Recent
Developments
in
External
Acous5c
Models
for
Flexible
Underwater
Vehicle
Dynamics
**
**Joint Collaborations with
Moonseok Lee, Youn-Sik Park and Youngjin Park
Center for Noise and Vibration Control
Department of Mechanical Engineering
KAIST
Daejeon, Korea 305-701.
K.
C.

Park,
Professor 
 
 
 
 
WCU
Visi5ng
Professor
Department
of
Aerospace
Engineering
 
Division
of
Ocean
Systems
Engineering
Sciences,

 
 
 
 
 
 
 
School
of
Mechanical
Engineering
University
of
Colorado 
 
 
 
 
KAIST
Boulder,
CO,
USA,
and
 
 
 
 
 
Daejeon,
Korea
Joint
KAIST‐University
of
Tokyo
Workshop
on
Ocean
Systems
Engineering,
Kashiwa,
Japan.


16
October
2009

Essentials in Developing New Technologies or
Advancing Existing Technologies
1.
Articulate Technology Needs (e.g., Floating City);
2.
Identify Present and Future Expected Customers;
3.
Survey Pillar Technology Base and Match with Existing
Ones;
4.
Identify New Technology Needs, and Existing Technologies that need to be significantly improved;
5.
Prioritize Research Needs and Match with Manpower
Needs.

University Roles for New Technology
Development
They say students do not learn much in university; yet it is where a student experiences profound transformation in terms of maturity and career readiness.
1.
Base Research (or Basic Research) and Professional
Manpower;
2.
However, university is a self-surviving entity; it wishes that industry would depend on university for technology innovation, expert professional production, even patents to utilize…
3.
Within university community, each campus must compete for talents (faculty and students recruits) and resources
(funds).

My Personal Preference/Goals as a Professor
1. Educate both undergraduate and graduate students;
1.
Conduct Basic Research, in particular:
1.
Analysis methods developments – FEM, transient algorithms, etc;
2.
New modeling theory – acoustic-structure interaction models ( Today’s talk );
3.
Multiphysics simulation, system identification, etc.
2.
Conduct Engineering Analysis such as:
1.
Space rendezvous dynamics and control;
2.
Underwater vehicle dynamics;
3.
Shell structures and membranous reflectors
4.
Containment vessels health monitoring
5.
MEMS resonators and Gyroscope performance
6.
Health monitoring of structures
7.
Contact-impact problems
..
..

My Past Activities
Past Activities:
Transient analysis methods (direct time integration)
Helicopter and general aviation crashworthiness
Shell finite elements
Computational methods for fluid-structure interactions
Large space structures and control
Space construction and space rendezvous dynamics
Partitioned analysis methods for coupled-field problems
Multi-body dynamics and space assembly
Structural system identification and damage detection
Contact-impact mechanics

My Current Activities
Current Activities:
Multi-physics dynamics and computational methods
Health monitoring of structural systems
MEMS Gyroscopes for space applications
Membranous structures for solar sails and reflectors
Hilbert-Huang transform for nonlinear dynamics
Loose coupling of tightly coupled multi-physics problems via partitioned analysis procedures.

Background
in
Today’s
Talk
1.
Today’s
talk
is
considered
as
a
new
theory
 as
opposed
to
 improving
exis5ng
theories;
2.
It
was
a
test
case
in
that
I
have
consistently
advocated
that
 more
KAIST
engineering
theses
should
take
on
developing
 new
methodologies,
new
theories
and
new
modeling
 instead
of
improving
exis5ng
engineering
tools;
3.
It
has
been
carried
out
at
KAIST
during
the
past
four
years
 by
Dr.
Moonseok
Lee
as
his
PhD
thesis;
4.
I
am
hoping
that
you
would
get
a
glimpse
of
what
it
takes
to
 take
on
research
that
requires
risk
and
open‐ended
5me
 commitment.
.
.

