ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 5Due Wednesday, March 20
1. Inman Problem 2.4
2. Inman Problem 2.11
3. Inman Problem 2.19
4. Inman Problem 2.20. Note, you can use Eq. 2.38 to plot
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 4Due Monday, March 4
1. Investigate the cause and ultimate solution to the London Millennium Bridge vibration
problem that we looked at during the
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 3Due Monday, February 25
1. Inman Problem 1.40
2. Inman Problem 1.41
Note: Use the Vibration Toolbox or code the equations yourself to make these p
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 2Due Friday, February 8
1. Inman Problem 1.3
Plot using MATLAB or the software of your choice.
2. Inman Problem 1.6
Hint: This is solved in the sam
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 1Due Friday, January 25
1. Determine the spring constant for a compliant object.
Find some object around your house, here at UT, at work, where eve
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Exam 2Take HomeDue Friday, May 3 (by 5p)
Intructions: Use computer codes to solve these problems where convenient. Note that
it may also be convenient to use
4. (20 points) A mechanical device is shown below. Consider only quasi-static motion,
where x ! 0. Sketch the constitutive relation. In other words:
(a) Sketch the plot of F versus x. (Note that
1
<
2
Name:
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Exam 1
Wednesday, March 27
Due Wednesday, April 3 at beginning of class.
This exam is open note, open book, open computer, but not open neighbor. All wo
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 5Due Friday, April 12
Note: Solve all problems analytically, unless directed otherwise
1. Inman Problem 3.2
2. Inman Problem 3.9
3. Inman Problem 3
ENGINEERING VIBRATIONS
ME 355KSpring 2013
Assignment 6Due Friday, April 19
Note: Solve all problems analytically, unless directed otherwise
1. Inman Problem 4.1
2. Inman Problem 4.2
3. Inman Problem 4
1.3
x
Solve m + kx = 0 for k = 4 N/m, m = 1 kg, x0 = 1 mm, and v0 = 0. Plot the solution.
Solution:
"
This is identical to problem 2, except v0 = 0. $ ! n =
#
initial conditions:
x (0) = c1 + c2 = x0
Plot for Inman 2.20
t=0:.01:3; % Creates time vector
f=cos(6*pi*t);
% Must be defined, even if zero
x0=0; % Creates initial displacement
v0=0; % Initial
[t,x,v]=vtb1_3('-10*v-300*x+.8*f',f,t,x0,v0); %
33.2
Calculate the solution to
(
!
!
x + 2 x + 3x = sin t + ! t " #
()
()
)
!
x 0 = 0 x 0 =1
and plot the response.
(
)
()
()
!
!
!
Solution: Given: x + 2 x + 3x = sin t + ! t " # , x 0 = 0, x 0 = 0
k
2- 3
2.4
An airplane wing modeled as a spring-mass system with natural frequency 40 Hz is
driven harmonically by the rotation of its engines at 39.9 Hz. Calculate the period of the
resulting beat.
Sol
1.39
Using the definition of the damping ratio and the undamped natural frequency,
derive equitation (1.48) from (1.47).
Solution:
!n =
!=
k
k
2
= !n
thus,
m
m
c
2 km
thus,
x
Therefore, ! +
c 2! km
=
Engineering Vibrations
Spring 2013
ME 355K (18390)
MWF 1011a, ETC 4.150
Preston S. Wilson ([email protected])
TEXT: Engineering Vibrations (3rd ed.), Daniel J. Inman (Pearson Prentice Hall, 200
5.3 Vibration Absorbers
Consider a harmonic disturbance to a singledegree-of freedom system
Suppose the disturbance causes large amplitude
vibration of the mass in steady state
A vibration absorber
Section 4.6 Modal Analysis of the
Forced Response
Extending the chapters 2 and 3 to
more then one degree of freedom
D. J. Inman
22/45
Mechanical Engineering at Virginia Tech
Forced Response: the resp
Engineering Vibrations
Spring 2010
ME 355K l I834")
MWF IO Ila. hFC 4.150
P. S. Wilson (pswulsonGvmailutcxasedu)
TEXT: Engineering Vibrations (3rd ed.). Daniel J. Inman (Pearson Prentice Hall. 2008')