Part I :
modelling and SDOF
systems
Chapter 1: Introduction
②
modeling
↳ A model seet mathematical
of eq.
describe
physical phenomenon
* Quarter Car model /example
우 M1
-goal : Isolate road-induced vibrations
using spring
and damper k Shock
absaber
. Z 1E 1
me-degree-of-freedom figue right
④
on
↳ describe
Assumes :
rigid fire +
possesses
1 Gord .
G
to motion of me
IIE] tKuZlt }
,t Cu ' kr .
mi t = C.
k
MM
9
to I DOF model
flexible tim ? ,
We can
go
↳
shock abarbe
Ri
representation more accurate ? ge
.물 }
~
~ BUT needs 2 word.
tire
☆
키너
船 m “公情 。 品 = 101
↳ We can
go
even
further 3DOF
system include drive
comfort
91ms Ide o
m/ + k( ( =
9 ,
s
M거
shock abarbe
(m mg)i) ( - ㅣ
Ri
with m =
mc =
ge
EItId m Ytie
며닮 " ' *이
당
, model
* Tasional
shaft
↳ Guide a
shaft w.
uniform diam ,
length C ,
do and di
and total mas M
)
-Can this I DOF model
represent as
shaft compared of 2 end rotan exe)
connected
by mossless
spring
>
- each roto's
polar moment
of inertia-half of
2
shaft's pola moment of Inertia
=>
Fp =
1Mr)dodi 1 Sheor modulus
Tldô-di6-
=
kp =
32 e
( torsional
=
stiffnens)
of
(excea)
어
to 3DOF model
Upgrade
~
↑
* Generalised Coordinates
↳ set
of genediced word
.
(,
g(t) , ..., am't) satisfies following conditions :
1)
they are consistent with their constraints
2)
they are
sufficient to describe an the
orbitrary config of system
3)
they are
independent
9 서미위없티
, Chapter 2:
Modeling
φ
없
k
2 1) The Second law Newton √
of um
童 nfl
.
비
B M
1 DOF
Snsider
moss-spring-damper system
- X
C
described
Motion
by
is x * X
** 바
Cow Newton
↳
Wing free body diagram - 2 X
地
-
k+ -
CT +
f 1t 1 =
m ≠ M
aflal
mt 뜰
더 - (X + kX =
fl)
fre body diagram
Simple method
for simple Systems
- in
practice more
comple system of many point
more and
Rigid body's
then
↳ We have to introduce extra Reaction
forces = mor coird
degrees of freedom
introduce New
modelling technique ? Lagrange
=
God of
using Lagrange
π
1) No forces
Reaction #
2)
equations #
degrees of
=
freedom?
2Virtual work d'Alembert
2 .
and
principle
Conside
Dynamics
model with
generalized Crd
9/t) =
(
때
.
㉙
β
↳ the evolution is im
represented trajectory
in
g/t) as a
spece
a
~
every point
on
trajectory concep to a combination (g(t), ..., 9m/H]
of time instant t
oqu
- sider
infinitesmell virtual
change 5g/) of g(t) :
8911t )
= Virtual
of Infiguration
8 原 (]
591t) =
variation
: gitl
59m(t)
↳
Sglt) is not
necessarily
the actual
displacement of the system under the
acting faces ?
5917) be chosen it satifies the I
con
arbitrary as
long as
system instants .
modelling and SDOF
systems
Chapter 1: Introduction
②
modeling
↳ A model seet mathematical
of eq.
describe
physical phenomenon
* Quarter Car model /example
우 M1
-goal : Isolate road-induced vibrations
using spring
and damper k Shock
absaber
. Z 1E 1
me-degree-of-freedom figue right
④
on
↳ describe
Assumes :
rigid fire +
possesses
1 Gord .
G
to motion of me
IIE] tKuZlt }
,t Cu ' kr .
mi t = C.
k
MM
9
to I DOF model
flexible tim ? ,
We can
go
↳
shock abarbe
Ri
representation more accurate ? ge
.물 }
~
~ BUT needs 2 word.
tire
☆
키너
船 m “公情 。 品 = 101
↳ We can
go
even
further 3DOF
system include drive
comfort
91ms Ide o
m/ + k( ( =
9 ,
s
M거
shock abarbe
(m mg)i) ( - ㅣ
Ri
with m =
mc =
ge
EItId m Ytie
며닮 " ' *이
당
, model
* Tasional
shaft
↳ Guide a
shaft w.
uniform diam ,
length C ,
do and di
and total mas M
)
-Can this I DOF model
represent as
shaft compared of 2 end rotan exe)
connected
by mossless
spring
>
- each roto's
polar moment
of inertia-half of
2
shaft's pola moment of Inertia
=>
Fp =
1Mr)dodi 1 Sheor modulus
Tldô-di6-
=
kp =
32 e
( torsional
=
stiffnens)
of
(excea)
어
to 3DOF model
Upgrade
~
↑
* Generalised Coordinates
↳ set
of genediced word
.
(,
g(t) , ..., am't) satisfies following conditions :
1)
they are consistent with their constraints
2)
they are
sufficient to describe an the
orbitrary config of system
3)
they are
independent
9 서미위없티
, Chapter 2:
Modeling
φ
없
k
2 1) The Second law Newton √
of um
童 nfl
.
비
B M
1 DOF
Snsider
moss-spring-damper system
- X
C
described
Motion
by
is x * X
** 바
Cow Newton
↳
Wing free body diagram - 2 X
地
-
k+ -
CT +
f 1t 1 =
m ≠ M
aflal
mt 뜰
더 - (X + kX =
fl)
fre body diagram
Simple method
for simple Systems
- in
practice more
comple system of many point
more and
Rigid body's
then
↳ We have to introduce extra Reaction
forces = mor coird
degrees of freedom
introduce New
modelling technique ? Lagrange
=
God of
using Lagrange
π
1) No forces
Reaction #
2)
equations #
degrees of
=
freedom?
2Virtual work d'Alembert
2 .
and
principle
Conside
Dynamics
model with
generalized Crd
9/t) =
(
때
.
㉙
β
↳ the evolution is im
represented trajectory
in
g/t) as a
spece
a
~
every point
on
trajectory concep to a combination (g(t), ..., 9m/H]
of time instant t
oqu
- sider
infinitesmell virtual
change 5g/) of g(t) :
8911t )
= Virtual
of Infiguration
8 原 (]
591t) =
variation
: gitl
59m(t)
↳
Sglt) is not
necessarily
the actual
displacement of the system under the
acting faces ?
5917) be chosen it satifies the I
con
arbitrary as
long as
system instants .
