Transcript DYNAMIC TESTING TECHNIQUES IN STRUCTURAL ENGINEERING

CIE 616
Experimental Methods in Structural Engineering
Fall 2010
Prof. Andrei M Reinhorn
Unified Force-Based
Real Time Dynamic Hybrid Simulation
Xiaoyun Shao, PhD
Andrei M. Reinhorn, PE, PhD
Initially Prepared: March 2007
1
2015/7/16
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
2
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
3
Introduction
– Quasi-static loading test method (QST)
– Shaking table testing method (STT)
– Effective force method (EFT)
– Pseudo-dynamic testing method (PDT)
– Real time pseudo-dynamic testing method (RTPDT)
– Real time dynamic hybrid testing method (RTDHT)
4
Quasi-static loading test method
(QST)

A test specimen is subjected to slowly changing
prescribed forces or deformations by means of
hydraulic actuators

Inertial forces within the structures are not
considered in this method. Dynamic nature of
earthquakes are not captured.

Purpose is to observe the material behavior of
structural elements, components, or junctions
when they are subjected to cycles of loading
and unloading.
5
Shaking table testing method (STT)

Test structures may be subjected to actual earthquake acceleration
records to investigate dynamic effects

Inertial effects and structure assembly issues are well represented

The size of the structures are limited or scaled by the size and capacity of
the shake table
6
Effective force testing method (EFT)

Applying dynamic forces to a test specimen
that is anchored rigidly to an immobile
ground; perform real-time earthquake
simulation

The test specimen is fully assembled as shake
table test. (mass, damping and stiffness)
m4x4a
m2
m3x3a
:
These forces are proportional to the
prescribed ground acceleration and the local
structural masses.
:

m5x5a
:
m3
:
m2x2a
Based on a force control algorithm
m1
m1x1a
:

7
Pseudo-dynamic testing method (PSD)

Applying slowly varying forces to a structural
model

Motions and deformations observed in the test
specimens are used to infer the inertial forces
that the model would have been exposed to
during the actual earthquake

