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Using “Laws of Nature” to Model a System

Using “Laws of Nature” to Model a System. Introduction to Engineering Systems Lecture 2 (8/31/2009). Prof. Andrés Tovar. Announcements. Learning Center Announcements: Bring headphones/earphones to the Learning Center THIS week! Bring textbook to LC 2 (this week)

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Using “Laws of Nature” to Model a System

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  1. Using “Laws of Nature” toModel a System Introduction to Engineering Systems Lecture 2 (8/31/2009) Prof. Andrés Tovar

  2. Announcements • Learning Center Announcements: • Bring headphones/earphones to the Learning Center THIS week! • Bring textbook to LC 2 (this week) • You may bring laptop to LC 2 (not necessary) • Visit Prof. Brockman in his office and get a $2.16 rebateon your textbook (his cut on each book sold)!! • Read Sections 1.1 to 1.4 (Lecture 1) and Chapter 4 (Lecture 2). Using "Laws of Nature" to Model a System

  3. MATLAB Free! $100 Math tool useful for all your engineering and science courses We’ll introduce it slowly over the course of both semesters Using "Laws of Nature" to Model a System

  4. Getting your own copy of MATLAB • Not required to install MATLAB, but strongly recommended • Should also install • McAfee anti-virus • Open AFS (H-drive) • SyncToy backup software • Download and installation instructions for all software at: http://www.nd.edu/~engcomp/installdoc.html • MATLAB DVD available from the reference desk at the Engineering Library (149 Fitzpatrick Hall) • Do not ask librarians for assistance with install. For questions, email: engtrouble@nd.edu • DVDs available for 24-hour checkout. • But should only take 15 minutes, so better to bring your laptop to the library as DVD’s are limited

  5. Loaner Laptop Pilot Program • Here is an opportunity for you to participate in a pilot program sponsored by the College of Engineering. • We have a number of Laptop PCs to be assigned to students selected to participate in this program. • If selected, you will be assigned the Laptop for the year. • In exchange for your participation, you must fulfill the terms and conditions of the program. • Let ND Engineering computing know of any problems • ND Engineering will perform maintenance

  6. If you are interested • You must send an email to Johanes Suhardjo (johanes@nd.edu) by 11:59 pm Wed 9/2 which provides • Your name, • campus address • phone number • Type of computer you now have on campus (laptop, desktop, both or none) • The College of Engineering will select the participants • You will be notified and can pick up the computer by Friday

  7. From last class Engineers are creative problem-solvers that make use of Science (analysis), Mathematics (language), and Technology (synthesis). Differences between Scientists, Engineers, and Mathematicians. Scientific method vs. Engineering process. Engineering disciplines. Using "Laws of Nature" to Model a System

  8. Our engineering problem • Performance Objective: • Limit deflection of tower to defined limit under a specified load using bracing • Design should be as efficient as possible (use least amount of material) • Major Constraints: • Tower height is fixed • Tower plan (shape) is fixed • Fixed amount of materials • Functional constraints on bracing Slide courtesy of Dr. Kijewski-Correa

  9. DESIGN STAGE CONSTRUCTION & VERIFICATION Investigate Designs using Model Construct Design Optimize Design Experimentally Verify Behavior Predict Behavior Our engineering design process MODEL DEVELOPMENT Gather Data Develop Model Verify Model • Four Ms • Measure: gather data • Model: develop and verify model • Manipulate: investigate, optimize, and predict • Make: construct and verify

  10. Measure Displacement How our data was collected • Repeated trials – what did you observe? • Multiple versions of the same design: 14x6= 84 models tested – why test so many towers? MODEL DEVELOPMENT Force Gather Data Develop Model Verify Model Using "Laws of Nature" to Model a System

  11. What are models? • Approximations of a real system • Kinds of models • Empirical models • Based on experimental data • Theoretical models • Based on “laws of nature” • Learning center is about empirical models. • Today we’ll focus on a theoretical models. • Work through the theory • Run the experiment • Compare theory and data using MATLAB in homework Using "Laws of Nature" to Model a System