My
Objec5ves
as
WCU‐OSE
Faculty
Member
•   

First,
work
with
students!
•   


Assist
OSE
faculty
to
promote
‘basic
research’

emphasis;
•   


By
engaging
in
the
above
two
ac5vi5es,
help
them
write
fundamental
papers
 that
will
be
cited
by
others
in
years
to
come
(out
of
many
papers,
I
am
sure).
•   


In
other
words,
I
am
intensely
academically
oriented.
But

then
beware
of

 ‘
 맑은 물엔 고기가 크게 자라지 않습니다 .’
•   



I
am
an
American
and
we
Americans
believe
in
pursuit
of
happiness!

Hence,
I
will
enjoy
doing
the
above
ac5vi5es.

Background
in
Today’s
Talk
–
Cont’d
Classifica5on
of
Fluid‐Structure
Interac5ons
•   

Waves
(e.g.,
hurricanes)
bombarding
the
 structures
•   

Liquid
Sloshing
in
Container
Compartment
•   

Intense
Pressure
Origina5ng
from
Tsunami
 and
Explosions
–
 Today’s

Topics

Waves
(e.g.,
hurricanes
&
North
Sea)
bombarding
 the
structures
(
Height:10‐25
m
and
Period:
10
‐15
 seconds,
speed
of
wave
∼ 1-5 /s )

Liquid
Sloshing
in
Container
Compartment

Today’s

Topics:
 Intense
Pressure
Origina5ng
 from
Tsunami
and/or
Explosions
(
wave
 speed
~
1450
m/s)
Also
applicable
to
Surface
Ships
and
Floa5ng
Large
Structures

Why
simula5on
and
why
not
real
experiments?
•
A
bicycle
can
be
tested
not
only
for
parts
but
the
whole
bicycle;
•   
A
car
can
be
crash‐tested,
although
expensive.
Even
for
cars,
 simula5on
using
component
test
data
saves
cost
and
expedite
 from
design
to
market
turnaround.
•   
To
test
an
airplane
for
its
crash
landing
safety?
No
way!

Too
 expensive
and
5me
consuming.
•   
How
about
satellites?

How
about
a
submarine?

How
about
a
 large
floa5ng
structures
such
as
oil/gas
drilling
plajorms?

Acous5c‐Structure
Interac5on
Problems
in
Ocean
Engineering
Sonar
Detec5on
Problem:
Send
pressure
waves
and
measure
the
scakered
(return)
 pressure.
By
analyzing
the
scakered
pressure,
one
can
iden5fy
 the
loca5on,
the
shape
and
the
speed
by
which
the
ship
or
 submarine
is
moving .
Dynamic
Response
of

Surface
and
Underwater
Ships:
Vibra5on
and
vulnerability
of
vehicles
subjected
to
intense
 pressure
waves
( Professor
Young
Shin
is
an
expert
in
this
field) .
All
future
ocean
infrasystems
must
withstand
hos5le
akacks
as
 well
as
tsunami
shock
waves.

Aren’t
There
Theories
Available
to
Model
Dynamics
of
Acous5c‐Structure
Interac5ons?
At
present,
we
use
two
separate
modeling
techniques:
 a. 
Various
acous5c‐rigid
scakering
model
for
underwater
detec5on
 b.
Acous5c‐flexible
interac5on
model
for
structural
response

Objec5ve
of
Present
Research:
Develop
one
model
that
is
applicable
both
to
 acous5c
scakering
and
flexible
structural

 dynamics
response.
Shock
Analysis

Related
Literature:
Baker and Copson(1949): My favorite theoretical text
G. Carrier(1951): Cylindrical shells excited by incident waves
Junger
and
Feit(1950s):
sound
scakering
by
thin
elas5c
shells
Mindlin
and
Bleich(1953):
Perhaps
the
first
plane
wave
approxima5on
Huang
(1969):
A
successful
solu5on
of
retarded
poten5al
for
a
sphere
Geers (1978): The seminal paper on doubly asymptotic approximation (DAA)
Felippa (1980): A systematic derivation for early-time response
Geers and Felippa (1983): Application of DAA to vibration problems
Astley et al (1998): Wave envelope elements that treats the scattering
in addition to radiation in applying retarded potential.

