs are fixed
• IRFs are damped with time
Non-floating (sub)structure Floating (sub)structure
• Boundary DoFs are not fixed• IRFs are increased with time
21Challenge the future
Truncating IRFs of a non-floating (sub)structure
Multiplying IRFs by a window functionDifferent types of window functions
• Rectangular window • Cosine Window
Effects of applying cosine window function on IRF of a non-floating structure
Amax maximum amplitudeA(t) amplitude at pickα design variable
22Challenge the future
Truncating IRFs of a floating (sub)structure
IRFfloating system IRFvibrational mode IRFpure rigid body mode
IRFpure rigid body mode :
Can be obtained analytically (null Space of stiffness matrix) IRFvibrational mode = IRFfloating system - IRFpure rigid body mode
IRFvibrational mode : Can be truncated by applying window function
23Challenge the future
Outlines
• What is IBS?
• Why is IBS important?
• How does IBS work?
• How to apply IBS for longer time simulations?
• Can it be applied on real problems (3D structures)?
24Challenge the future
Applying IBS on a 3D structure
Problem Definition:
• Offshore wind turbine (3D)
• 2 substructures: Jacket structure and
wind mill (tower +RNA)
• External force: unit step at the
interface
• Applied method: Truncated IBS
25Challenge the future
Truncated IBS solving procedure
1. Computing the IRFs (jacket structure and wind mill)
2. Removing rigid body impulse response form the IRFs
(windmill)
3. Windowing the vibrational IRFs
4. Computing convolution product using truncated IRFs
5. Adding rigid body responses (wind mill)
6. Computing interface forces
26Challenge the future
Results
0 50 100 150 200 250 3000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-8
time(s)
u 11(t
)
IBS
NI
Dynamic response of DoF(1) at the interface due to a unit step exciting DoF(1) of the interface (truncation at t=130 (s))
27Challenge the future
Results
300 302 304 306 308 310 312 314 316 318 3202.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1x 10
-8
time(s)
u 11(t
)
IBS
NI
Dynamic response of DoF(1) at the interface due to a unit step exciting DoF(1) of the interface (zoomed at the last 20(s))
28Challenge the future
Conclusion and future work
Conclusion :• Results of IBS (IF impact model) are exactly equal to results of
Newmark time integration (average constant velocity)• Truncation (cosine window) is a reliable solution for reducing
computation cost of IBS
Future work :• Studying results of applying IBS on more 3D structures• Trying more types of window functions• Improve IBS to cover also non-linear problems