Energy Boundary Element Method for Computing High Frequency ...
Energy Boundary Element Method for Computing High Frequency ...
Energy Boundary Element Method for Computing High Frequency ...
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<strong>Energy</strong> <strong>Boundary</strong> <strong>Element</strong> <strong>Method</strong> <strong>for</strong><br />
<strong>Computing</strong> <strong>High</strong> <strong>Frequency</strong> Acoustic Fields<br />
around Vehicle Structures<br />
Nick Vlahopoulos<br />
Professor<br />
NA&ME Dept; ME Dept.<br />
University of Michigan<br />
Koen De Langhe<br />
Product Line Manager Noise & Vibration<br />
CAE Division<br />
LMS International
Presentation Outline<br />
•Development of EBEM<br />
•Technical background<br />
•Validation cases (automotive & aircraft)<br />
•Airborne noise analysis combining EBEM with EFEM<br />
•Integration with Virtual Lab<br />
•Conclusions
Development of EBEM<br />
Originally EBEM was developed <strong>for</strong> propagating acoustic<br />
energy in the field from EFEM acoustic intensity results<br />
EFEM model<br />
Structural model<br />
External/Internal fluid<br />
EFEM results:<br />
Structural vibration,<br />
Interior acoustic energy<br />
Radiated acoustic intensity<br />
Intensity<br />
EBEM results (external medium):<br />
Acoustic energy<br />
Acoustic intensity
EBEM and Airborne Noise Analysis<br />
External SPL is required <strong>for</strong> an airborne noise analysis<br />
Measurements are used <strong>for</strong> defining external acoustic field<br />
EBEM computes the external acoustic field – loading<br />
<strong>for</strong> airborne simulations
Technical Background<br />
Governing Integral Equations:<br />
e~<br />
Y<br />
2<br />
⎛ ρ k ρ<br />
∫ ( )<br />
⎟ ⎞<br />
= σ P<br />
⎜ + dS<br />
S 2 4 2 2<br />
⎝ 64π<br />
r 32π<br />
r ⎠<br />
2<br />
~ k ρc<br />
I Y<br />
= ∫ σ<br />
S<br />
( P)<br />
ErdS<br />
2 2<br />
32π<br />
r<br />
Numerical Implementation:<br />
n<br />
e ~ ⎡<br />
⎤<br />
Y<br />
= ∑ σ<br />
j<br />
⎢⎣<br />
∫ G(<br />
, Y ) dS<br />
S j<br />
⎥⎦<br />
j=<br />
1<br />
ξ IY<br />
= ∑ σ<br />
j∫<br />
~<br />
n<br />
j = 1<br />
⎡<br />
⎢⎣<br />
S<br />
j<br />
H(<br />
ξ,<br />
Y)<br />
dS<br />
⎤<br />
⎥⎦<br />
ρ<br />
G ( ξ Y)<br />
+<br />
2 4<br />
64π<br />
r<br />
, 2<br />
k<br />
2<br />
( ξ,<br />
Y) 32π<br />
r ( ξ,<br />
Y)<br />
2<br />
ρ<br />
= H ( ξ Y )<br />
2<br />
k ρc<br />
2<br />
32π<br />
r<br />
, =<br />
2<br />
E<br />
r<br />
( ξ,<br />
Y) [ K ]{} σ = { P}<br />
JSV 278 (2004) pp. 413 - 436
Compared to traditional BEM…<br />
Conventional BEM<br />
~550,000 elements up to<br />
8,000Hz<br />
Treatment of irregular<br />
frequencies<br />
EBEM<br />
~2,200 elements with no upper<br />
frequency limit<br />
No irregular frequencies<br />
No phase in<strong>for</strong>mation
Compared to SEA…<br />
SEA uses artificial reverberant<br />
acoustic subsystems <strong>for</strong><br />
modeling an unbound external<br />
acoustic field<br />
Coupling loss factors between<br />
external acoustic subsystems<br />
EBEM is mesh based
Validation Case Studies<br />
Windshield<br />
Roof AB<br />
Roof BC<br />
Glass AB<br />
Glass BC<br />
Door AB<br />
Door BC<br />
Source 1<br />
Source 2<br />
Source 5<br />
Source 3<br />
Source 4<br />
Truck: ~4,600 elements; 6min <strong>for</strong> the entire frequency range<br />
Sedan: ~2,100 elements; 1.5 min <strong>for</strong> the entire frequency range<br />
Aircraft: ~1,900 elements; 1 min <strong>for</strong> all frequencies
Windshield<br />
Roof<br />
Automotive Validation<br />
Glass<br />
Door<br />
Source 1<br />
Source 2<br />
Source 5<br />
Source 3<br />
Source 4<br />
Locations of sources<br />
and measurement locations<br />
Floor
Windshield<br />
Roof<br />
Glass<br />
Door<br />
Source 1<br />
Source 2<br />
Source 5<br />
Source 3<br />
Source 4
Windshield<br />
Roof<br />
Glass<br />
Door<br />
Source 1<br />
Source 2<br />
Source 5<br />
Source 3<br />
Source 4
Experimental Set – Up from NASA/TM-2001-210840<br />
Airframe model, microphones, and source<br />
Impinging jet source
Validation<br />
~300 ft<br />
Insertion loss calculations<br />
Acoustic pressure on field point<br />
mesh in free field and in the<br />
presence of the aircraft;<br />
The difference between the two<br />
is the IL
Test<br />
EBEM<br />
200Hz<br />
1,600Hz
EBEM – EFEM Case Study: Internal noise prediction in NASA<br />
test-bed cylinder due to an external acoustic source
EFEM validation <strong>for</strong> NASA Aluminum Test-Bed Cylinder
Magnitude of difference between test and analysis averaged over all frequencies<br />
Third octave bands from 315Hz to 6,300Hz<br />
∑ dB(<br />
e)<br />
test<br />
− dB(<br />
e)<br />
N<br />
N<br />
EFEA
EBEM computes the external acoustic loading<br />
on the cylinder – provides the excitation <strong>for</strong> EFEM<br />
Acoustic energy density loading on the source side
EFEM - models the structure and the interior acoustic<br />
space<br />
Source side<br />
Side opposite to the source<br />
Distribution of vibrational energy density on the shell<br />
of the cylinder
EFEM - models the structure and the interior acoustic<br />
space<br />
Source side<br />
Internal acoustic SPL<br />
Side opposite to<br />
the source<br />
Results in the interior of the cylinder – solid elements<br />
are used to model the air
EBEM toolbox<br />
Integration with VL
There are three buttons in the toolbox;<br />
pre-processing, analysis, post-processing<br />
Pre-processing panel;<br />
Tabs <strong>for</strong> each required step
Summary<br />
•EBEM is a high frequency acoustic prediction tool<br />
•Efficient computation of the acoustic loading from<br />
air-borne sources<br />
•Mesh based – utilization of conventional pre and<br />
post-processors and integration with VL<br />
•Complements conventional BEM at high frequencies<br />
•Provides the acoustic loading <strong>for</strong> airborne SEA and<br />
EFEM computations
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