acoustic simulation with fem

8/10/2019 Acoustic Simulation With FEM

1/47

Acoustic Simulations with FEM

1. FE Model

2. Modal Analysis

3. Response Analysis

( , )P x t

PPhysics:

HAW/M+P, Ihlenburg, CompA Acoustics with FEM 1

The ear perceives local oscillations of pressure in the acoustic medium.

t

Mathematics:

Pressure is a scalarfunction scalarwave equation

Helmholtz equation

time-harmonic

2 0p k p + =


2/47

1. FE Model

The cavity volume is partitioned into 3-D elements (Hexa, Tetra, etc.).


Each node is associated with one DOF (pressure).

( )ip x

The acoustic element is actually a simplified version of the solid element.

( ), ,p x y z


3/47

$TITLE = FLUID WITH ACOUSTIC SOURCE 1$SUBTITLE= 2

$LABEL = 3

$DISPLACEMENTS 4

$REAL-IMAGINARY OUTPUT 5

$SUBCASE ID = 1 6

$FREQUENCY = 2.0000000E+01 7

10224 S -1.427161E-11 0.000000E+00 0.000000E+00 8-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 9

-CONT- 3.049356E-15 0.000000E+00 0.000000E+00 10

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 11

Output of acoustic FRF run to pch file

Re, Im


( ),ip x

Practical conclusion: do not animate results as displacements!


4/47

Solid Fluid2p n

2t

3t

1t

2p

n1p n


x xy xz

y y yz

xz yz z

0 00 0

0 0

PP

P

The fluid element is a solid element representing the hydrostatic stress state.

The nodal unknowns are the pressure values p(x). Since the pressure satisfies asecond-order differential equation (wave or Helmholtz equation), linear interpolationcan be used inside the elements.


5/47

Volume Elements in MSC/ Nastran

CHEXA EID PID G1 G2 G6


Linear Interpolation 8 corner nodes. .

Quadratic interpolation: + 12 edge nodes.


6/47

Fluid Elements in Nastran:

Solid elements are used for fluid modeling.

The elements are marked as PFLUID in the PSOLID card.

Additional entry -1 to the GRID cards.

GRID 10562 937.500 187.500 62.5000 -1

CHEXA 10231 3 10001 10219 10399 10222 10227 10401+

+ 1 10531 10404

PSOLID 3 3 PFLUID


$LUFT

MAT10 3 1.189-12 3.43+05

The nodal unknowns are the pressure values P(x,t).

The .pch output for the fluid nodes is the complex-valued amplitude p(x).

1 20037 G 1.270340E-04 0.000000E+00 0.000000E+00 2

1 -CONT- 0.000000E+00 0.000000E+00 0.000000E+00 2

1 -CONT- 1.962794E-04 0.000000E+00 0.000000E+00 2

1 -CONT- 0.000000E+00 0.000000E+00 0.000000E+00 2

Real

Imag


7/47

PSOLID PID MID CORDM IN . FCTN

PSOLID Card in MSC/Nastran



8/47


9/47

The modal equation (1) is a generalized eigenproblem with

Specialized EVP:

0 =Ax Bx

=2

Eigenvalue Problems (EVP)

Generalized EVP:

0 =Ax x=B I

Solution: , , 1,i N =x N n


[ ]1 2, , , n = x x xThe eigenvectors are collected column-wise in a matrix:

of dimension . The modes are mass-normalized, i.e.

It follows that

n N

The eigenfrequencies are printed out in a table (see next slide).

Ti j ij=x Mx

2T

i i iK =x x


10/47

E I G E N V A L U E A N A L Y S I S S U M M A R Y (READ MODULE FOR FLUID)

BLOCK SIZE USED ...................... 7

NUMBER OF DECOMPOSITIONS ............. 1

NUMBER OF ROOTS FOUND ................ 17

NUMBER OF SOLVES REQUIRED ............ 14

Eigenfrequencies in .f06 file (Nastran)


R E A L E I G E N V A L U E S F O R F L U I D

MODE EIGENVALUE RADIANS CYCLES NO. GENERALIZED GENERALIZED

MASS STIFFNESS

` 1 -6.824732E-06 2.612419E-03 4.157794E-04 1.000000E+00 -6.824732E-06

2 1.164884E+06 1.079298E+03 1.717756E+02 1.000000E+00 1.164884E+06

3 4.704586E+06 2.169006E+03 3.452080E+02 1.000000E+00 4.704586E+06

4 1.075588E+07 3.279615E+03 5.219670E+02 1.000000E+00 1.075588E+07

5 1.955165E+07 4.421725E+03 7.037393E+02 1.000000E+00 1.955165E+07


11/47

Mode shapes (eigenvectors)

Box: Passg. Car cabin:



12/47


13/47

Damping effects in cavities

Sound energy of is lost (within or from a bounded cavity) by:

a) volume damping (internal friction within the cavity volume)

b) interface damping (friction with boundary interfaces, particularly porous materials)

c) radiation damping and transmission (sound is leaving the cavity)

b)


a) c)


14/47

Volume (Material) Damping

2(1 i ) + = K M p f

FEM:

Loss factor


Nastran: PARAM, GFL


15/47

Consider the reduced undamped equation

and add a modal damping matrix to obtain the

system for damped vibrations in the form

Modal Damping (Fluid)

2 2 2diag( )T T i = = K M y I y f

diag(2 )i i

It is usually not easy to determine the modal damping factors . In practice one often usesfre uenc -constant modal dam in arameters.

