Vibrations Table of Contents

blue-seal

Department of Mechanical and Materials Engineering

This is the EML 4220 Mechanical Vibrations/ EML 4930 Special Topics and Projects Summer 2018 page

Here is the EML4220/EML4930 Syllabus

We will meet once a week at a time acceptable to you and I.

READ Chapter 1 and Sections 2.1-2.5

Here are problems 1-3, 1-7 and 1-8, 1-9 and 1-10

Here are problems 1-12, 1-13a and 1-13b,

Here are problems 1-29, 1-30, 1-35 and 1-35b

Here are problems 1-53, 1-54, and 1-59

Here is a videotape on energy methods and equivalent elements

Even though I have given you access to the solutions, you need to try to do the problems first so that you will know where you get stuck and then use the solutions to see you get past the problem. Just looking at the solutions does not help you understand the methodology in relation to the way you think about solving the problem. Just as with Dynamics, the only way to learn vibrations is to do as many problems as you can.

Here are problems 2-4, 2-6 and 2-7 Note that more comments about 2-7

Are found on the top of the page for problem 2-13

Here are problems 2-13 , 2-15. Note that the problem here is LIKE 2-13 in your book

But is not problem 2-13

This material and all the linked materials provided, except where stated specifically, are copyrighted © Cesar Levy 2018 and is provided to the students of this course only. Use by any other individual without written consent of the author is forbidden.

Here are problems 2-17, 2-18, 2-19

Here are problems 2-26, 2-38

Here is the rest of 2-38, and problems 2-68, 2-79

Here is the rest of 2-79

Here is problem 2-69

Here is problem 2-33, problem 2-45, and problem 2-71

From here we begin Problems in free vibration with damping….

READ Chapter 2.6-2.8

Here is a videotape of materials on damped systems and log decrement.

Here is a videotape for coulomb friction

Here are problems 2.88 and 2.90

Here are problems 2.84, 2.92 and 2.95

Here are problems 2.93, 2.96 and the rest of 2.90

Here are problems 2.106, and 2.122

Here are problems 2.112, 2.113 and 2.115 part a

Here is the rest of 2.115 and 2.116 and the rest of 2.116

Here is problem 2.145

Some of these problem solutions for the previous problem sets are not activated as they are under copyright. Problems from the next set of problems will be revealed when you have attempted them and you ask them to be revealed.

Please start looking at the following problems

Here are problems 3.1, 3.2, 3.8, 3.10

Do problems 3.18, 3.19,3.25, 3.26—No solutions will be given for these…solutions to 3.19 and 3.25 are given in the back of your book.

Here are problems 3.29 and 3.33part1, 3.33part2 and 3.32

Here is a videotape of problems related to damped and undamped systems

Please start looking at the following problems

Here are problems 3.1, 3.2, 3.8, 3.10

Do problems 3.18, 3.19,3.25, 3.26—No solutions will be given for these…solutions to 3.19 and 3.25 are given in the back of your book.

Here are problems 3.29 and 3.33part1, 3.33part2 and 3.32

Here is a videotape of problems related to damped and undamped systems

Here is a video related to beats, undamped forced motion

Here is a video related to rotating unbalance

Other problems of Chapter 3 to be covered.

Here are problems 3.54, 3.58

Here are solutions to problem 3.53. Problems 3.26, 3.48, 3.51 and 3.59 solutions can be viewed privately.

These problems below deal with force transmitted (chapter 9) and with vibration measuring equipment (Chapter 10). Please go through them to understand the concepts.

Here are problems 9.27, 9.32 and 9.34

Here is the rest of 9.34pt2 and 9.35

Here are problems 10.11, 10.12, 10.15

Here is a video dealing with relative motion and its importance in accelerometer design. Relative Motion is explained in Chapter 3, but the applications are in Chapter 10.

A video dealing with problems related to this topic as well as vibration absorber, accelerometers, vibrometers can be found at the following link.

Please start reading chapter 4 which deals with non-periodic forcing functions of the type we discussed at the very end of the EML3222 classes (in Chapter 9 of Rowell’s book).

You are assigned problems 4.15, 4.16 and 4.23. Once you have completed them, you can view the solution below.

Here are problems 4.15 and 4.16 Here is problem 4.23

Chapter 5 begins two degree of freedom systems --linear motion, rotational systems, combined linear-rotational systems (like suspension type). Start reading Chapter 5, sections 1-5 and 7.

Here are problems that you should try: 5.1, 5.4, 5.5, 5.20, 5.21, 5.34. Only the first problem is worked out in its entirety for you to view. The others can be viewed privately.

Here is a video dealing with problems for vibration of 2DOF systems

Chapter 7, Sections 1-3 begins solving 2 degree of freedom systems numerically by using energy methods.

Problems for Chapter 7: Please do Problems 5.1, 5.4, 5.55, 5.20, 5.21, 5.34 Using, Dunkerley and Using Rayleigh’s methods and compare to the values you obtained (see problems above). Practice on the problems 5.1, 5.4, 5.5, 5.20, 5.21, 5.34 by determining the M and K matrices and using values for the vector A

Please read Chapter 5, Section 6 and its application found in Chapter 9, Sect 11. This will be the last topic to be discussed in the course.

Please look at problems 9.54, 9.57 and 9.60 that deal with this last topic. Please note that these problems will not be uploaded but can be viewed privately if requested.