**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 shouldall of it).master

Topicswhich go a bit beyond many of the standard books

1)UsingMatlabfor simulations, plotting and animation.

2)Use ofAngular Momentum balanceto get equations of motion for complex systems.

3) Mechanisms(linked rigid objects)

4) DAEf (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 WedIntro. Position, velocity and acceleration in cartesian and polar coordinates.

Topic:

Homework:0. Read all www pages.

2) August 25 FriPos, Vel, Accel cont'd

Topic:

Homework:1 (ODE integration, 2 (simple animation)

3) Aug 28 MonODE45 and simple animations

Topic:

Homework:

4) Aug 30 WedRotation matrix and computer animation

Topic:

Homework:3-6 (&7 if you have time).

5) Septem 01 FriNewtons laws and ballistics, various force laws. Solutions for famous particle dynamics problems.

Topic:

Homework:*** Monday Sept 4 is Labor Day ***

6) Septem 6 WedPower, work, energy, momentum, angular momentum. Potential energy and conservative forces.

Topic:

Homework:

7) Septem 8 FriThe axioms of mechanics, multi-particle systems

Topic:

Homework:

8) Septem 11 MonMultiparticle systems, Momentum, Angular Momentum, Intro to cats

Topic:

Homework:

9) Septem 13 WedMechanics summarized, Cats and Astronauts

Topic:

Homework:

10) Septem 15 FriRotation with zero angular momentum (continued).

Topic:

Homework:

11) Septem 18 Mon.Introduction to kinematic constraints and DAEs, bead on a curved wire.

Topic:

Homework:

12) Septem 20 WedPendulum examples.

Topic:

Homework:

13) Septem 22 FriPendulum (cont'd)

Topic:

Homework:

14) Septem 25 Mon2D Angular velocity. Dynamics of one or more rigid objects in 2D (Lin Mom, Ang Mom, Kin Energy).

Topic:

Homework:

15) Sept 27 WedVibrating inverted pendulum. Equivalence between gravity and accelerating reference frames.

Topic:

Homework:

16) Sept 29 FriVibrating inverted pendulum ( cont'd), also with DAEs.

Topic:

Double pendulum (intro).

Homework:

17) Octob 02 MonDouble pendulum (cont'd).

Topic:

Homework:

18) Octob 04 WedDouble pendulum (cont'd).

Topic:

DAEs with multiple rigid objects.

Minimal and 'maximal' coordinates.

Homework:

19) Octob 6 FriChaplygin Sleigh (grocery cart, braked car directional stability)

Topic:

Homework:

*** Fall Break Sept 9-10 Mon and Tues ***

20) Octob 11 Wed.Lagrange Eqs., Matlab symbolics for Lagrange eqs.

Topic:

Homework:

21) Octob 13 FriRotating frames, 5-term acceleration formula

Topic:

Homework:

22) Octob 16 Mon5-term Acc formula continued

Topic:

Homework:*** 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 WedExamples of 2D mechanisms and problems

Topic:

Homework:

24) Octob 20 FriGeneralized forces and Lagrange eqs.

Topic:

Homework:

25) Octob 23 MonDAEs for many bodies (cont'd). Rolling.

Topic:

Homework:

26) Octob 25 WedIntro. to Vibrations, 1 DOFspring and mass.

Topic:

Homework:

27) Octob 27 FriMore Single DOF vibrations: damping

Topic:

Homework:

28) Octob 30 MonSinusoidal forcing and resonance

Topic:

Homework:

29) Novemb 01 WedLogarithmic decrement, measurement

Topic:

Homework:

30) Novemb 03 Fri1 DoF review

Topic:

Homework:

31) Novemb 6 MonMisc 1 DoF things: Friction, Superposition, Fourier Series

Topic:,Intro to multi-DOF vibrations

Homework:

32) Novemb 8 WedMulti DoF (cont'd)

Topic:

Homework:

33) Novemb 10 FriForcing and vibration absorption

Topic:

Homework:

34) Novemb 13 MonNormal modes using Inv(M)

Topic:

Homework:*** 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:Normal modes using sqrt(M)

Topic:

Homework:

36) Novemb 17 FriState Space, Matrix exponential

Topic:

Homework:

Matrix exponential (cont'd)

37) Novemb 20 Mon

Topic:

Homework:

*** Thanksgiving, no class Wed, Fri, Nov 22-24****

39) Nov. 27 MonNormal modes with damping

Topic:

Homework:

40) Nov 29 WedModal damping

Topic:

Homework:

41) Dec. 01 FriStructural Vibrations (computer demo)

Topic:

Homework:

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.