AA 312: Structural Vibrations
Winter 2007

 

Instructor

Prof. Kristi A. Morgansen
morgansen@aa.washington.edu

Office Hours

Monday 11:30-1pm
Condon 318 (6-5950)

Teaching Assistant

Randall Svac
oposse1@aa.washington.edu
Homework Section:

 

Friday 11:30-12:30pm
Condon 224
T 9:30-10:20

Lectures: MTWF 8:30-9:20am, Condon 135
Homework section:  T 9:30-10:20, Condon 135

Course Description

Vibration theory. Characteristics of single and multidegree-of-freedom linear systems. Analysis of the free response, response to harmonic excitation, and general forced response of linear systems. Distributed parameter systems. Application to simple aerospace structural problems.

Prerequisites: Dynamics -- ENGR 230, Vector analysis -- MATH 126, Suggested: Introduction to differential equations -- MATH 307

Goals: 1) To learn how to describe an aerospace system in vibration, 2) To learn who to design and model aerospace structures in vibration.

Objectives: 1) Students will know how to develop and solve dynamic models free of rotational and harmonic force motion of single degree-of-freedom systems; 2) Students will be able to solve single degree-of-freedom general forced vibration problems;  3) Students will be able to model analytically and numerically systems with multiple degrees-of-freedom; 4) Students will be able to model and compute vibration of continuous systems.

Topics:

  1. Single-degree-of-freedom systems: modeling, free vibration of undamped and damped systems
  2. Forced vibration of single-degree-of-freedom systems to harmonic excitation: Laplace transform
  3. Forced vibration of single-degree-of-freedom systems to general dynamic excitation: convolution integral, integration method.
  4. Multiple degree-of-freedom systems:  lumped-parameter models, Lagrange’s equations to lumped-parameter models.
  5. Free vibration of multiple degree-of-freedom systems: normal frequencies and modes
  6. Eigenvalues and eigenvectors: matrix orthogonality; numerical computation
  7. Forced vibration of multiple degree-of-freedom systems
  8. Distributed-parameter systems: modeling, longitudinal and torsional vibrations; transverse beam vibration, vibration of plates and membranes

Expectations

My role:  The role of an instructor is to help the students acquire new knowledge and skills more quickly than they could on their own, to guide the approach to learning with effective tools, to provide completeness of subject matter, and to place material in context relative to the larger field.

Student role:  The role of a student is, of course, to learn.  Students in this course are expected to read the textbook sections associated with a topic before the material is presented in class, to prepare questions on the reading (need for clarification, connections to previous material, placement of the material in a larger context, etc), to not wait until 24 hours before assignments are due to begin them, to utilize the office hours of the professor and TA, and to interact professionally with all members of the course.

Office hours:  All students are requested to attend office hours once during the first week of class.  This request allows me a chance to get to know you personally, and familiarizes you with the path tomy office. 

Homework and Exam Policy

Collaboration on homework assignments is allowed. You may consult outside reference materials, other students, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. No collaboration is allowed on the midterms or the final exam.

Homework format:  When composing your homework for submission, please adhere to the following guidelines:  (1) all problems should be submitted in the same order as in the assignment, (2) give each problem the same label as in the assignment, (3) begin each problem by restating the problem then indicate how you will approach the solution, (4) show all relevant work indicating how you reach your solution, and (5) indicate or discuss why your answer is correct or appropriate (e.g. check your answer), (6) clearly mark your answer, (7) keep relevant information associated (e.g. eigenvectors belong to specific eigenvalues), (8) take pride in your work—neatness counts in whatever profession you have in the future, so practice now!  For more information see the Five Steps to Problem Solving. 

Homework section:  Homework is due at the beginning of lecture on Tuesdays (8:30am).  Solutions will be discussed during section.

Grading

The final grade will be based on homework, a midterm, and a final exam.  Grading is not done on a curve, but on a scale.  Specifically, if the top grade at the end of the course is not a 4.0, a constant is added to all grades so that the top grade is a 4.0.  Grade scaling is determined before extra credit is applied to any grades.  If everyone performs well, the possibility exists for everyone to receive a 4.0.

·  Homework: 30%. Late homework will not be accepted without prior permission from the instructor.

·  Midterms: 20% each. The midterms will be Wednesday January 24, and Wednesday February 14.

·  Final exam: 30%. The final exam will be on March 13, 8:30-10:20am. 