Substructure techniques
RT-PSD

Same as the PSD test except that it is conducted
in the real time

Introduce problem in control, such as delay
caused by numerical simulation and actuator
8
Introduction
Experimental Methods for Seismic Structural Performance:
•
•
•
•
Quasi-Static Loading Testing (QST)
Shaking Table Testing (STT)
Effective Force Testing (EFT)
Pesudo-dynamic Testing (PSD)
9
Introduction
Mx  Cx  f  x  MRug
W1: Northridge Acceleration
0.15
Acceleration (g)
0.1
0.05
0
-0.05
-0.1
-0.15
0
2
4
6
8
10
12
Tim e (s ec)
14
16
18
20
22
24
16
18
20
22
24
W2: Northridge Displacement
0.6
Displacement (in)
0.4
0.2
0
-0.2
-0.4
-0.6
0
P  MRu g
2
4
6
8
10
12
Tim e (s ec)
f  x  Mx  Cx  MRug
14
ug
:
m5x5a
:
m4x4a
Mx  Cx  f  x, x 
m3x3a
:
Mx  Cx  f  x, x 
Fi
Fi
:
m2x2a
:
m1x1a
(a) Effective force
method
Effective Force Test
f  x
F2
F1
(b) Pseudodynamic
substructure
Pseudo-dynamic Test
(c) Real-time dynamic
Shake Table Test
substructure
10
Introduction
Modern Seismic Simulation Techniques
– Substructure simulation
• Simulation conducted for (either experimentally or numerically) only part of the
structure to obtain the performance of the whole structure by extrapolation
– Pseudo-dynamic simulation
• Simulation conducted with inertia effect of the structural system is numerically
simulated in the computer and applied by hydraulic actuators or shake tables
– Dynamic simulation
• Simulation conducted with structures’ inertia effect physically realized in the
specimen and dynamical load is provided by actuators or shake tables
– Hybrid simulation
• Simulation procedure combined both physical experiment and numerical
computation to estimate/predict the structural seismic behavior
*PSD /substructure are by definition a hybrid simulation.
11
Introduction
•
Combination of the above simulation techniques render all kinds of different
modern seismic simulation methods
–
Real Time (Substructure) Pseudo-dynamic Simulation
•
Simulated inertial effect applied by actuator (Nakashima, 1992, Darby et al. 1999 Blakeborough et al.
2001)
•
•
Simulated inertial effect applied by shake Table (Nield et al. 1995)
Simulated inertia effect applied by actuator while shake table introduce acceleration ( Tamura and
Kobayashi, 1998)
–
(Substructure ) Dynamic Simulation
•
•
–
Quasi Dynamic Simulation
•
•
Using both shake table and actuator in one dynamic simulation (Kausel, 1998)
Substructure dynamic simulation ( Ito et al. 2000, 2004)
Hybrid simulation of dynamic/pseudo-dynamic (Cheng, 2006)
Each test method are relatively independent requires a full development of the
numerical algorithms and controllers for the corresponding loading system that
cannot be used for other type of test.
12
Introduction
A force-based seismic simulation method and the corresponding controller platform
that can UNIFY current seismic simulations methods
Real Time Dynamic Hybrid Simulation (RTDHS) – Combined use of earthquake
simulators, actuators and computational engines for simulation.
Response Feedback
Computational
Substructure
Physical
Substructure
Physical
Substructure
Shake Table
Computational
Substructure
Structural Actuator
Has to operate in
force control
Acceleration input: Table
introduce inertia force
Ground/Shake Table
13
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
14
Unified Formulation --
Substructure Partition
General Equation of Motion
Mx  Cx  Kx  MRug
Top Computational
M
  X  C
substructure
 tt
  t    tt
 E  αi  Mii  Xi 
P   αiMii  Ru  Xi 


te
g
C   X  K
K  X 
M
ti   t   tt
ti   t 
 tt








C
X  K
Ct  
K t   Xi 
ii   i 
ii 
 it
 it

 Ce X  C X  Ke X  K X 
ii i
ie e
ii i
ie e 


 Ru   0 
g  Pte 
Eα M 
i
ii 

 Pet Middle
    E  αi  Mii  Ru g  Xi   Cit Xt  Ct ii Xi  K it Xt  K t ii Xi 
Experimental

  Xi  Ceii
substructure
  
M ee

  Xe    Cei
 

α j M jj  

X j  
α i M ii
Cie
Cee
C je
  Xi  K eii
  
Cej   Xe    K ei
 
Ce jj  
X j  
K ie
K ee
K je
  Xi 
α i M ii
 

K ej   Xe    


K e jj  
X j 

 Peb     E  α j  M jj  Ru g  X j   Cb jj X j  C jb Xb  K b jj X j  K jb Xb 
M ee

 Pet 

 
 Ru g   0 
 Peb 
α j M jj 
 PbeBottom
  α j M jj  Ru g  X j   C je Xe  Ce jj X j  K je Xe  K e jj X j 
Computational
 E  α j  M jj
  X j  Cb jj C jb   X j  K b jj K jb   X j 
 E  α j  M jj

 Pbe 




Ru















g
0
substructure M
Mbb 
 


bb 
  Xb   Cbj Cbb   Xb   K bj K bb   Xb 
15
Unified Formulation
α i M ii




M ee
  Xi  Ceii
  
  Xe    Cei
 
α j M jj  
X j  
Cie
Cee
C je
  Xi  K eii
  
Cej   Xe    K ei
 
Ce jj  
X j  
K ie
K ee
K je
  Xi 
α i M ii
 

K ej   Xe    

K e jj   X j 

M ee

 Pet 

 
 Ru g   0 
 Peb 
α j M jj 
Mep xep  Cep xep  Kep xep  Mep Reug  Tep
Mep  M p ep  Mv ep
Mass splitting
M
p
ep
  E - αm  Mep
α i

