ME 4730/5730, Dynamics and Vibrations

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

Homework assignments: pdf . Updated 9/17/2015.

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.
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

1) August 26 Wed
Topic:
Intro. Position, velocity and acceleration in cartesian and polar coordinates.
Homework: 1 (Read up),  2 (polar coordinates with force = zero).

2) August 29 Fri
Topic:
Newtons laws and ballistics, various force laws
Homework: 3 (Canonball)

3) Aug 31 Mon
Topic:
Solutions for famous particle dynamics problems.
Homework: 4 (Mass hangs from spring.),  5 (central force), 6 (canonball 2)

4) Septem 02 Wed
Topic:
Power, work, energy, momentum, angular momentum
Homework: 7 (what means rate of change of angular momentum?)

5) Septem 04 Fri
Topic:
Potential energy and conservative forces.

*** Monday is Labor Day ***

6) Septem 9 Wed
Topic:
Summary of single particle mechanics, Multi-particle systems
Homework: 8 (2 or 3 particles in circular motion),  9 (Montgomery's 8),

7) Septem 11 Fri
Topic:
The axioms of mechanics, multi-particle systems
Homework: 10 (Konig's Theorem),  11 (Angular momentum for multiple particles)

8) Septem 14 Mon
Topic:
Multiparticle systems, Momentum, Angular Momentum, Intro to cats

9) Septem 16 Wed
Topic:
Mechanics summarized, Cats and Astronauts
Homework:  12 (rotation with zero angular momentum), 13 (two masses connected by a spring)

10) Septem 18 Fri
Topic:
Rotation with zero angular momentum (continued).

11) Septem 21 Mon.
Topic:
Introduction to kinematic constraints and DAEs, bead on a curved wire.

12) Septem 23 Wed
Topic:
Pendulum examples.

13) Septem 25 Fri
Topic:
Pendulum (cont'd)

14) Septem 28 Mon
Topic:
2D Angular velocity. Dynamics of one or more rigid objects in 2D (Lin Mom, Ang Mom, Kin Energy).

15) Sept 30 Wed
Topic:
Vibrating inverted pendulum. Equivalence between gravity and accelerating reference frames.

16) Octob 02 Fri
Topic:
Vibrating inverted pendulum ( cont'd), also with DAEs.
Double pendulum (intro).

17) Octob 05 Mon
Topic:
Double pendulum (cont'd).

18) Octob 07 Wed
Topic:
Double pendulum (cont'd).
DAEs with multiple rigid objects.
Minimal and 'maximal' coordinates.

19) Octob 9 Fri
Topic:
Chaplygin Sleigh (grocery cart, braked car directional stability)

*** Fall Break Mon and Tues ***

20) Octob 14 Wed.
Topic:
Lagrange Eqs., Matlab symbolics for Lagrange eqs.

21) Octob 16 Fri
Topic:
Rotating frames, 5-term acceleration formula

22) Octob 19 Mon
Topic:
5-term Acc formula continued

*** Prelim 1, Tuesday October 20, 7:30 - 9 (plus up to 90 minutes extra time ) ***
Covers through HW handed in by Oct 19, including Matlab.

23) Octob 21 Wed
Topic:
Examples of 2D mechanisms and problems

24) Octob 23 Fri
Topic:
Generalized forces and Lagrange eqs.

25) Octob 26 Mon
Topic:
DAEs for many bodies (cont'd). Rolling.

26) Octob 28 Wed
Topic:
Intro. to Vibrations, 1 DOFspring and mass.

27) Octob 30 Fri
Topic:
More Single DOF vibrations: damping

28) Novemb 02 Mon
Topic:
Sinusoidal forcing and resonance

29) Novemb 04 Wed
Topic:
Logarithmic decrement, measurement

30) Novemb 06 Fri
Topic:
1 DoF review

31) Novemb 9 Mon
Topic:
Misc 1 DoF things: Friction, Superposition, Fourier Series, Intro to multi-DOF vibrations

32) Novemb 11 Wed (class is held on Veterens day)
Topic:
Multi DoF (cont'd)

33) Novemb 13 Fri
Topic:
Forcing and vibration absorption

34) Novemb 16 Mon
Topic:
Normal modes using Inv(M)

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

35) Novemb 18 Wed:
Topic:
Normal modes using sqrt(M)

36) Novemb 20 Fri
Topic:
State Space, Matrix exponential

37) Novemb 23 Mon
Topic:
Matrix exponential (cont'd)

*** Thanksgiving starts Tuesday night ****

39) Nov. 30 Mon
Topic:
Normal modes with damping

40) Dec. 02 Wed
Topic:
Modal damping

41) Dec. 04 Fri
Topic:
Structural Vibrations (computer demo)

Study Period: Saturday Dec 5 - Tuesday Dec 8

Final Project Due Dec 9, 4:30 PM (Univ. set date and time): pdf report + computer demo (sign up to be posted)

FINAL EXAM:  Date, time and place to be determined (let me know when you find it, and I'll post it.)
Comprehensive, including Matlab. No notes, books or  calculators.