Name: NID:
(Write legibly)
EML 4220 EXAM #1
Spring 2014
Feb 17, 2014
3:30 PM 4:20 PM
Instructions:
1. To obtain maximum credit for a problem, you must present your solution clearly.
Accordingly:
a.
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 Dam
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 o
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
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( ) s
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
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
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
() = ( +
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 o
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 (o
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. (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 s
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
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
Lecture 5: 1DOF Free VibrationI
(Chapter -2, Vibrations textbook)
Dr. Sudeshna Pal, ENG I, Room 246
Harmonic Motion
Periodic
Motion: Any motion that repeats itself at equal
intervals of time ().
Har
Lecture 9: Forced Vibration
(Chapter -3, Vibrations textbook)
Dr. Sudeshna Pal, ENG I, Room 246
Example-3(Damped Free Vibration)
A piston of mass 4.53 kg is traveling in a tube with a velocity of 15.2
Problem 3
Using the following code, the response for the given system was studied for four (4)
different values of the parameter K.
clear all
close all
clc
i = 1;
for K=[0.5 1 2 0.065]
num = [0 0 0.2*