ADVANCED DYNAMIC TESTING TECHNIQUES IN STRUCTURAL ENGINEERING

1. CIE 616 FALL 2004 ADVANCED DYNAMIC TESTING TECHNIQUES IN STRUCTURAL ENGINEERING by Andrei M Reinhorn Xiaoyun Shao

2. Contents • Introduction of dynamic testing methods • Effective force testing • Pseudo dynamic testing • Real time hybrid dynamic testing

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. • purpose is to observe the material behavior of structural elements, components, or junctions when they are subjected to cycles of loading and unloading. • dynamic nature of earthquakes are notcaptured

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. Other testing methods (STT) • Effective Force Method • Pseudo-dynamic testing • Real Time Dynamic Hybrid Testing (new developement)

7. Effective force testing method (EFT) • Effective Force Technique • Hybrid Testing & Computing • Real-Time Pseudo-Dynamic Hybrid Testing System • Real-Time “Dynamic” Hybrid Testing System Applies the inertial ground motion generated forces through synchronized actuators - NEW

8. 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 • these forces are proportional to the prescribed ground acceleration and the local structural masses. • based on a force control algorithm

9. Effective Force Technique • Hybrid Testing & Computing • Pseudo-Dynamic Hybrid Testing System • Real-Time “Dynamic” Hybrid Testing System Applies forces in substructure through actuators only – real time operation is a benefit but not a must

10. 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

11. Real time pseudo-dynamic testing method (RTPDT) • 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

12. Effective Force Technique • Hybrid Testing & Computing • Real-Time Pseudo-Dynamic Hybrid Testing System • Real-Time “Dynamic” Hybrid Testing System Applies forces in substructure through shake table and actuators – real time operation is a must

13. Real-Time Seismic Hybrid Testing

14. Real time dynamic hybrid testing method (RTDHT) • based on shaking table test combined with substructure techniques. • part of the structure (the physical model) is constructed and tested on the shaking table • The rest part of the structure (the numerical model) is numerically modeled in the compute • the earthquake effect on the superstructure was calculated as a interface force and applied to the substructure by the actuators (force control based)

15. Block Diagrams of Various Testing Methods

16. Open Loop Test

17. Open Loop Control (in concept) Effective Force Test

18. Closed Loop Test

19. Closed Loop Test Pseudo-dynamic Test with Substructure

20. Closed Loop Test

21. Summary of dynamic test methods

22. Effective Force Testing Equation of motion Subscript refers to motion relative to a fixed reference frame (absolute displacement)

23. Open Loop Control (in concept) Effective Force Test

24. Effective Force Test – Hardware Components • Servo-Hydraulic Actuators • Servo-Hydraulic Control System • Elastic Spring • Measurement Instrumentation (DAQ) • Computer • Simulator • Controller

25. Effective Force Test – Hardware Configuration

26. Effective Force Test -Dynamic force control Series elasticity and displacement feedback

27. Effective Force Test -Dynamic force control Series elasticity and displacement feedback Ideal: C = 1/G

28. Effective Force Test -Dynamic force control The advantages of using the series spring • the actuator can be well tuned and operated in displacement control • it provides for one more parameter than can be altered in the control design (the oil stiffness cannot be) • the term KLC(1-CG) in the transfer function indicates that the smaller the value of KLC the less sensitive is the transfer function to deviations of C from 1/G

29. Effective Force Test – Effect of Time Delay The dynamic characteristics of hydraulic actuators inevitably include a response delay , which is equivalent to negative damping Experimental Numerical

30. Effective Force Test – Predictive Control Smith Predictor

31. Effective Force Test – Predictive Control Without compensation Withcompensation

32. Effective Force Test – Software • Simulink® • Realtime Workshop®5 • XPC Target

33. Pseudo dynamic testing Define a model of the structure system Define the desired excitation – usually base acceleration Calculate the expected response of structure – displacement Use an actuator to apply the desired displacement in the structure Measure the resistance force in the structure (or estimate it from measurements) Repeat the above steps – start from second

34. Pseudo-dynamic testing

35. Pseudo dynamic testing

36. Pseudo-dynamic testing – Hardware Components • Servo-Hydraulic Actuators • Servo-Hydraulic Control Systems • Measurement Instrumentation • On-line computer

37. Pseudo-dynamic testing – Hardware Configuration (Local)

38. Pseudo dynamic testing Discretized equation of motion of the structure at time intervals for , Equation solved in computer step by step, with Ri as the reaction force measured from the specimen under test. Result is the displacement command of next step that will be applied to the specimen at each node of mass by actuators.

39. Pseudo dynamic test—integration algorithm • Both explicit and implicit time-stepping integration algorithm can be applied for solving equation of motion in Pseudo-dynamic tests. • Explicit methods compute the response of the structure at the end of current step based on the state of the structure at the beginning of the step. • Central difference method (Takanashi et al. 1975), • Newmark- Beta method (1959), • Modified Newmark’s method (1986), • The γ-function pseudodynamic algorithm (Chang et al. 1997) • Unconditionally stable explicit method(Chang, 2002) (continued on next)

40. Pseudo dynamic test—integration algorithm(continued) • Implicit methods require knowledge of the structural response at the target displacement in order to compute the response. • the displacement is dependent on other response parameters at the end of the step • iteration is required in the algorithm to satisfy both the imposed kinematic conditions and the equilibrium conditions at the end of the time step • Newmark – Alpha method (Hilber et al. 1977) • Hybrid implicit algorithm (Thewalt and Mahin, 1987) • Newton iteration (Shing, 1991) ,

41. Pseudo dynamic test—integration algorithm(continued) • implicit iteration algorithm provide improved stability characteristics and permit the used of larger integration time steps • iteration on experimental model is not practical since structure materials are path dependent • explicit methods are easier to implement • Explicit integration methods are preferred for PSD simulation when stability limits are satisfied for the structural model under investigation

42. Pseudo dynamic test—integration algorithm(continued) Example: Modified Newmark’s Method Substitute into and solve for

43. Pseudo-dynamic testing – substructuring principle • may fabricate only part of the structure whose hysteretic behavior is complex and apply the test to this part • remaining part treated in the computer

44. Pseudo-dynamic testing – substructuring principle subscripts a and e denote the degrees of freedom within the analytical and experimental substructures. • Tested part. Calculate displacement command for next step. • Interface force: • Analytical part. Calculate interface state used in interface force.

45. Pseudo-dynamic testing – Hardware Configuration (Internet)

46. Pseudo-dynamic testing –Software • Response analysis – Matlab Simulink • Controller implementation – Matlab Stateflow

47. Response Feedback Computational Substructure Computational Substructure Structural Actuator Shake Table Ground/Shake Table Physical Substructure Physical Substructure Dynamic hybrid testing - I • Combined use of earthquake simulators, actuators and computational engines for simulation • Details later in the presentation

48. Well understood Structural Actuator Focus of interest Foundation Laminar Soil Box Shake Table Dynamic hybrid testing - II

49. Response Feedback Structural Actuator Has to operate in Force Control Distributed mass Foundation Laminar Soil Box Shake Table Acceleration input: Table introduces inertia forces Real-time dynamic hybrid testing - II

50. Response Feedback Computational Substructure Computational Substructure Structural Actuator Shake Table Ground/Shake Table Physical Substructure Physical Substructure Substructure Testing – Unified Approach