ENGRMAE 147 Vibrations (2014-2015)

ENGRMAE 147 Vibrations

(Required for ME. Selected Elective for MSE.)
Catalog Data:

ENGRMAE 147 Vibrations (Credit Units: 4) Analysis of structural vibrations of mechanical systems. Modeling for lumped and distributed parameter systems. Topics: single and multi-degree of freedom systems, free and forced vibrations, Fourier series, convolution integral, mass/stiffness matrices, and normal modes with design project. Prerequisite: MAE80; Mathematics 2E. Materials Science Engineering and Mechanical Engineering majors have first consideration for enrollment. (Design units: 1)

Required Textbook:
. Edition, , 1969, ISBN-13 978-0073529271.

Recommended Textbook:
None
References:
None
Coordinator:
Faryar Jabbari
Relationship to Student Outcomes
This course relates to Student Outcomes: EAC a, EAC b, EAC c, EAC e.
Course Learning Outcomes. Students will:

1. Develop models for structural and mechanical oscillations. (EAC a)

2. Use sophomore level analytical techniques (mathematics, physics, dynamics) to analyze and understand critical features and characteristics of vibration problems. (EAC e)

3. Model multi-degree of freedom vibratory systems. (EAC c)

4. Use linear algebra and Laplace transforms for analysis of systems. Adopt systems view based on transfer functions, state-space models, and frequency response analysis in order to develop practical design techniques and rules for vibration control and vibration isolation. (EAC a)

5. Build and test experimentally a microcontrolled vibration system. (EAC b)

Prerequisites by Topic
  • Elementary differential equations and linear algebra
  • Introductory level dynamics (equations of motion, energy techniques, Newton’s Laws, rotating frames, etc.)
Lecture Topics:
  • Springs, dashpots, harmonic motion, complex variables, Fourier series, Laplace Transforms
  • Free vibration of single degree of freedom
  • Harmonic excitations
  • General forcing functions
  • Two degree of freedom systems
  • Multi-degree of freedom systems
  • Design issues in rotating shafts, vibration isolators, vibration absorbers and sensing instruments
Class Schedule:

Meets for 3 hours of lecture and 1 hour of discussion each week for 10 weeks.

Computer Usage:

Class management is through emails and class home pages. The projects require calculations that can be performed on a variety of platforms (any CAD software program such as MATLAB).

Laboratory Projects:

There are three paper designs, and a simple demonstration in class to visual mode shapes. The main laboratory aspects are included in MAE106.

Professional Component

Contributes toward the Mechanical Engineering Topics courses and Major design experience.

Design Content Description
Approach:

Students work in groups of 4 or 5 (self selected – with final approval by the instructor). Each project is limited to 5 pages of write up (plus another 5 pages of appendix or supporting material). A group leader is responsible for timely completion, group dynamics and overall communication with the instructor. The three projects are the following (often only 2 out of three are required and the third is for extra credit): 1. One-degree-of-freedom system: a typical rotating unbalance (washing machine, centrifuge) is modeled and analyzed. Maximum displacements, and force transmitted to the ground support are used as potential conflicting design objectives. 2. Two-degree-of-freedom systems: A simplified half-car model is used to study issues related to vibration analysis for systems under variable frequency excitations. Concepts for avoiding high levels of vibration, their physical interpretation and their potential manufacturing consequences are discussed. 3. Two-degree-of-freedom systems: A simple two mass system is used to study essential features and design trade-offs in a vibration absorber. The main emphasis is on obtaining a better understanding of the role that critical parameters and characteristics of the system play in the overall performance. The goal is to help students develop a broader view which integrates analytical training with design concerns. Design projects are discussed regularly during lecture, from week 3 to week 9.

Lectures: 100%
Laboratory Portion: 0%
Grading Criteria:
  • Homework: 7%
  • Midterm(s): 45%
  • Projects: 10%
  • Final: 38%
  • Total:100%
Estimated ABET Category Content:

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 3.0 credit units

Engineering Design: 1.0 credit units

Prepared:
October 13, 2014
Senate Approved:
April 29, 2013
Approved Effective:
2013 Fall Qtr