Two
Views
on
External
Acous5c‐Structure
Interac5ons
•
Solve
the
wave
equa5on
with
approximate
infinite
radia5on
boundary
condi5ons ;
•   

 Approximate
Kirchhoff’s
retarded
poten5al
that
properly
incorporates
the
infinite
radia5on
boundary
condi5ons.
•   

There
are,
of
course,
a
host
of
approaches
that
try
to
exploit
the
desirable
features
of
the
two
views.

Mo5va5ons
for
Present
Study
When
the
primary
interest
is
to
obtain
structural
response
arising
 from
external
acous5c‐structural
interac5ons,
exis5ng
 DAA
(Doubly
Asympto5c
Approxima5on;
Geers,
1978) 
models
seem
 adequate;
However, 
when
one
is
interested
in
the
acous5c
field,
e.g.,
for
 iden5fica5on
of
sound
sources,
exis5ng
DAAs
are
considered
 inadequate,
primarily
due
to
its
inconsistent
impulse
response
 characteris5cs.
In
addi5on,
DAAs
are
obtained
via
an
impedance
matching
 procedure
between
early‐5me
and
late‐5me
approxima5ons.
New
approxima5ons
without
resor5ng
to
impedance
matching
 should
be
at
least
intellectually
pleasing!

Mo5va5ons
for
Present
Study
‐
con5nued
For
model
determina5on
through
system
iden5fica5on,
one

 assumes

the
system
model
in
terms
of
discrete
event
equa5on

 as
Internal
dynamics:


x 
(n+1) 

=
A
x n 

+
B
u n
Measure
output:











y n 
=
C
x n 

+
D
u n
System
iden5fica5on
is
to
obtain
(A,
B,
C,
D)
with
given
input
(u n )
 and
measured
output
( 
 y n )
Kirchhoff’s
retarded
poten5al
(as
will
be
shown
shortly)
 does
not
rend
to
this
standard
system
iden5fica5on
model!
Hence,
a
high‐fidelity
ordinary
differen5al
acous5c
model

 is
needed.

(Why
spherical
waves?)
‐
 That
is
how
waves

 propagates
in
homogeneous
medium.

(adopted
in
exis5ng
models)

(via
filtering
concept)

Theore5cal
Founda5on
for
Present
Approxima5ons
Series
expansion
of
the
retarded
operator, 
 in 
 where
 has
been
responsible
for
unstable
form
unless
a
modifica5on
is
 incorporated.
Possible
stabiliza5on:
Employ
 advanced
poten5al!

The
Role
of
Advanced
Poten5al
in
Computa5onal
Context
Physically,
while
the
retarded
operator
(RO)
is
to
foresee
the
wave
 front,
the
advanced
operator
(AO)
looks
back
the
wave
front.
Hence,
computa5onally 
 RO
is
a
predictor
while
AO
is
a
backward
 interpolator,
hence
a
stable
operator.

Geometrical
Interpreta5on
of
Retarded
and
Advanced
Waves
Wave
Front,
Time
=
t
Advanced
Wave
Front,
=me
=
t
+
r/c
(
It
is
a
backward
 interpola5on.
Hence,
 generally
stable
to
 compute)
Time
(t)
Retarded
Wave
Front,
=me
=
t
–
r/c
(
It
is
a
forward
extrapola5on.
Hence,
generally
unstable
to
 compute!)

Key
Idea
for
Present
Approxima5ons

Observa5ons
on
the
Present
Basic
Approxima5on
The
fact

that

sR/c
<
1
implies
that
the
approxima5on

 is
accurate
for
late‐5me
response
due
to
the
inherent

 property
of

 the
Final
Value
Theorem
of

the
Laplace
Transform.
Observe
that























and

























are

 transient
terms,
hence
domina5ng
early‐5me
responses.
Hence,
these
terms
would
not
be
accurate
with
the

 expansion
restric5on
of

sR/c
<
1.

