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

Contents –Introduction of dynamic testing methods –Effective force testing –Pseudo dynamic testing –Real time hybrid dynamic testing

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)

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 not captured

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

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

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 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

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

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

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

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

Real-Time Seismic Hybrid Testing

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)

Block Diagrams of Various Testing Methods

Open Loop Test

Open Loop Control (in concept) Effective Force Test

Closed Loop Test

Pseudo-dynamic Test with Substructure

Closed Loop Test

Summary of dynamic test methods AdvantagesDisadvantages PDT  Size of the specimen can be large or very large  Inertial forces are not true forces and distorted by discrete parameter model, actuators and computers  Rate effects are neglected because of quasi-static loading RTPDT  Size of the specimen can be large or very large  Inertial forces are not true forces and distorted by discrete parameter model, actuators and computers  Actuator time delay is introduced STT  True inertia forces in assembly  Size of the specimen is limited RTDHT  True inertia forces on the specimen  Specimen can be large or very large  Part of the inertia forces are simulated with errors (same as PDT)  Actuator time delay is introduced

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

Open Loop Control (in concept) Effective Force Test

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

Effective Force Test – Hardware Configuration

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

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

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 K LC (1-CG) in the transfer function indicates that the smaller the value of K LC the less sensitive is the transfer function to deviations of C from 1/G

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

Effective Force Test – Predictive Control Smith Predictor

Effective Force Test – Predictive Control Without compensation With compensation

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

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

Pseudo-dynamic testing

Pseudo dynamic testing

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

Pseudo-dynamic testing – Hardware Configuration (Local)

Pseudo dynamic testing Discretized equation of motion of the structure at time intervals for, Equation solved in computer step by step, with R i 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.

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)

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),

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

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

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

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.

Pseudo-dynamic testing – Hardware Configuration (Internet)

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

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

Dynamic hybrid testing - II Shake Table Laminar Soil Box Foundatio n Well understood Focus of interest Structural Actuator

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

Physical Substructur e Computation al Substructure Ground/Shake Table Shake Table Structural Actuator Computation al Substructure Physical Substructur e Response Feedback Substructure Testing – Unified Approach

Unified approach to substructure testing If, then the control requires a shake table and an actuator to implement the substructure testing. If, then the controller require just an actuator to implement the substructure testing as pseudo-dynamic testing: Note: –In pseudo-dynamic testing, inertia effects are computed. –In dynamic hybrid testing ( ), the actuator should operate in force control.

Hybrid Controller Implementation (UB-NEES) Design done jointly between MTS and UB Flexible architecture using parallel processing

Implementation of RTDHT Structure Actuator Shake Table

Substructure response Hybrid testShake table Second (simulated) floor Structure Actuator Shake Table First (physical) floor