α m　 


αe



α j 
M p ep xep  Cep xep  K ep xep  M p ep R eu g  Tep  α m M ep  R e u g  xep   M p ep R e u g  T "ep
Load splitting
αl  s 
M p ep xep  Cep xep  K ep xep  M p ep R e  E  αl  s   u g   T "ep  M p ep R e αl  s  u g 
16
Unified Formulation
MDOF Experimental Substructure in Hybrid Testing (General Case)
TOTAL DYNAMIC LOAD
TEST STRUCTURE MODEL
M pep xep  Cep xep  Kepxep
M p ep R e  E  αl  s   u g 
T
ep
Test
Type
PseudoDynamic
Testing
α
m
m
Test
Structure Model
Cep xep  Kep xep
α s  E
l

Table
Acceleration
Actuators
Forces
0
 Tep  M ep  R eu g  xep 
0
  Tep  M ep R eu g 
ug
Tep


E
Dynamic
Testing
α
 α mMep  Reu g  xep   M p ep R eαl  s  u g
0
0  α s  E
l
QuasiDynamic
Testing
0α
Mep xep  Cep xep  Kep xep
α s  E
l
α s  0
l
m
E
M pep xep  Cep xep  Kep xep
 E  α  s  u
l
g
  Tep  M ep R eα l  s  u g 
α s  E
l
α s  0
l
0
  T "ep  M p ep R eu g 
ug
T"ep
0  α s  E
l
 E  α  s  u
l
g
  T "ep  M p ep R eα l  s  u eq 
17
Unified Formulation
Single Story Structure in Hybrid Testing
18
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
19
Physical Platform
Shared Common Random Access Memory Network 20
Physical Platform
Real Time Dynamic Hybrid Simulation Controller
Real Time Structure Simulator
Set up Equation of Motion
of the Whole Structure
Property matrix
at the interface
DOF
Calculate the
Interface force
Solve the equation of
motion using time history
analysis
Structure
Simualtor
Map the state of
interface DOF
System Compensation Controller
Ground
Acceleration
Input
Interface
Force
Applied
Acceleration
Applied
interface
force
Compensator
For Shake
Tables
Acceleration
Commands to
Table
Controllers
Compensator
For Structure
Actuators
Displacement
Commands to
Actuator
Controllers
Load Division Between Shake
Tables and Structure Actuators
Interface Force
Calculator
Unified System
Controller
Compensation
Controller
21
Real Time Structure Simulator
Real Time Structure Simulator
Set up Equation of Motion
of the Whole Structure
Property matrix
at the interface
DOF
Calculate the
Interface force
Solve the equation of
motion using time history
analysis
Structure
Simualtor
Map the state of
interface DOF
System Compensator Controller
Ground
Acceleration
Input
Interface
Force
Applied
Acceleration
Applied
interface
force
Compensator
For Shake
Tables
Acceleration
Commands to
Table
Controllers
Compensator
For Structure
Actuators
Displacement
Commands to
Actuator
Controllers
Load Division Between Shake
Tables and Structure Actuators
Interface Force
Calculator
Unified System
Controller
Compensator
Controller
22
System Compensation Controller
•
Unified System Controller (USC)
–
–
•
Perform the unified formulation derived above for RTDHS
Redistribute the load between the shake tables and structure actuators
Compensation Controller
–
Provide the compensation necessary for applying the desired load by hydraulic loading
equipment
Compensation for Structure Actuator: Apply desired force to experimental substructure
– Dynamic Force Control
– Time Delay Compensation
– Effective Force Control
Compensation for Shake Table: Introduce desired acceleration input to experimental substructure
– When the applied acceleration is predetermined, no compensation is necessary for shake table.
– If quasi-dynamic test involved and using closed acceleration feedback to determine equivalent
acceleration, then time delay compensation need to be applied in shake table compensator.
Compensation for Hybrid Simulation
– Compensate for different time delay between shake table and structure actuator.
23
Unified System Controller
Tep
Interface
Force

ep
ep

M pAcceleration
ep x ep of Cep x ep  K ep x ep
x
Experimental
Substructure DOFs
M

