Nonlinear Dynamics Laboratory Equipment Andrew DickJoe Houtz Jeremy RedleckiAshley Rice James Streeter Client: Mechanical Engineering Dept. at RITFaculty Mentor: Dr. J.S. Török

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

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

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

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 1. Demonstration 2. Experimentation 3. Design oriented experimentation Extensive testing to validate equipment and gather data required for the completion of the project

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

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

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

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

Facet Three: Feasibility Assessment Technical aspects Economical aspects Market Schedule Performance

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

Chua’s Circuit Kirchoff’s laws Lorenz Equations:

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

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

Multi-Well Oscillator Research Magneto-elastic system Theory

Multi-well Oscillator: Simulation and Analysis Control parameters: , Damping Factor F, Force Amplitude

Multi-well Oscillator Apparatus Design Analyses Stress Fatigue Frequency Magnetic

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

Chaotic Waterwheel: Simulation and Analysis Waterwheel Equations:

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

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 Apparatus141 parts$ Multi-well Oscillator Apparatus153 parts$ Chaotic Waterwheel Apparatus 447 parts $ Complete set of three Apparatuses741 parts $ Available Balance$104.71

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

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