CE 488 Introduction to Vibrating Systems  
Fall 2004      
       
Instructor Name Hilmi Lus  
  Office M 3175  
  Office Hours M 12:00-13:00, W 11:00-12:00  
  Tel. (212) 359 6594  
  e-mail hilmilus@boun.edu.tr  
  home page http://www.ce.boun.edu.tr/eng/people/faculty/lus/  
       
Teaching Assistant    
       
Course Data Hours T 678  
  Location M 3100  
       
Course Description (Elective - Not yet in catalog)  
CE 488 Intro. to Vibrating Systems    
(3+0+0)3
Vibrating systems. Elementary vibrations of undamped and damped Single-Degree-of-Freedom (SDOF) systems. Response of SDOF systems to general excitations. Transform methods. Elements of analytical dynamics. Vibrations of Two-DOF systems. Vibrations of Multi-DOF systems. State space formulations. Numerical integration. Vibrations of a string. Non-linear vibrations of SDOF systems.
     
Couse Objectives    

This course in designed to present the theory and the tools of vibration analysis. The main objective of this course is to help the students develop an ability to
(a) differentiate between static and dynamic loads and systems encountered in common engineering practice
(b) model systems for vibration analysis
(c) develop quick, back-of-the-envelope answers when encountered with vibration problems
(d) participate in research or at least develop an appreciation of/interest for the current research in the subject

     
Text Book    
Meirovitch, L., "Fundamentals of Vibrations" , McGraw-Hill, Int. Ed., 2001.
     
Reference Books    
Meirovitch, L., "Elements of Vibration Analysis", McGraw-Hill, QA935 .M53 1975.
Meirovitch, L., "Analytical Methods in Vibrations", Macmillan,   QA935 .M5 1967.
Inman, D. J., " Vibration : with control, measurement, and stability" , Prentice Hall, TA355 .I52 1989.
Timoshenko, S., " Vibration problems in engineering" , D. Van Nostrand Company Inc.,   TA355 .T55 1937.
 
Reseach Journals    
Journal of Sound and Vibration, ASME Journal of Vibration and Acoustics, ASME Journal of Applied Mechanics, ASCE Journal of Engineering Mechanics, Earthquake Engineering & Structural Dynamics, Mechanical Systems and Signal Processing. All available in the library, most available in electronic format.
     
Design Content    
A project based on a design oriented problem, most probably regarding earthquake related analysis, will constitute part of the final grade. Estimated design content for the course is about 10%.
     
Computer Usage    
Assignments will include simulations and numerical solutions that will require usage of computers. The suggested software for programming is MATLAB; sufficient coverage will be given in class and via handouts.
     
Class Policies    
Quiz
 20% At least 5 quizzes will be given, the lowest grade will be omitted  
Midterm
40% Two midterms will be given  
Final
 30%    
Project
 10% Design oriented project.  
     
Contribution of the Course to Program Objectives  
This course is intended to contribute to the following program outcomes:  
ü
(a)
 An ability to apply knowledge of mathematics, science and engineering
(b)
 An ability to design and conduct experiments, as well as to analyze and interpret data
(c)
 An ability to design a system, component, or process to meet desired needs
ü
(d)
 An ability to function on multi-disciplinary teams
ü
(e)
 An ability to identify, formulate and solve engineering problems
(f)
 An understanding of professional and ethical responsibility
(g)
 An ability to communicate effectively
(h)
 The broad education necessary to understand the impact of engineering solutions in a global and societal context
ü
(i)
 A recognition of the need for, and ability to engage in life-long learning
ü
(j)
 A knowledge of contemporary issues
ü
(k)
 An ability to use the techniques, skills and modern engineering tools necessary for engineering practice
     
Course Assessment    
The course will be assessed by the students based on a template prepared by the instructor. The main points of the assessment will pertain to the successes/failures regarding the objectives stated here, and the evaluation of these objectives with respect to the claimed contributions to the program outcomes.
     
     
     

Week

Topics

Reading Assignments

Suggested Problems

Objectives

1

Vibrating Systems

 Chapter 1

1.2, 1.4, 1.6, 1.8, 1.9, 1.11, 1.12, 1.13, 1.17 

Concept of oscillation. Concept of Degree of Freedom (DOF). Discrete and Continuous Systems. Structural and Mechanical Systems. Modeling.

2

Elementary Vibrations of Undamped Single-DOF Systems

Chapter 2

2.2, 2.3, 2.12, 2.13, 2.14, 2.15

Governing equation of motion. Response to initial conditions. Response to a harmonic excitation. Static vs. dynamic response and magnification.

3

Elementary Vibrations of Damped Single-DOF Systems

2.19, 2.20, 2.22

Energy dissipation. The viscous dashpot. Governing eq. of motion. Response to initial conditions. Response to a harmonic excitation. Transient and steady state response.

4

Response of SDOF Systems to General Excitations, QUIZ 1

Chapter 3,
Sections 4.1-4.6

3.3, 3.14, 3.15, 3.18, 4.5, 4.9

Response to impulse and unit-step functions. Rise time, overshoot, and settle time. Convolution Integral. Numerical evaluation.

5

Transform Methods, QUIZ 2

Sections 4.6, 4.7, Appendix A,
Appendix B

Handout I

Response to periodic excitations and the Fourier expansion. Laplace transform. Transfer function. Bode plots. Nyquist plot. Stability.

6

MIDTERM I

 

 

 

7

Elements of Analytical Dynamics

Chapter 6

6.1, 6.2, 6.6, 6.8, 6.9, 6.12

Work and Energy. Generalized coordinates. Principle of Virtual Work. D`Alambert's Principle. Lagrange's eqs. of motion. Hamilton 's formulation.

8

Vibrations of Two-DOF Systems, QUIZ 3

Chapter 5

5.1, 5.2, 5.3, 5.7, 5.8, 5.13, 5.16

Free vibrations of undamped systems. Characteristic polynomial and the eigenvalue problem. Modes and decoupling, natural coordinates. Beat phenomenon. Response to harmonic excitations. Vibration absorbers.

9

Vibrations of Multi-DOF Systems, QUIZ 4

Chapter 7

7.1, 7.2, 7.4, 7.5, 7.6, 7.22, 7.23, 7.50

Undamped free vibrations and the eigenvalue problem. Orthogonality of eigenvectors. Damping. Analysis in modal coordinates. Rayleigh Quotient. Transfer functions and FRFs.

10

State Space Formulations, QUIZ 5

Sections 4.8-4.13,
7.17-7.20

Handout II

Defining `state'. State space formulation for a SDOF system. Solution of the first order equation. Complex modal parameters. Formulations for MDOF systems.

11

MIDTERM II

 

 

 

12

Numerical Integration, PROJECT

 

4.23, 4.46, 7.67 

Discretization in time. Central difference method. Alternative methods for integrating the second order equations. Discrete time state space equations.

13

Vibrations of a String

 Sections 8.1, 8.2,
8.4 (partial),
8.5 (partial)

Handout III

Relation between discrete and continuous systems. Governing partial differential equation. Free vibrations and the eigenvalue problem. Eigenfunctions and orthogonality.

14

Non-linear Vibrations of SDOF Systems

Sections 11.1-11.5

11.1, 11.3, 11.9

The pendulum. Fundamental concepts in stability. Phase plane plots. Conservative systems. Limit cycles.