FLORIDA INTERNATIONAL UNIVERSITY

Mechanical and MaterialsEngineering Department

 

Summer 2006                                   Mechanical Vibrations                                      EML4220

 

2005/2006 Catalogue Data: Theory and application of mechanical vibrations.  Includes damped and undamped vibrations with one or more degrees of freedom.  Computer Methods emphasized.

 

Instructor: Dr. Cesar Levy, 305-348-3643, EAS3462,


Goals:

Understand Undamped SDOF systems and its relation to a vibrating system

Understand Damped SDOF systems-viscous (underdamped, critically damped and overdamped) and coulomb friction, their differences and relation to real world

Understand Forced Motion due to harmonic loading and rotating unbalance

Understand Forced Motion due to oscillating support and its application--how vibrometers, velometers and accelerometers work

Understand forced motion due to a general periodic and nonperiodic loading

Understand how to derive Eqs. Of Motion for two degree of freedom systems or higher

Understand forced motion for two degree of freedom systems.

Understand how to find frequencies using Rayleigh and Dunkerley Methods

 

Prerequisite: EGN 3321 (Dynamics), EMA 3702 (Mechanics and Materials Science), a computer course (EML 2032 preferred

 

 

COURSE CONTENT

Topics by week

1.       What is vibrations and its importance

1-2.   Equivalent Systems and Equations of Motion

2.       Free Vibrations of M‑K system, Energy Methods

3.       SDOF with damping                                                                                                  Q1                      

3-4.   Forced SDOF without damping                                                                               

4.       Forced SDOF with damping

5.       Effect of Changing Mass or Spring                                                       

5-6.   Oscillating Base and Force Transmission                                    

6.       Rotating Unbalance and Relative Motion                                                             Q2

7.      Vibration Measuring Equipment                                                  

7-8.   Vibration Under General Forcing Function

8.       Coordinate Coupling 2DOF systems                    

9.       Forced Vibration of 2DOF system + Vibration Absorber                                    Q3

9-10.  Dunkerley and Rayleigh Methods

 

 

 

1. Importance of Vibrations; Basic Concepts‑‑period, amplitude, circular frequency, units; Classification of Vibrations‑‑ random, periodic, harmonic, aperiodic; Vibrational Analysis Procedures; Quick Review of Dynamics‑‑Kinetics and Principle of Linear and Angular Motion of a Particle, Mass Center and a System of Particles.

 

2. Undamped Free Vibrations for a Single Degree of Freedom (SDOF) System: Spring‑Mass System; Equivalent Springs and Masses; Energy Method‑‑KE<‑>PE transfer.

 

3. Damped Free Vibrations for an SDOF System; Spring‑Mass‑Dashpot System; Overdamped, Underdamped, Critically Damped System, damped frequency, damping factor, general solutions, Quick Review of second order linear constant coeff. Diff. Eqs.; Coulomb Damping, frequency displacement decrease, differences between coulomb and viscous damping.

 

4. Harmonically Forced Vibrations (HFV) of an SDOF System; Undamped and Damped Vibrations‑‑magnification factor, resonance conditions; beats; force transmission; HFV with coulomb damping; eccentric masses; relative motion, base excitation, effect of mass and spring variation applications‑‑velometers, vibrometers, accelerometers

 

5. General Forcing Conditions and Response; Fourier Analysis; Duhamel's Integral; Response of a Damped System.

 

6. Two Degree of Freedom (TDOF) Systems; Linear and Torsional Systems; Matrix Notation; Coupling and coupling coefficient; amplitudes, natural frequencies‑‑how to find them.

 

7. Multidegree of Freedom Systems; Stiffness Matrix; Flexibility Matrix; Mass Matrix; Energy Methods.

 

8. Numerical Analysis for Lumped Parameter Systems; Rayleigh's and Dunkerley's Method.

_________________________________________________________________________

 

Textbook: Mechanical Vibrations by S. S. Rao, 4th Edition.

 

Grading:  will be determined on the basis of                               3 Quizzes                20% each

                                                                                                          Final                     35%

                                                                                                          Computer Prob.     5%

 

HW's will be assigned but none will be collected for grading. Booklet of many completed problems will be placed in the library.  However, it is to your advantage to do the assigned problems since similar problems will appear on the quizzes

 

 

Grading Scheme: 90 and above A                       77 ‑ 79 B‑                         63 ‑ 66     D+         

                                 87 ‑ 89      A‑                       74 ‑ 76 C+                        60 ‑ 62     D

                                 83 ‑ 86      B+                       70 ‑ 73 C                          Below 60 F

                                 80 ‑ 82      B                          67 ‑ 69 C‑

 

 

We will be meeting 3 times a week M, W, R 1140-1255 since we will be meeting for ten weeks only.  Our meeting room will be EAS ____.  My office will be in EAS 3462 and my office hours will be M and W between 1600-1730 and T from 1300-1600.

 

Final Exam is tentatively scheduled Thursday 13 July 2006 or Monday 17 July 2006.  Time will be announced.

 

THIS IS A PRELIMINARY SCHEDULE--ALL CHANGES WILL BE ANNOUNCED IN CLASS.