  T'
α R

 M R u  T "

 M R  E  α  s   u


α s
 T  α M R u  x   M
pm e
ep e
ep
g
ep
ep
e
l
E  αm Re
g
l
p
ug
Input Ground
Acdeleration
ep
m
ep
Input, output and predefined
coefficients
Unified
Interface
Force
p
M ep
•
e
E  αl  s 
g
ep
ep
uep '
R eαl  s  u g

Unified
Acceleration

 p s
P2

Mx  Cx  Kx  Interface
Mu
Force g  T
•
Structure acceleration feedback can
be implemented either in open loop or
in closed loop

T

  M p    s  u   p  s  M2 p
eq
M
 l


P2'
Unified
Interface
Force



p
  1  ll ss  M ueq  1   p  s   T



u eq

ub
ub'
1  l  s 

 ug   m x 
T 

1


M

s


s











m
p
Input Ground
Unified
 l
1   m  M
Acdeleration
Acceleration
   1 m 



1 p s
1/ BaseAcceleration
M2

 1x2b   sm M  u g   m x   1    s   T
l
p


Acceleration of
Experimental
Substructure DOFs
TopForce
24
Compensation Controller
---for Structure
Actuator
Dynamic Force Control – Series Elasticity and Displacement Feedback
Desired Spring
Deformation
Structure
Displacement
Feedback
25
Compensation Controller
---for
Structure Actuator
Effective Force Control -- Velocity Feedback
mx  cx  kx  mug
mx   c  ca  x  kx  mug
mx   c  ca  x  kx  mug  ca x
26
Compensation Controller
---for
Structure Actuator
Time Delay Compensation – Smith’s Predictor
Smith’s Predictor
X
+
+
+
+
Estimate Error
-
+
Controller Output
Process
Gp
Plant
B
Tp
Y
Dead Time
Bm
-Ym Tm
Estimated
Dead Time
Gm
Estimated
Plant Model
Gsp G pTp
Gp
Gp
Y
G 

