Readings and Homework, Fall 2014
ME 4730/5730, Dynamics and Vibrations

----    This page in progress on 12/1/2014   ----

Please read the Homework policy a few times, once before doing each of the first few homework assignments.

Homework assignments: pdf . Updated 12/1/2014.

Homework Solutions: Will be posted on Piazza.

Planned coverage (what you should know by the end of the semester)

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 schedule

1) August 27 Wed
Topic: Intro. Position, velocity and acceleration in cartesian and polar coordinates.

2) August 29 Fri
Topic:Newtons laws and ballistics, various force laws

*** Labor Day ***

3) Septem 03 Wed
Topic: Solutions for famous particle dynamics problems.

4) Septem 05 Fri
Topic: Power, work, energy, momentum, angular momentum

5) Septem 08 Mon
Topic: Potential energy and conservative forces.

6) Septem 10 Wed
Topic: Summary of single particle mechanics, Multi-particle systems

7) Septem 12 Fri
Topic: The axioms of mechanics

8) Septem 15 Mon
Topic: Multiparticle systems, Momentum, Angular Momentum and Energy (Konig Thm).

9) Septem 17 Wed
Topic: Cats and Astronauts,

10) Septem 19 Fri
Topic: Introduction to kinematic constraints and DAEs, bead on a curved wire.

11) Septem 22 Mon. GUEST LECTURER Matt Sheen
Topic: Optimization and Root finding for finding periodic motions.

12) Septem 24 Wed
Topic: DAEs cont'd, Dumbel in space.

13) Septem 26 Fri
Topic: 2D Angular velocity. Dynamics of one or more rigid objects in 2D (Lin Mom, Ang Mom, Kin Energy).

14) Septem 29 Mon
Topic: Pendulum examples.

15) Octob 01 Wed
Topic: Vibrating inverted pendulum.

16) Octob 03 Fri
Topic: Vibrating inverted pendulum ( cont'd), also with DAEs.
Equivalence between gravity and accelerating reference frames.
Double pendulum (intro).

17) Octob 06 Mon
Topic: Double pendulum (cont'd).

18) Octob 08 Wed
Topic: Double pendulum (cont'd).
DAEs with multiple rigid objects.
Minimal and 'maximal' coordinates.

19) Octob 10 Fri
Topic: Chaplygin Sleigh (grocery cart, braked car directional stability)

*** Fall Break Mon and Tues ***

20) Octob 15 Wed. GUEST LECTURER Matt Kelle
Topic: Lagrange Eqs., Matlab symbolics for Lagrange eqs. y

21) Octob 17 Fri
Topic: Rotating frames, 5-term acceleration formula

22) Octob 20 Mon
Topic: 5-term Acc formula continued

*** Prelim 1, Tuesday October 21, 7:30 - 9 (plus up to 90 minutes extra time ) ***
       Covers through HW handed in by Oct 20.

23) Octob 22 Wed GUEST LECTURER Matt Kelley or Sheen
Topic: Examples of 2D mechanisms and problems

24) Octob 24 Fri
Topic: Generalized forces and Lagrange eqs.

25) Octob 27 Mon
Topic: DAEs for many bodies (cont'd). Rolling.

26) Octob 29 Wed
Topic: Intro. to Vibrations, 1 DOFspring and mass.

27) Octob 31 Fri
Topic: More Single DOF vibrations: damping

28) Novemb 03 Mon
Topic: Sinusoidal forcing and resonance

29) Novemb 05 Wed
Topic: Logarithmic decrement, measurement

30) Novemb 07 Fri
Topic: 1 DoF review

31) Novemb 10 Mon
Topic: Misc 1 DoF things: Friction, Superposition, Fourier Series, Intro to multi-DOF vibrations

32) Novemb 12 Wed
Topic: Multi DoF (cont'd)

33) Novemb 14 Fri
Topic: Forcing and vibration absorption

34) Novemb 17 Mon
Topic: Normal modes using Inv(M)

*** Prelim 2, Tuesday Nov 18, 7:30 - 9 (plus up to 90 minutes extra time) ***
       Covers through HW handed in by Nov 17.

35) Novemb 19 Wed: Mystery guest lecturer
Topic: Normal modes using sqrt(M)

36) Novemb 21 Fri
Topic: State Space, Matrix exponential

37) Novemb 24 Mon
Topic: Matrix exponential (cont'd)

*** Thanksgiving starts Tuesday night ****

39) Dec. 01 Mon
Topic: Normal modes with damping

40) Dec. 03 Wed
Topic: Modal damping

41) Dec. 05 Fri
Topic: Structural Vibrations (computer demo)

Study Period: Saturday Dec 6 - Tuesday Dec 9

Final Project Due Dec 10,15,16: pdf report + computer demo (sign up to be posted)

FINAL EXAM Comprehensive: December 17th from 2 to 4:30, Upson B17.
Comprehensive. No notes. No calculators.