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 the total solution, but using the
vibration toolbox le
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 course introduction at the beginning of the
semester. I
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 plots.
3. Using the system values from 1.41 above:
(a) C
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 same way that we did in class for a vertical spring in gra
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 ever, and conduct an experiment
to determine the spring co
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 a hybrid method, in which part of the problem is done
a
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 .)
(b) Indicate the following points on the x-axis: x
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 work must
be completed alone. Show all work if you want p
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 3.18
4. Inman Problem 3.25
5. Inman Problem 3.29
6. Inma
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 4.3
4. Inman Problem 4.4
5. Inman Problem TB4.1 on p. 38
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 = 1 ! c2 = 1 " c1
%
k
= 2 rad/s' . Calculating the
m
&
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); % Runs analysis.
plot(t,x); % Plots displacement versus
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
c
= 1.732 rad/s, " =
= 0.5774, ! d = ! n 1 # " 2 = 1.4
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.
Solution: Given:
Beat period:
2.5
! n = 2 ! (40) = 80 ! ra
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
=
= 2!" n
m
m
c
k
!
x+ x=0
m
m
becomes,
(t) + 2!" n x (t)
Engineering Vibrations
Spring 2013
ME 355K (18390)
MWF 1011a, ETC 4.150
Preston S. Wilson (pswilson@mail.utexas.edu)
TEXT: Engineering Vibrations (3rd ed.), Daniel J. Inman (Pearson Prentice Hall, 2008)
SOFTWARE: Matlab, available in the METER computer la
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 is a second spring mass
system added to this primary m
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 response of an
mdof system to a forcing term
k1
c1
x1
x2
k2
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')
SOFTWARE: Matlah, available in the METER computer lab.
Deriva'ves encountered using energy methods with linear single DOF systems:
d
Using our original energy rela.on: (T + U ) = 0 ,
(1)
dt
d
d1
2
results in