Tp 
Tp
X 1  Gsp G pTp 1  Gm  GmTm  G pTp
1  Gp
27
Compensation Controller for Hybrid Simulation
Shake Table and Structure Actuator
28
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
29
RTDHS Test Design
Real Time Dynamic Hybrid Simulation Controller
Real Time Structure Simulator
Set up Equation of Motion
of the Whole Structure
Property matrix
at the interface
DOF
Calculate the
Interface force
Solve the equation of
motion using time history
analysis
Structure
Simualtor
User Preparation
Map the state of
interface DOF
System Compensator Controller
Ground
Acceleration
Input
Interface
Force
Applied
Acceleration
Applied
interface
force
Compensator
For Shake
Tables
Acceleration
Commands to
Table
Controllers
Compensator
For Structure
Actuators
Displacement
Commands to
Actuator
Controllers
Load Division Between Shake
Tables and Structure Actuators
Interface Force
Calculator
Unified System
Controller
Compensator
Controller
UB-RTDHS Software Package
30
Real Time Structure Simulator
Input Data:
The input step is similar to most
finite
element
program,
which
includes the coordinate of joints
and their orientations; material
properties;
element
definition;
lumped mass at each joint as well
as the ground acceleration time
history.
31
Real Time Structure Simulator
Stiffness, Mass Matrix Assembly:
The stiffness and mass matrix are formed
by following the same procedure as for
static analysis based on the information
input. Therefore the commercial finite
element
analysis
programs,
such
as
ABACUS, SAP2000, IDARC and ANSYS,
are available to conduct this preprocessing.
32
Real Time Structure Simulator
Damp Matrix Assembly:
The damp matrix is then formed using the
Rayleigh damp formula by considering the
damping coefficients as a combination of
mass-proportional damping and stiffnessproportional damping.
33
Real Time Structure Simulator
Substructure Partition:
The dynamic matrices of the whole
structure model as well as the motion
vector are partitioned to represent each
substructure.
34
Real Time Structure Simulator
Stiffness, Mass Matrix
Condensation:
The
mass
and
stiffness
matrix
are
condensed to reduce the total DOFs of the
computational substructures’ model for real
time simulation based on the assumption of
their linear behavior during simulation. The
condensation
condensation
methods
and
include
dynamic
static
modal
condensation.
35
Real Time Structure Simulator
Numerical Integration:
One of the numerical integration methods
can be used here to solve step by step the
responses of the whole structure based the
reduced order governing equation of motion
of the structural modal.
36
Real Time Structure Simulator
Interface Force Calculation:
With the available sub matrices defined and
the simulated responses at the interface
DOFs, one may use derive the interface
forces necessary to be applied by the
dynamic actuators.
37
Real Time Structure Simulator
Errors:
The errors between the measured response
and the simulated response are used to
adaptive the controller and update the
numerical model in the structure simulation.
– Adaptive Control:
• MCS (Stoten, 1993)
– Online Modal Estimation
38
Real Time Structure Simulator
Start
Off line
preparation
Input Data
1.Joint, Element
2. Material Library
Input Data
Ground Acceleration
Mass, Stiffness Matrix Assembly of the
Computational Substructure (Static)*
* This procedure can
done using commercial
finite element software
such as ABACUS,
SAP2000, IDARC,
ANSYS, etc.
Damping Matrix
Assembly
Updating Numerical Model
– Mass, Stiffness, Damp Matrix
Form Dynamic
Loading
Dynamic Matrix Partition
Motion Vector Partition
Numerical Model
Condensation
User preparation work list:
• Structural model assembly
Condensation
Transformation
Equation of Motion
•
•
•
Determine ground acceleration
input
Perform substructure partition
Perform model condensation of the
computational substructure
Numerical Integration
Response s of DOFs
On Computational Substructure
Interface Force Calculation
For Each Substructures
Error
Adaptive
Controler
Go to SCC for Compensation
Real time
operation
Responses of DOFs on
Experimental Substructure
User input to RTSS:
• Ground acceleration history ( ug)
• Reduced order structural model
(ROM)
• Substructure partition information
39
Figure 1. Flowchart of Real Time Structure Simulator
Unified System Controller (USC)
Tep
 


Interface
Force
xep
Acceleration of
Experimental
Substructure DOFs


α mRe
M ep

E  αm  Re
M ep
ug
Tep'
Unified
Interface
Force
– Physical mass in the specimen
– Total mass necessary
αl  s 
E  αl  s 
uep '
Unified
Acceleration
Input Ground
Acdeleration
P2
ug
 p s

M2

ub

u eq
1/ M2
P2'
Unified
Interface
Force
l  s 
1  l  s 

Input Ground
Acdeleration


Interface
Force
x2b
User input to USC:
• Ground acceleration history ( u g)
• Mass splitting coefficient α m
1 p s



•
Load splitting coefficient αl
•
•
Ground acceleration history ( ug)
Mass splitting coefficient  m
– Physical mass in the specimen
– Total mass necessary
ub'
Unified
Acceleration
•
Load splitting coefficient l  p
m
Acceleration of
Experimental
Substructure DOFs
40
Compensation Controller for Hybrid Simulation
From
USC
Input to Compensation Controller (Research Engineer):
• Spring design and stiffness identification
• Additional damping identification
• Loading system identification and numerical model
• Physical specimen identification and numerical model
41
Outline
• Introduction
– Currently used seismic testing methods
– Proposed Real Time Dynamic Hybrid Simulation (RTDHS)
• Unified Formulation for RTDHS
• Unified Control Platform for RTDHS
• RTDHS Test Design
• A three story RTDHS example
42
Three Story Model
m3
k3
Top Substructure
c3
m2
k2
x2, u2
Experimental Substructure
c2
m1
k1
x3, u3
c1
x1, u1
Base Substructure
ug
Ground
Inertial Reference Frame
43
Step 1: Model Assembly
Step 2: Determine Ground Acceleration
Equation of Motion
 m3
0

