ME 318Mechanical VibrationsWinter 2008

2007-2009

Catalog Description:Free and forced vibration response of single and multiple degree of freedomsystems. Experimental studies of the dynamic behavior of structuresand machines. Instrumentation methods utilized in field and laboratory. 3lectures, 1 laboratory.

Prerequisites:

MATH 344 – Linear Analysis II

ME 326 – Intermediate Dynamics

EE 201 – Electric Circuit Theory

Textbook:Mechanical Vibration, William J. Palm III, 2007

General Information:

Homework will be assigned weekly and collected on the following Wednesday at the beginning of class. No late homework will be accepted. The lowest homework score for the quarter will be discarded when calculating your final grade.

Grading:

Class Participation, Quizzes, andHomework10%

Midterm Exams30%

Final Exam35%

Lab25% (15% Reports, 10% Final)

Notes:

  1. You must pass the lecture and lab independently.
  2. The grade breakdown above is a guideline and may be modified in individual circumstances (i.e. if a student performs much better on the comprehensive final than on the midterms this may be taken into account in the final grade).

Instructor:

Andrew Davol, Phone: 756-1388,Office:13-226

Office Hours:

Monday 1:10 pm – 2:00 pm

Tuesday

Wednesday11:10 am – 1:00 pm

Thursday1:10 pm –2:00 pm

Friday11:10 am – 12:00 pm

Learning Objectives:

  1. Derive mathematical models for simple vibration systems.
  2. Compute natural frequencies of simple systems.
  3. Evaluate the response of single degree-of-freedom systems to periodic or transient force or base excitation.
  4. Determine critical speeds of rotating machinery.
  5. Select vibration isolation systems.
  6. Evaluate the effect of damping on the above systems.
  7. Synthesize mathematical models of physical systems.
  8. Instrument systems for vibration analysis.
  9. Operate electromechanical shake tables.
  10. Interpret transient and steady state vibration from a physical standpoint.
  11. Compute amplitude ratios, natural frequencies, and damping ratios from experimental data.
  12. Solve differential equations, both linear and nonlinear, utilizing numerical techniques on one of the local computing systems.
  13. Utilize basic FFT spectral analysis equipment for vibration analysis of machinery systems and interpret results.
  14. Instrument and analyze systems with more than one degree of freedom.
  15. Write short technical reports in a professional manner.

Lecture

/ Date / Topic /

Reading

1 / 1 / Mon. Jan. 7 /

Introduction to Vibrations

/ 1.1-1.2
2 / Wed. Jan. 9 / Spring and Damping Elements / 1.3-1.4
3 / Fri. Jan. 11 / Spring – Mass Systems / 1.5-1.7
2 / 4 / Mon. Jan. 14 / Equation(s) of motion / 2.1-2.4 review
2.6 thoroughly
5 / Wed. Jan. 16 / Free Vibration of Undamped Systems / 3.1-3.2
6 / Fri. Jan. 18 / Free Vibration of Undamped Systems / 3.3
3 / Mon. Jan. 21 / Martin Luther King Day
7 / Wed. Jan. 23 / Free Vibration of Viscously Damped Systems / 3.4-3.7
8 / Fri. Jan. 25 / Free Vibration of Viscously Damped Systems / 3.4-3.7
4 / Mon. Jan. 28 / Exam I
9 / Wed. Jan. 30 / Free Vibration with Coulomb Damping / 3.8
10 / Fri. Feb. 1 / Harmonic Response / 4.1
5 / 11 / Mon. Feb. 4 / Harmonic Response / 4.2
12 / Wed. Feb. 6 /

Base Excitation

/ 4.3
13 / Fri. Feb. 8 /

Rotating Imbalance

/ 4.4
6 / 14 / Mon. Feb. 11 /

Critical Speed (shaft whirl)

/ 4.5
15 / Wed. Feb. 13 / Equivalent Damping / 4.6-4.7
Fri. Feb. 15 / Washington’s Birthday Observed
7 / 16 / Mon. Feb. 18 / General Forced Vibration - Periodic / 5.1
17 / Wed. Feb. 20 / General Forced Vibration – LaPlace Transforms / 5.2-5.4
Fri. Feb. 22 / Pulse and Impulse Response / 5.5
8 / 18 / Mon. Feb. 25 / 2 Degree of Freedom – Free Vibration / 6.1
19 / Wed. Feb. 27 / Exam II
20 / Fri. Feb. 29 / Multi Degree of Freedom – Eigenvalue Problem / 8.1-8.2
9 / 21 / Mon. March 3 /

Modal Analysis

/ 8.3
22 / Wed. March 5 / Effects of Damping / 8.4
23 / Fri. March 7 / TBD
10 / 24 / Mon. March 10 /

TBD

25 / Wed. March 12 / TBD
26 / Fri. March 14 / Review

Final Exam:

Section 1 – MWF 3:10 – 4:00Monday March 17, 1:10 pm – 4:00 pm

Section 2 – MWF 4:10 – 5:00Wednesday March 19, 4:10pm – 7:00 pm