EXAM#l SDOF Free Response on 211212013
Determine these parameters on the above signal of
,.,/,
= -4
,
!,n,
+
,
(Write down the units if exist.)
- -$ ,
1) Label the location of the phase angle, 4, in the figure.
+
,f+
Estimate the value of 4 by your eyes.
Laplace Transform Table
L [ x (t )] = X ( s )
Window 2.1
under damped
Window 1.5
Example 1.3.3
critically damped
over damped
(2.18)
Window 2.3
)
&
m & + c x + kx = F = (t )
x
sin( x y ) = sin x cos y cos x sin y
cos( x y ) = cos x cos y m sin x sin y
TOPIC II : SDOF Harmonic & Base Excitation Response Summary
&
m & + c x + kx = F 0
x
sin
t
cos
& + 2 n x + n2 x = f 0
&
x
=
C
C cr
sin
t
cos
C cr = 2m n = 2 km
x p (t ) = X sin( t )
x p (t ) = sin tAs cos tB s
x p (t ) = X cos( t )
x p (t ) = As cos
TOPIC I : SDOF Free Response Summary
x
Undamped Free Response m& + kx = 0
(Solution Format)
x(t ) = A1 cos nt + A2 sin nt
x
Damped Free Response & +
c
k
&
x+ x =0
m
m
2
& + 2 n x + n x = 0
&
x
=
C
C cr
C cr = 2m n = 2 km
(Solution Format)
Underdamped
x (
Chapter 4 MDOF Systems
(Multiple Degree of Freedom systems)
Extending the first 3 chapters
which are SDOF (Single Degree Of Freedom) Systems
Oakland University
Mechanical Engineering
Prof. Yin-ping (Daniel) Chang
1/53
The first step in analyzing multiple
1
HW#2 SDOF Harmonic & Base Excitation Response Solution
1.
% ME421 - HW#2 - Prob#1, Example 2.8.2 Figure 2.32 on Inman's book p.163 & 164
% CH2 2-1 to 2-6 SDOF Harmonic & Base Excitation Response
% by OU ME Professor Yin-ping (Daniel) Chang - Winter 2013
HW#l SDOF Free Response Solution
HW#l SDOF Free Response Solution
HW#l SDOF Free Response Solution
,
4
HW#1 SDOF Free Response
4.
SOLUTION
Plot the following solutions (or responses, signals, output) of a SDOF
m/k vibration system by Matlab, with m = 1 kg
4
HW#3 Transfer Function & Simulink Modeling Solution
4
Matlab code. Refer to Prof. Chang's Matlab codes posted online.
t=0:0.025:3*pi;
m=1;
c=2;
k=10;
wn=sqrt(k/m);
z=c/(2*m*wn);
wd=wn*sqrt(1-z^2);
% Step Response by Transfer Function Modeling (step comm
EXAM#3 Transfer Function & Simulink Modeling on 4/4/2013
1. A m=1, c=2, k=4 system, x0=v0=0, is subject to a unit impulse input, complete the following:
a.
b.
@ E.OM.
Write down E.O.M., take Laplace Transform, and express X(s) in Laplace domain forma