  12. Empirical model Displacement D (mm) Force F (N) Using "Laws of Nature" to Model a System

  13. Empirical model NUMERICAL EXPERIMENT PHYSICAL EXPERIMENT

  14. Falling objects When an object is drop disregarding air resistance does a heavier object take less time to fall or have bigger final velocity? What would be the final velocity in each case? • Aristotle (384 BC – 322 BC)believed that heavier things fall faster, with a speed proportional to their weight. • Galileo (1564 – 1642) experimentally showed that (empirical model): • Apollo 15 astronaut Dave Scott simultaneously dropped a hammer and feather on the moon (where there is no air), and they both fell straight down at the same rate, and hit the ground at the same time. Using "Laws of Nature" to Model a System

  15. Falling objects What would be the final velocity in each case? • Newton (1643 – 1727) Theoretical models dependent on time and space. • Leibniz (1646 –1716) Theoretical models based on potential and kinetic energy. Using "Laws of Nature" to Model a System

  16. Colliding pendulums pool ball golf ball • Given 2 pendulums with different masses, initially at rest • Say, a golf ball and a pool ball • Would you be willing to bet that you could figure out where to release the larger ball in order to knock the smaller ball to a given height? • How could you improve your chances? Using "Laws of Nature" to Model a System

  17. Colliding pendulums Descartes’ (1596-1650) three laws of motion: Each thing, insofar as in it lies, always perseveres in the same state, and when once moved, always continues to move. Every motion in itself is in a straight line, and therefore things which are moved circularly always tend to recede from the center of the circle which they describe. If a moving body A collides with moving body B and if A has less force to continue in a straight line than B has to resist it, A will deflect in the opposite direction and, retaining its own motion, will lose only the direction of its motion. If, however, A has a greater force than B does, then body A will move with body B and give it as much of its motion to as it loses. Using "Laws of Nature" to Model a System

  18. Colliding pendulums golf ball pool ball • According to Descartes’ 3rd Law, will happen when the golf ball (in motion) strikes the pool ball (at rest)? • Which ball has the greater “force of motion”? • Which of the two cases described in the 3rd Law applies? • What if we reversed the situation so the pool ball collides with the golf ball? Using "Laws of Nature" to Model a System

  19. Colliding pendulums Where to release the pool ball to knock to golf ball to a given height? • Leibniz‘s(1646 –1716) conservation of energy: • Huygens‘(1629 – 1695) principle of relative velocity: • Newton‘s(1643 – 1727) conservation of momentum: Using "Laws of Nature" to Model a System

  20. Agree or Disagree? strongly disagree strongly agree somewhat disagree somewhat agree Laws of nature are typically discovered by individuals in a moment of inspiration. If you repeat an experiment, and come up with a different value each time, it generally means that something went wrong. Leonardo DaVinci was highly unusual in his day, because he excelled not only in both the arts and sciences, but also because he made discoveries in different branches of science, such as mechanics and biology. Isaac Newton’s papers contain graphs of equations, with quantities such as “distance” on the y-axis and “time” on the x-axis, that are similar to the kinds of graphs that high school students learn to draw in algebra classes today. Engineering practice generally requires a lot of “advanced mathematics” that is typically only taught in college. One of the most important skills for an engineer to have is the ability to memorize formulas to be able to recall the right one for a given situation. Using "Laws of Nature" to Model a System

  21. What does this have to do with other engineering majors? chemical process modeling with Aspen Plus electronic circuit modeling with Cadence PSpice They all use computer modeling tools that solve equations based on relevant theories. The basic principles of modeling apply to all engineering majors Using "Laws of Nature" to Model a System

  22. What’s Next? • Use a computer tool (theoretical model) to predict the behavior of a design • model tower deflection using SAP2000 • What’s an empirical model and how do we build one? • and use this knowledge to build an empirical model for the tower from the data collected in the learning center • Use another computer tool to simplify modeling and data analysis • use MATLAB to compare SAP2000 and measured results—much more efficient than punching numbers into a calculator! • How can we cope with the uncertainty in a model in order to place a smart bet? • choose a bracing scheme for the tower that’s highly likely to be able to withstand the load . . . • without over-engineering it and unnecessarily increasing the cost Using "Laws of Nature" to Model a System

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