Readings and Homework, Fall 2017
ME 4730/5730, Dynamics and Vibrations
---- SUBJECT TO CHANGE, all semester long ----
---- This page in progress on 8/26/2017 ----
Please read the Homework policy a few times, once before doing each of the first few homework assignments.
Homework Solutions: TBD
Dynamics: Basic mechanics of 2D mechanisms by Newton-Euler, Lagrange or DAEs. Theory and practice
Basics: Ruina & Pratap (RP) The whole book (mostly review, but you should master all of it).
Topics which go a bit beyond many of the standard books
1) Using Matlab for simulations, plotting and animation.
2) Use of Angular Momentum balance to get equations of motion for complex systems.
3) Mechanisms (linked rigid objects)
4) DAE f (Differential Algebraic Equations) formulation of equations of motion
Vibrations: We will cover most of the content of most elementary Vibrations books.
Forced, damped harmonic oscillator (inside and out).
Linearization, normal modes and damped normal modes, matrix exponential, structural vibrations.
Lecture and homework schedule (Fall 2017, to be updated)
Homework is due the first Wednesday that is at least 6 days after the assigned date. It is subject to change until midnight on the end of Thursday 6 days before it is due.
1) August 23 Wed
Topic: Intro. Position, velocity and acceleration in cartesian and polar coordinates.
Homework: 0. Read all www pages.
2) August 25 Fri
Topic: Pos, Vel, Accel cont'd
Homework: 1 (ODE integration, 2 (simple animation)
3) Aug 28 Mon
Topic: ODE45 and simple animations
4) Aug 30 Wed
Topic: Rotation matrix and computer animation
Homework: 3-6 (&7 if you have time).
5) Septem 01 Fri
Topic: Newtons laws and ballistics, various force laws. Solutions for famous particle dynamics problems.
*** Monday Sept 4 is Labor Day ***
6) Septem 6 Wed
Topic: Power, work, energy, momentum, angular momentum. Potential energy and conservative forces.
7) Septem 8 Fri
Topic: The axioms of mechanics, multi-particle systems
8) Septem 11 Mon
Topic: Multiparticle systems, Momentum, Angular Momentum, Intro to cats
9) Septem 13 Wed
Topic: Mechanics summarized, Cats and Astronauts
10) Septem 15 Fri
Topic: Rotation with zero angular momentum (continued).
11) Septem 18 Mon.
Topic: Introduction to kinematic constraints and DAEs, bead on a curved wire.
12) Septem 20 Wed
Topic: Pendulum examples.
13) Septem 22 Fri
Topic: Pendulum (cont'd)
14) Septem 25 Mon
Topic: 2D Angular velocity. Dynamics of one or more rigid objects in 2D (Lin Mom, Ang Mom, Kin Energy).
15) Sept 27 Wed
Topic: Vibrating inverted pendulum. Equivalence between gravity and accelerating reference frames.
16) Sept 29 Fri
Topic: Vibrating inverted pendulum ( cont'd), also with DAEs.
Double pendulum (intro).
17) Octob 02 Mon
Topic: Double pendulum (cont'd).
18) Octob 04 Wed
Topic: Double pendulum (cont'd).
DAEs with multiple rigid objects.
Minimal and 'maximal' coordinates.
19) Octob 6 Fri
Topic: Chaplygin Sleigh (grocery cart, braked car directional stability)
*** Fall Break Sept 9-10 Mon and Tues ***
20) Octob 11 Wed.
Topic: Lagrange Eqs., Matlab symbolics for Lagrange eqs.
21) Octob 13 Fri
Topic: Rotating frames, 5-term acceleration formula
22) Octob 16 Mon
Topic: 5-term Acc formula continued
*** Prelim 1, Tuesday October 17, 7:30 - 9 (plus up to 90 minutes extra time ), Hollister B14 ***
Covers through HW handed in by Oct 13, including Matlab.
23) Octob 18 Wed
Topic: Examples of 2D mechanisms and problems
24) Octob 20 Fri
Topic: Generalized forces and Lagrange eqs.
25) Octob 23 Mon
Topic: DAEs for many bodies (cont'd). Rolling.
26) Octob 25 Wed
Topic: Intro. to Vibrations, 1 DOFspring and mass.
27) Octob 27 Fri
Topic: More Single DOF vibrations: damping
28) Octob 30 Mon
Topic: Sinusoidal forcing and resonance
29) Novemb 01 Wed
Topic: Logarithmic decrement, measurement
30) Novemb 03 Fri
Topic: 1 DoF review
31) Novemb 6 Mon
Topic: Misc 1 DoF things: Friction, Superposition, Fourier Series, Intro to multi-DOF vibrations
32) Novemb 8 Wed
Topic: Multi DoF (cont'd)
33) Novemb 10 Fri
Topic: Forcing and vibration absorption
34) Novemb 13 Mon
Topic: Normal modes using Inv(M)
*** Prelim 2, Tuesday Nov 14, 7:30 - 9 (plus up to 90 minutes extra time) , Hollister B14***
Covers through HW handed in by Nov 13, including Matlab.
35) Novemb 15 Wed:
Topic: Normal modes using sqrt(M)
36) Novemb 17 Fri
Topic: State Space, Matrix exponential
37) Novemb 20 Mon
Topic: Matrix exponential (cont'd)
*** Thanksgiving, no class Wed, Fri, Nov 22-24****
39) Nov. 27 Mon
Topic: Normal modes with damping
40) Nov 29 Wed
Topic: Modal damping
41) Dec. 01 Fri
Topic: Structural Vibrations (computer demo)
Study Period: Saturday Dec 2 - Tuesday Dec 5
Final Project Due ~Dec 9 (TBD, Univ. sets date and time): pdf report + computer demo (sign up to be posted)
FINAL EXAM: Thursday Dec 7, 2 - 4:30 PM. Place to be determined (let me know when you find it, and I'll post it.)
Comprehensive, including Matlab. No notes, books or calculators.