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 (D
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 t
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
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
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
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 Lapl