Textbook (required)

Daniel J. Inman, "Engineering Vibration," Second Edition, Prentice Hall, Upper Saddle River, New Jersey, 2001.

 

Matlab Engineering Vibration Toolbox:  The course textbook comes with access to the Engineering Vibration Toolbox.  If the toolbox is not installed on a machine that you are using (either department of personal machine), take the following steps to install and run the functions in the package:

·              Use the command ‘help vtoolbox’ to get a list of the commands available.


References (on reserve in Engineering Library)

1.            Roy R. Craig, Jr, "Structural Dynamics: An Introduction to Computer Methods," John Wiley & Sons, Inc., 1981.

2.            W.T. Thompson and M.D. Dahleh, "Theory of Vibrations with Applications," 5th Ed., Prentice-Hall, Englewood Cliffs, New Jersey, 1998.

3.            G.V. Berg, "Elements of Structural Dynamics," Prentice-Hall, Eaglewood Cliffs, New Jersey, 1989.

4.            S. Graham Kelly, "Fundamentals of Mechanical Vibrations," Second Edition, McGraw Hill, 2000.

Schedule

This schedule is an initial guideline and is subject to adjustment as the course progresses.

Prof. Morgansen will be traveling the following dates:
            Feb. 1-4

Date

Topics

Readings

Assignments

Jan 3

Introduction

 

 

Jan 5

Single-Degree-of-Freedom Systems

1.1

 

Jan 8

Undamped Free Vibration

1.2

 

Jan 9

Damped Free Vibration

1.3

 Homework #1 Assignment

--> (Solution)

Jan 10

 

 

 

Jan 12

Modeling and Energy Methods

1.4, notes

 

Jan 15

MARTIN LUTHER KING
(Holiday)

 

 

Jan 16

 

 

 Homework #2 Assignment

--> (Solution)

Jan 17

Stiffness

1.5

 

Jan 19

Measurement and Design Considerations

1.6-1.7

 

Jan 22

Harmonic Excitation: Undamped Systems

2.1

 

Jan 23

Harmonic Excitation: Damped Systems

2.2

 Homework #3 Assignment

--> (Solution)

Jan 24

QUIZ I
(Solutions)

 

  Sample Problems (QUIZ I):

Sample 1, Sample 2

Solutions 1, Solutions 2

Jan 26

 

 

 

Jan 29

Forced Vibration: Impulse Response Function

3.1

 

Jan 30

Response to an Arbitrary Input

3.2  

 Homework #4 Assignment

--> (Solution)

Jan 31

Convolution Method

Impulse notes,

Impulse example

 

Feb 2

Transform Methods

3.4, partial fraction Mathematica example

 

Feb 5

Two-Degrees-of-Freedom Systems: undamped

4.1

 

Feb 6

 

 

 Homework #5 Assignment

--> (Solution)

Feb 7

Eigenvalues and Natural Frequencies

4.2

 

Feb 9

Modal Response

4.3

 

Feb 12

 

 

 

Feb 13

Systems with Viscous Damping

4.5

 

Feb 14

Modal Analysis of Forced Responses

4.6

 Homework #6 Assignment

--> (Solution)

Feb 16

QUIZ II
(Solutions)

 

 Sample Problems (QUIZ II) :

Sample, Solutions

 

Feb 19

PRESIDENT'S DAY 
(Holiday)

 

 

Feb 20

Distributed Parameter Systems

6.1

  Homework #7 Assignment

-->(Solution)

Feb 21

Modes and Natural Frequencies

6.2

 

Feb 23

 

 

 

Feb 26

Vibration of Rods and Bars

6.3 

 

Feb 27

Torsional Vibration of Rods and Bars

6.4

 Homework #8 Assignment

--> (Solution)

Feb 28

Bending Vibration of a Beam

6.5

 

Mar 2

 

 

 

Mar 5

Vibration of Membranes and Plates

6.6

 

Mar 6

 

 

 Homework #9:  Assignment

--> (Solution)

Mar 7

Modal Analysis and Forced Response

6.8

 

Mar 9

 

Movies of vibrational modes of membranes:

http://www.kettering.edu/~drussell/Demos/MembraneSquare/Square.html

http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html

 Extra credit problems:  Assignment

--> (Solution)

Mar 13

FINAL EXAMINATION (8:30am-10:20am)

 

Sample Problems

Solutions (p.1-7), Solutions (p.8-12)  Updated Solutions

 Final and solutions from 2005