Modifica5ons
for
Transient
or
Early‐Time
Response
(a)
Consistency
for
Impulse
Response
compared
with
analy5cal
solu5ons;
(b)
Incorpora5on
of
classical
results
wherein
early‐5me
response
is
dominated
by
plane
waves;
The
preceding
requirements
are
met

fortuitously
if
one
approximates







in
the
following
terms 



 by
replacing
with

Impulse
Response
Consistency
Present
model
sa5sfies
the
early‐5me
consistency

 independent
of
the
choice
of
the
weigh5ng
parameter,
 χ

Determina5on
of
Weigh5ng
Parameter ,
χ
1.
Plot
the
characteris5c
roots
of
the
exact
analy5cal
solu5on
for
a
sphere
2.

Assume
χ in
the
following
form:
And
determine
the
best
fiung
constants,

Analy5cal
Pressure
Characteris5c
Root
Loci
for
a
Sphere

Determina5on
of
Weigh5ng
Parametric
Matrix ,
χ
•   

It
specializes
to
the
modal
form
of
χ
to
spherical
geometries
 n

 when
applied
•   

It
should
be
robust
with
respect
to
computa5onal
errors
for
general
geometries
A
general
matrix
form
of

 χ 


that
sa5sfies
the
above
 requirements
is
found
to
be
The
case
of

S=0 
 is
symbolically
equivalent
to
DAA2
with
curvature
Correc5on
which
is
found
to
be
prone
to
instability
for
n
=
0
mode.

Model
parameter
selec5on
•   Proposed

modal
equa=ons
and
DAA
correc=on
2
with
curvature

 n = 0 n > 0
%
$
Proposed model curvature DAA2
[ s + 1] 2 p
0
= [ + 1] u
0
[ + 1] p
0
= s u
0
[ s 2
+ + ) + ( + 1)] p n
= [ + ] n
()*+,"-"./")'0-)1'.2#,#&"-",3456.78#9:."$"&"-*;
!
!
<
=>
!
<
?
@
!
%
!
!
<
=>
!
<
?
@
!
%A@?
<
B
!
<
<
#
!
"
!
!
1=C.
1=<.
1=@.
1=C.
1=4.
1=:.
1=6.
!
#
!
$
!
%
!
!
" !
#
!"#$
$ % &

Comparison
of
Analy5cal
and
Present
Principal
Roots
with
χ 1 n
=
n,
χ 1
0
=
1

Computer
Implementa5on
of
Interac5on
Problems

Problems
that
can
be
treated
by
the
present
models

Governing
Interac5on
Equa5ons

Applica5on
Benchmark
Test:
elas5c
sphere
subjected
to
Incident
acous5c
excita5ons

simula5on
Numerical
Simula5on
•   Transient
responses
of
a
submerged
spherical
shell
 excited
by
cosine‐type
impulse
pressure
–   A
spherical
shell
surrounded
with
fluid
medium.
–   In
water
medium
–   h/a=0.01,
ρ s
/ρ=7.7,
c s
/c=3.7
p
I
= − cos θδ ( )
O
θ a r v w
Q
R
PQ
P
I e r u s s e r
P t n e i d c n
4
3.5
3
2.5
2
1.5
1
P
I
=7 !
-1/2
Exp[7
2
(t-0.5)]
0.5
0
0 0.5
E , ρ s
, v h 1 1.5
2 2.5
Tc/a
3 3.5
4 4.5
5

simula5on

Conclusions
   

 A
stable
approximate
model
for
external
acous5c
and
structural
interac5on
problems
has
been
derived
by
employing
a
combina5on
of
retarded
and
advanced
poten5als.
   

The
maximum
order
of
“regular”
approxima5on
is
found
to
be
two.
   


The
present
approximate
model
is
consistent
with
respect
to
impulse
response,
important
for
inverse
iden5fica5on
as
the
Frequency
Response
Func5ons
are
in
fact
the
5me‐domain
counterpart
of
impulse
response
func5ons.
   


It
remains
to
assess
the
present
approxima5ons
as
applied
to
more
realis5c
problems.