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Nonlinear Dynamics Laboratory Equipment

Client: Mechanical Engineering Dept. at R•I•T Faculty Mentor: Dr. J.S. Török. Nonlinear Dynamics Laboratory Equipment. Andrew Dick Joe Houtz Jeremy Redlecki Ashley Rice James Streeter. Presentation Outline. Nonlinear Dynamics and Chaos Project Goals Design Process Preliminary Design

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Nonlinear Dynamics Laboratory Equipment

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  1. Client: Mechanical Engineering Dept. at R•I•T Faculty Mentor: Dr. J.S. Török Nonlinear Dynamics Laboratory Equipment Andrew Dick Joe Houtz Jeremy Redlecki Ashley Rice James Streeter

  2. Presentation Outline • Nonlinear Dynamics and Chaos • Project Goals • Design Process • Preliminary Design • Expenses and Budget • Spring Quarter Schedule • Conclusion

  3. Nonlinear Dynamics and Chaos • Nonlinear Dynamics • Physical systems will nonlinear electrical/mechanical components • State Equations contain nonlinear terms • Closed form solutions are unlikely • Variety of dynamic behavior • Chaos • Deterministic systems, not stochastic • Long-term apparent erratic behavior • Dynamics governed by ‘strange’ attractor • Sensitive Dependence on initial conditions

  4. 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

  5. Description • Dynamic systems governed by nonlinear equations • Ability to demonstrate nonlinear and chaotic behavior • Equipped with data acquisition equipment to collect data for analysis • Compatible with three tier system of experimentation • Demonstration • Experimentation • Design oriented experimentation • Extensive testing to validate equipment and gather data required for the completion of the project

  6. Equipment Set • Chua’s Circuit • Nonlinear Electric Circuit • Multi-well Oscillator • Magneto-Elastic System • Chaotic Waterwheel • Mechanical-Fluid System

  7. Design Facets • Recognize & quantify the need • Concept development • Feasibility assessment • Establishing design objectives & criteria • Analysis of problems & synthesis into the design • Preliminary design

  8. Facet One: Needs Assessment • Laboratory equipment usage • One, two and three tier experiments • Design constraints • Financial parameters • $2000 budget • Performance parameters

  9. Facet Two: Concept Development • Brainstorming • Research existing systems • Group consensus of preliminary concepts • Develop drawings & descriptions of each preliminary concept • Group exercises • Concept drawing • Empathy method • Preliminary BOM

  10. Facet Three: Feasibility Assessment • Technical aspects • Economical aspects • Market • Schedule • Performance

  11. Facet Four: Design Objectives & Performance Specifications • Safety codes and standards • List of design objectives • Yes/no question format • Evaluation checklist • Performance specification table

  12. Chua’s Circuit • Kirchoff’s laws Lorenz Equations:

  13. Chua’s Circuit:Simulation and Analysis • PSpice simulation • Matlab • Frequency Spectrum

  14. Chua’s Circuit Apparatus Design • Op-amps represent Chua’s Diode. • Output voltages can be connected to an oscilloscope, LabView, or speakers. • Setup: • A base is to be fabricated • Transparent cast acrylic cover • Two speakers

  15. Multi-Well Oscillator • Research • Magneto-elastic system • Theory

  16. Multi-well Oscillator:Simulation and Analysis • Control parameters: • d, Damping Factor • F, Force Amplitude

  17. Multi-well Oscillator Apparatus Design • Analyses • Stress • Fatigue • Frequency • Magnetic

  18. Chaotic Waterwheel • Willem Malkus and Lou Howard developed the first chaotic waterwheel at MIT in the 1970’s.

  19. Chaotic Waterwheel:Simulation and Analysis Waterwheel Equations:

  20. Chaotic Waterwheel Apparatus Design In flow Encoder bearing Overflow • General operation • Analyses • Flow analysis • Moment of inertia analysis • Stress analysis • Brake • Encoder Bearing Needle valve Out flow Brake

  21. Expenses and Budget • Bill of material created for each device • Raw material, purchased components, electrical components, sensors, nuts and bolts. • Cost per device and complete set • Chua’s Circuit Apparatus 141 parts $267.71 • Multi-well Oscillator Apparatus 153 parts $597.01 • Chaotic Waterwheel Apparatus 447 parts $1135.81 • Complete set of three Apparatuses 741 parts $1895.29 • Available Balance $104.71

  22. Spring Quarter Schedule • Phase One: Construction  4 weeks • Quality/performance test components • Fabricate components • Assemble equipment • Phase Two: Testing  4 weeks • Confirm/optimize design • Determine critical parameters • Develop experimentation procedures • Phase Three: Documentation  2 weeks • Complete user manual • Final Design Report • Critical Design Presentation

  23. Conclusion • Successfully completed design facets 1 through 6 • Conducted many different analyses on each of the devices • Completion of a preliminary design • Expenses and Budget • Spring Quarter Schedule

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