 0
0
m2
0
0  u3   c3
 
0  u2    c3
u   0
m1  
1

Where:
 m3
0

 0
0
m2
0
c3
  x3   k3
 
c2   x2     k3
x   0
c2  c1  
1

 k3
0
c3  c2
c2
k3  k 2
k2
  x3 
 
k2   x2   0
x 
k2  k1  
1
0
u3   x3 
  
Absolute acceleration 
u
 2    x2   lu g
u   x 
 1  1
0   x3   c3
 
0   x2    c3
x   0
m1  
1

c3
c3  c2
c2
  x3   k3
 
c2   x2    k3
x   0
c2  c1  
1

0
 k3
k3  k 2
k2
  x3 
 m3
 
k2   x2     0
x 
k2  k1  
1
 0
0
0
m2
0
0
0  lu g
m1 
44
Step 3: Substructure partition
 m3
0

 0
0
m2
0
0   x3   c3
 
0   x2    c3
m1   x1   0
m3
k3
 k3
k3  k 2
k2
  x3 
 m3
 
k2   x2     0
k2  k1   x1 
 0
0
0
m2
0
0
0  lu g
m1 
x3, u3
c3
m x  c x  k x  m u 
3 3 3 3 3 3
3 g
x2, u2
k x c x
3 2 3 2
(k *displacement +c *velocityof experimental substructure )
3
3
Experimental Substructure
c2
m1
k1
c3  c2
c2
  x3   k3
 
c2   x2    k3
c2  c1   x1   0
0
Top Substructure
m2
k2
c3
c1
m x  c x  k x  m u  k x  c x
2 21 2 21 2 21
2 1 3 32 3 32
x1, u1
Base Substructure
m x  c x  k x  m u 
11 11 11
1 g
ug
Ground
k x c x
2 21 2 21
Force measured at the base of experimental substructure
Inertial Reference Frame
45
Step 4: Modal condensation
Motivation:
– Accelerate the online structure simulation to fit for real time testing.
– Behavior of the structure under investigation: computational substructure well
known while experimental substructure less known.
– Adopt commercial FEM software in assembling the structural model
Methods:
Static condensation (Guyan Reduction)
Dynamic condensation (Reyleigh-Ritz Reduction)
Discretization
Condensation
46
Step 5: Prepare Data Input for
RTSS
– Ground acceleration history
– Substructure partition information
– Reduced order structural model (ROM)
m3
k3
Top Substructure
x2, u2
k x c x
3 2 3 2
(k *displacement +c *velocityof experimental substructure )
3
3
Experimental Substructure
c2
m1
k1
m x  c x  k x  m u 
3 3 3 3 3 3
3 g
c3
m2
k2
x3, u3
c1
m x  c x  k x  m u  k x  c x
2 21 2 21 2 21
2 1 3 32 3 32
x1, u1
Base Substructure
m x  c x  k x  m u 
11 11 11
1 g
ug
Ground
k x c x
2 21 2 21
Force measured at the base of experimental substructure
Inertial Reference Frame
47
Step 6: Prepare Data Input for USC
– Mass splitting coefficient  m
– Load splitting coefficient l  p
Experimental Substructure EOM
m x
c x
k x
 m u  k x
c x
2 21
2 21
2 21
2 1
3 32
3 32


