MAE 130C
Mechanics III: Vibrations
SUMMER 2008

Announcements

some notes...? Also, note: for a good problem for Lagrangian mechanics where the partial T with respect to qi is not equal to zero, check out chapter 7 #15 in the last homework. Solutions are now online.

Sample final available!!

Extra office hours are on Wednesday 5-7 pm and Thursday 3-5 pm. There will be no cookies >=[ ... maybe...

Midterm solutions now available.

Please note that the answer to 3.24 is Delta = 2.68 mm.

New link added in the "Interesting Links" section. Check out the use of vibrations theory in NASA's new rockets.

August 20: MIDTERM REVIEW SESSION: Steve will be having a review session on Wednesday, August 20, from 2 to 4 pm in U-409 (the normal location for his office hours).

August 19: Practice Midterm can be found here (or in the other link, I guess...)

August 15: Steve's Thursday lecture notes are now available.

Homework submissions: Homeworks must be in Professor Nesterenko's box (next to his door) by 5 pm, Tuesdays. Do not bring them to lecture. Thanks!

August 13: Steve's Tuesday lecture notes with key relations and corrections posted. Also, notes on Fourier series have been updated; the new version has error corrections and is in a higher resolution.

August 11: Notes and a worked example on Fourier Series have been posted in the "General Vibration Links" section of the website. Please thank Steve for writing up these supplements!



Inspirational (?) Quotes, courtesy of Robb Kulin:
"Always behave like a duck - keep calm and unruffled on the surface, but paddle like the devil underneath.”
~ Jacob Braude ~

"I try to take one day at a time, but sometimes several days attack me at once."
~ Jennifer Unlimited ~

"I hope you've had the time of your life."
~ Green Day ~

General Vibrations Links       Homework & Solutions       Homework Guidelines     Syllabus



MAE 130C Mechanics III: Vibrations (4) (Cross-listed with SE101C).
Free and forced vibrations of damped one-degree of freedom systems; vibration isolation, impact and packaging problems. Analysis of discrete multiple degree-of-freedom systems using matrix representation; normal mode of frequencies and modal matrix formulation.  Lagrange’s equations. Modal superposition for analysis of continuous vibrating systems. Problems of elastic bars and beams include free, impact-excited and sinusoidally forced vibrations. Lectures include methods of problem formulation and problem solution with application to realistic engineering problems.
Prerequisites: Math. 21D and AMES 121A,B (MAE 130A,B) or SE 101A,B with grades of C- or better.
 
Textbook: Thomson, William T. and Dahleh, Marie D., Theory of Vibration with Applications, Fifth Edition Prentice-Hall, Inc., Upper Saddle River, NJ, 1998.
 
Prerequisites by topic: Integral and differential calculus, differential equations, Newton’s laws, engineering statics and rigid body dynamics.
 
Instructor:  Professor Vitali F. Nesterenko
                      277 EBU II; Phone: 822-0289
                      E-mail: vnesterenko@ucsd.edu
Lectures:    Tuesday and Thursday 5:00 - 7:50 pm, Center Hall 115
Discussion session: Thursday 8:00 - 8:50 pm, Center Hall 115;
Office hour: Tuesday 8:00-8:50 pm, 277, EBU-II.

TA: Andrew Liu
E-mail: aliu@ucsd.edu
Phone: haha, no =)   
Office hours:   Mondays and Fridays 5-7 pm @ EBU II rm 105
 
TA: Steve Oberrecht
E-mail: soberrec@ucsd.edu
Phone: >=[   
Office hours:   Tuesdays and Thursdays 3-5 pm @ U-409
 

Reader: John Luke Wolff
E-mail: johnlukewolff@yahoo.com

Grading:
Weekly homework  5%
Midterm exam  45%
Final exam  50%

Homework: Problems will be assigned on Tuesday of each week and collected seven days later before 5:00 p.m on next Tuesday (EBU II, 277, BUT NOT DURING THE LECTURE).  The usual practice will be: “No late homework”.  Solutions to the homework sets will be available for this course the day after they are due.  Homework problems may be discussed with fellow students, and consultation with TA for general direction on the problem solution is encouraged; however, submitted solutions must be your own work.
Lecture policy: Attendance is expected, but is not mandatory.  You are responsible for ingesting and digesting all information presented in class whether or not you are in attendance.
Exam policy: Exams will be closed book, only a formula sheet will be allowed for all examinations.  The Final will be comprehensive.
Tentative exam dates:                      Midterm   August 21, 5:00 - 7:00pm
                                                               Final   September 6, 7:00 - 9:59 pm
 
Course Topics:
1. Periodic motion, Fourier series, spectrum.
2. One degree-of-freedom transient and steady state response
3. Applications to vibration isolation and measurement
4. Response to impact and impulse excitation
5. Two degree-of-freedom undamped systems. Initial conditions, beat frequencies, static and dynamic coupling, free vibration, and normal modes, forced vibrations.
6.  Properties of n degree-of-freedom systems: matrix formulation, eigenvalues and eigenvectors, modal matrix, and reduction to normal coordinates
7.  Free and forced vibration of n degree-of-freedom systems
8. Normal mode vibration of continuous systems
9. Lagrange’s Equation

Course Objectives:
1. The basic principles underlying the vibration of mechanical systems.
2. Identification, formulation and finding of the solutions of engineering problems in vibrations.
3. The concepts of Lagrange’s Equation.
 
Methods of evaluation:
1.  Homework will be regularly collected and graded.
2. Exams
 
Performance Criteria:
Objective 1
1.1 Students will demonstrate an understanding of linear vibration theory and the basic formulations for a degree-of-freedom and continuous systems.

Objective 2
2.1 Students will demonstrate the ability to formulate the equations of motion for multi-degree-of-freedom systems.
2.2 Students will demonstrate the ability to calculate the normal modes of a system.
2.3 Students will demonstrate that they can concert between the normal and the physical coordinates.
2.4 Students will demonstrate that they can determine and apply the appropriate solution method to calculate the response of the system.

Objective 3
3.1 Students will demonstrate an understanding of Lagrange's Equation as applied single and multi-degree-of-freedom systems.
3.2  Students will be able to evaluate the generalized forces of conservative forces using their potential energy.
3.3 Students will be able to evaluate the generalized forces of arbitrary external forces.
3.4 Students will demonstrate an ability to apply Lagrange's Equation where appropriate.