1. May 16th, 2003 © 2002-2003, Team 02021 Nonlinear Dynamics Laboratory Equipment Andrew DickJoe Houtz Jeremy RedleckiAshley Rice James Streeter Customer: Mechanical Engineering Dept. at RITFaculty Mentor: Dr. J.S. Török

2. May 16th, 2003© 2002-2003, Team 02021 Outline Project Goals Preliminary Design RedesignFabrication Equipment Testing Experiments and Demonstrations ConclusionQuestions

3. May 16th, 2003© 2002-2003, Team 02021 Project Goals Design, build, and test nonlinear dynamics laboratory equipment to aid in the teaching of nonlinear dynamics Develop a set of procedures and manuals for experiments and demonstrations

4. May 16th, 2003© 2002-2003, Team 02021 Preliminary Design Chua’s Circuit Nonlinear Electrical System Nonlinear Electrical System Chua’s Diode Chua’s Diode Speakers Speakers Acrylic Cover Acrylic Cover Multi-well Oscillator Magneto-Elastic System Magneto-Elastic System Magnets Magnets Motor & Eccentric Mass Motor & Eccentric Mass Strain Gauges Strain Gauges

5. May 16th, 2003© 2002-2003, Team 02021 Preliminary Design Chaotic Waterwheel Acrylic Wheel Acrylic Wheel Pillow Block Bearing Pillow Block Bearing Encoder Bearing Encoder Bearing Brake Brake Steel Base and Frame Steel Base and Frame Submersible Water Pump Submersible Water Pump Flow Meter Flow Meter

6. May 16th, 2003© 2002-2003, Team 02021 Redesign Rare Earth Magnets Multi-well Oscillator Multi-well Oscillator Printed Circuit Board Chua’s Circuit Chua’s Circuit Ground Fault Circuit Interrupt Chaotic Waterwheel Chaotic Waterwheel Printed Circuit Board Design

7. May 16th, 2003© 2002-2003, Team 02021 Redesign Optical Encoder Chaotic Waterwheel Chaotic Waterwheel Air Bearing Chaotic Waterwheel Chaotic Waterwheel Air Bearing Brake Assembly Optical Encoder Coupling

8. May 16th, 2003© 2002-2003, Team 02021 Fabrication

9. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Chua’s Circuit Testing Procedure Modeled circuit Modeled circuit PSpice software Simulated circuit while varying resistor Simulated circuit while varying resistor Produced output voltage time series Built circuit Built circuitTroubleshooting

10. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Chua’s Circuit Single Period BehaviorHigh Period BehaviorChaotic Behavior

11. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Multi-well Oscillator Testing Procedure Built electromagnet test bracket Built electromagnet test bracket Varied unbalanced mass connected to motor Varied unbalanced mass connected to motor Collected strain gauge output though LabVIEW Collected strain gauge output though LabVIEW Analyzed steel beam using Laser Vibrometer Analyzed steel beam using Laser Vibrometer

12. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Multi-well Oscillator Periodic above one magnetChaotic above both magnets Periodic above two magnets

13. May 16th, 2003© 2002-2003, Team 02021 Chaotic Oscillation

14. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Chaotic Waterwheel

15. May 16th, 2003© 2002-2003, Team 02021 Equipment Testing – Chaotic Waterwheel Testing Procedure Varied system parameters Varied system parameters Observe a range of nonlinear behaviors Observe a range of nonlinear behaviors Water Inflow Rate IncreaseDecrease System Stability Decrease Increase Control Parameters Primary: Water Flow Rate Primary: Water Flow Rate Secondary: Wheel damping (brake) Secondary: Wheel damping (brake)

16. May 16th, 2003© 2002-2003, Team 02021 Experiments and Demonstrations Demonstrations Show nonlinear dynamics and chaotic behavior to students Show nonlinear dynamics and chaotic behavior to studentsExperiments Objectives Objectives Background Background Prelab Prelab Experiments Experiments Analysis Analysis Questions Questions Design Oriented Experiments R·I·T Mechanical Engineering

17. May 16th, 2003© 2002-2003, Team 02021 Experiments and Demonstrations Chua's Circuit Period-Doubling Bifurcation Period-Doubling Bifurcation Orbit Diagram Orbit Diagram -6-4-202468 -8 -6 -4 -2 0 2 4 6 Rossler System a=b=0.2, c=3.5 X value of system Y value of system Control Parameter Orbit Diagram

18. May 16th, 2003© 2002-2003, Team 02021 Experiments and Demonstrations Chaotic Waterwheel Nonlinear and Chaotic Behavior Nonlinear and Chaotic Behavior Attractor Reconstruction Attractor Reconstruction X(t)=[B(t),B(t+  )] 2-D AttractorReconstructed Attractor Chaotic Behavior Nonlinear Behavior

19. May 16th, 2003© 2002-2003, Team 02021 Experiments and Demonstrations Multi-well Oscillator Dynamics of Forced Oscillator Dynamics of Forced Oscillator Attractor Reconstruction Attractor Reconstruction Poincaré Map Poincaré Map P(X)=X(k*n) for forcing period k Chaotic Behavior Reconstructed AttractorPoincaré Map

20. May 16th, 2003© 2002-2003, Team 02021 Conclusion Created 3 unique devices to display nonlinear dynamics Chua’s Circuit Chua’s Circuit Multi-well Oscillator Multi-well Oscillator Chaotic Waterwheel Chaotic Waterwheel On schedule and within budget Potential for future innovations