1    m x  c x
m  2 21 2 21  k2 x21







c
k
Apply Table Acceleration  m   s  u   p  s   3 x32  3 x32  
2 l
1
m

m2

2




Base acceleration


Physical Specimen
Apply Actuator Force



 1  l  s   m2u1   m m2 x21  c2 x21  1   p  s   c3 x32  k3 x32


Top force
48

Unified Formulation
Single Story Structure in Hybrid Testing
49
Step 7: Other preparation
•
General physical test design
–
–
–
–
•
Physical test setup installation
–
–
–
–
•
Experimental substructure (physical specimen) design, fabrication drawings
Instrumentation design and configuration
Test protocol list
Series spring and connection design (by RE)
Specimen
Instrumentation
Series spring
Loading devices -- dynamic actuators / shake tables
Physical test setup identification
– Design compensation controller (by RE)
* Cooperation with research engineer, technicians, lab manager, etc.
50
Proof-of-Concept Test
Small Scale Pilot Experimental Setup
•
•
Shake table is controlled in displacement
Reduced mass model and full mass model
51
Proof-of-Concept Test
Three Story Hybrid Simulation
Generalized Equation for All Cases




 c3

k3





1   m  m2 x21  c2 x21  k2 x21  m2 l  s  u1   p  s   m x32  m x32    1   l  s   m2u1   m m2 x21  c2 x21  1   p  s   c3 x32  k3x32
 2
2


Top force


Base acceleration



m3
k3
c3
m2





Implementation
Case
Loading cases
Equations of motion
0.23  m2 x21  c2 x21   k2 x21 
Case1：For
   0.77    s   0 and   s   0 
m2u1  0.77  m2 x21  c2 x21    c3 x32  k3 x32 
Top Substructure
m
l
p
Top
m x  c x  k x  m u 
k x force
c x
3 3 3 3 3 3
3 g
3 2 3 2
c
 
k
Case2：For

m2 x21  c2 x21 
u1  0.5  3 x32 substructure
 3 x32   )
(k *displacement
+ck2 x*velocityof
21  m2 0.5experimental
x2, u2
m

m2

3
   0    s   0.5 and   s   0.5 3
 2
 
m
l
p
x3, u3
Base acceleration
k2
Experimental Substructure
c2
m1
k1
x1, u1

 0.5m2u1  0.5 c3 x32  k3 x32

m x  c x  k x  m u  k x  c xTop force
2 21 2 21 2 21
2 1 3 32 3 32

c

k
Case3：For


m2 x21  c2 x21  k2 x21  m2 u1   3 x32  3 x32  


m
m
   0    s   1 and   s   1 


 2
2


m
l
p
Base acceleration
c1
Base Substructure
Case4：For
Ground
Inertial Reference Frame

 0    s   0.0 and   s   0.0 
c x  k x  pm u 
k x c x
m m xl 
11 11 11
1 g
2 21 2 21
x

c
x

k2 x21of experimental substructure
Force m
measured
at
the
Case5：For
2 21 2 21 base
   0    s   1 and   s   0.0 
u1 
 m2
  c3 x32  k3x32 
m
l
p

ug

m2 x21  c2 x21  k2 x21   m2u1  c3 x32  k3x32
Top force
Base acceleration
Top force
52
Proof-of-Concept Test
Experimental Result of Three Story Hybrid Simulation -- Acceleration
Case1
Case2
Case3
Case4
Case 5
Simulation
Matlab
8
7
6
Amplitude
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Frequency (Hz)
53
Conclusions
• Reviewed the current seismic simulation methods
• Proposed force-based RTDHS combining
– Shake table, dynamic actuators and numerical simulation
– Substructure, Pseudo-dynamic, Dynamic and Hybrid simulation techniques
• Unified formulation
– Substructure partition
– Loading splitting coefficient (mass, dynamic load)
• Unified control platform
– Real time structure simulator
– System compensation controller
• Design a RTDHS
– Procedure
– Example – a three story hybrid simulation
54
Thank You!
&
Questions?
55