EML 4220 Vibration Analysis
Spring 2012
Instructor: Dr. Miao Liu
Teaching Assistant: Mr. Hossein Rasgoftar
EML 4220
Syllabus
Instructor:
Teaching Assistant:
Textbook:
Dr. Miao Liu
E-mail: miao.liu@ucf.edu
Office Hour: M F 4:00-5:30PM or by appointment
Free-vibration Analysis of
an Undamped 2-DOF system
EML 4220
Equation of Motion
1 1 () + (1 + 2 )1 () 2 2 () = 0
2 2 () 2 1 () + (2 + 3 )2 () = 0
Assuming that it is possible to have harmonic motion of 1 and 2 at the same
frequency and the same phase angl
Response Spectrum
(Shock Spectrum)
EML 4220
Response spectrum:
A response spectrum (shock spectrum) is a nondimensional plot showing the variation
of the maximum response with the natural frequency (or natural period) of a singledegree-of-freedom system t
20. Find the transfer functions for the block diagrams in Fig. 3.50.
Solution:
(8)
Block diagram for Fig. 3.50 (a)
Y _ G1
1—? _ l + G] + 02.
Block diagram for Fig. 3.50 (b): reduced
0.030‘06
= G' + (1+ menu + Gian
Z
n 29. A certain servomechanism sy
1. (1.5 point each) Multiple choice. (Onl one answer is correct)
1
52 +3
(1) The transfer function of a system is H (S) = , which ﬁgure shows its impulse response
(2) Which system is mar inall stable?
s+3 1
A)' (52+2)2 (52+1)(S+1)(s+3)
C) _s+4_ W“NW
Chapter 4
Vibration Under General Forcing Condition
Response under a general periodic force
Response spectrum
Response Under a General Periodic Force
EML 4220
Periodic Forces ()
Period = 2
() = ( + )
Fourier Series of ()
0
() =
+
2
2
=
cos +
=1
()cos
Response of a Damped System Under
Harmonic Motion of the Base
EML 4220
displacement of the mass from its static equilibrium position
response
excitation
displacement of the base
net elongation of the spring is
Equation of Motion
+ ( ) + ( ) = 0
11-1
Res
EML 4220
Harmonic Motion and Analysis
Periodic motion
Simple harmonic motion
Harmonic analysis
Time and frequency spectrum
4-1
EML 4220
Periodic Motion
motion that is repeated after equal interval of time
Harmonic Motion
A periodic motion in which the d
EML 4220
Chapter 2 Free Vibration of 1-DOF Systems
Free vibration of an undamped translational system
Free vibration of an undamped torsional system
Free vibration with viscous damping
Free vibration with Coulomb damping
Exam 1 on Feb 7th
1
Free Vibration
EML 4220
Review of FBD
Kinematics
Review of Dynamics
Kinetics
Review of Complex Algebra
sin =
exp exp()
2
cos =
exp + exp()
2
exp = = cos + ()
1
EML 4220
2
EML 4220
Spring, Mass or Inertia and Damping Elements
Spring Elements
A type of mechanical lin
Free Vibration of 1-DOF Systems
EML 4220
Free vibration of an undamped torsional system
If a rigid body oscillates about a specific reference axis torsional Vibration
displacement
measured in terms of an angular coordinates
restoring moment torsion of an
EML 4220
Chapter 3 Harmonically Excited Vibration
(Forced Vibration)
Forced Vibration of an undamped system
Forced Vibration of a damped system
Self-excitation and stability analysis
Laplace transform and frequency transfer function*
Cancellation of offic
Response of a damped system
under harmonic force
EML 4220
If () = 0 cos , then the equation of motion changes to
+ + = 0 cos
expect the particular solution also harmonic
Assume () = cos(
2 cos( ) sin( ) + cos( ) = 0 cos
[( 2 )cos( ) sin( )] = 0 cos
cos
Response of a Damped System
EML 4220
Under Multi-frequency Excitation
1. Multi-frequency excitation
() =
sin( + )
=
> 0 for each
2. The steady-state response due to a multi-frequency excitation is obtained using the
response for a single frequency exci