2 2diag ( ) i diag (2 )i i i = I y f

i


Constant (over the volume) material damping is

numerically equivalent to constant (over the range ofeigenfrequencies) modal damping with the relation

Relation to material damping: Equations (1) and (2) can be compared formally by setting

Modal transform then leads to the diagonal damping matrix

2i

i i =K C

2d ia g ( ).i

Nastran: TAMDMP1


16/47

Interface Damping

00 0' ,

Zp ik p Z c= =

The normal impedanceZn=pn/vn of a plane wave can be written as


n

Nastran:

generate fluid skin (preprocessor) QUAD, CTRIA CAABSF (editor) introduce material data in PAABSF card


17/47

Resistance

(Damping)

,

i

n n

n n n

p Z v

Z R X

=

= +

Reactance

(Mass,Stiffness)

R


( )nX

n

const.nR

const.nX


18/47

$ rho*c for rho=1e-12, c=6e4, Z=20rho*c

INCLUDE 'cavity_skin.bdf'

$$234567|1234567|1234567|1234567|1234567|1234567|1234567|1234567|1234567|

$_______2_______3_______4_______5_______6______7________8_______9_______

$ PID TZREID TZIMID S A B K RHOC

PAABSF 10 120.e-8 6.e-8

Example



19/47

Zn= rn+ ixnMeasured Impedances (1/2)


F. Fahy, Foundations of Eng. Acoustics, S. 171ff


20/47

Physical Mathematical FEM

Rigid wall----

Summary: boundary conditions for the Helmholtz equation

0p

n

=

reflecting


Absorption CAABSF

Free surface SPC

0

n

ik pn Z

=

0p =

re ec ng o a mos

nonreflecting

reflecting


21/47

SOL 108

CEND

TITLE= FLUID WITH ACOUSTIC SOURCE, DIRECT FREQUENCY RESPONSE

FREQ=200

DLOAD = 1000

$ Pressure in all nodes are output

DISP(PLOT) = ALL

$

BEGIN BULK

$ DAMPING

PARAM, GFL, 0.05

$ Source in Node 1000

Frequency Response to Acoustic Source, Direct Solution


$ SID EXCITEID DELAY DPHASE TP RHO B

ACSRCE 1000 101 1001 1. 1.$2345678_2345678_2345678_2345678_2345678_2345678_2345678_2345678

TABLED4 1001 0.0 1.0 0.0 1.E6

0.0 0.0 1.0 0.0 ENDT

$ FRQUENCY RANGE

FREQ 200 1.e3 2.e3

INCLUDE 'box_fluid.bdf'

$PARAM,COUPMASS,1

$ directs output to .op2 file

PARAM, POST, -1

$

ENDDATA

for plots of operational shapes


22/47

Frequency Response to Acoustic Source, Modal Solution

$ COPIED AND ADAPTED FROM REFERENCE MANUAL

SOL 111

CEND

TITLE= FLUID WITH ACOUSTIC SOURCE

FREQ=200

METHOD(FLUID)=50

DLOAD = 1000

$ Pressure output of selected MP to punch file

SET 123=10224,10235,10243,10251

DISP(SORT1,PUNCH) = 123

$

BEGIN BULK

PARAM, GFL, 0.05

for graphs of frequency response inselected nodes


$ SID EXCITEID DELAY DPHASE TP RHO B

ACSRCE 1000 101 1001 1. 1.TABLED4 1001 0.0 1.0 0.0 1.E6

0.0 0.0 1.0 0.0 ENDT

$ FRQUENCY RANGE

$2345678_2345678_2345678_2345678_2345678_2345678_2345678_2345678_

FREQ1 200 20.0 10.0 8

EIGRL 50 1.2e3

INCLUDE 'box_fluid.bdf'$

PARAM,COUPMASS,1

$

ENDDATA


23/47

09:18:41 Analysis started.

09:18:41 Finite element model generation started.

09:18:41 Finite element model generated 425 degrees of freedom.

09:18:41 Finite element model generation successfully completed.09:18:41 Application of Loads and Boundary Conditions to the finite element model started.

09:18:41 Application of Loads and Boundary Conditions to the finite element model

successfully completed.

09:18:41 Solution of the system equations for frequency response started.

09:18:41 Solution of the system equations for frequency response successfully completed.

09:18:41 Frequency response analysis completed.

09:18:41 29 records read from JID file

"c:/home/lehre/compa/nastran/box/fluid_s111/box_fluid_s108.dat"09:18:41 A total of 969 records were read from 2 files.

09:18:41 NSEXIT: EXIT(0)

09:18:41 Analysis complete 0

Log, Direct solution


11:17:26 Analysis started.11:17:28 Finite element model generation started.

11:17:29 Finite element model generated 425 degrees of freedom.

11:17:29 Finite element model generation successfully completed.

11:17:29 Application of Loads and Boundary Conditions to the finite element model started.

11:17:29 Application of Loads and Boundary Conditions to the finite element model successfully

completed.

11:17:29 Solution of the system equations for normal modes started.

11:17:31 Solution of the system equations for normal modes successfully completed.11:17:32 Solution of the system equations for frequency response started.

11:17:32 Solution of the system equations for frequency response successfully completed.

11:17:33 Frequency response analysis completed.

11:17:33 27 records read from JID file

"c:/home/lehre/compa/nastran/box/fluid_acsrce/box_fluid_s111_pch.dat"

11:17:33 A total of 967 records were read from 2 files.

11:17:33 NSEXIT: EXIT(0)

11:17:33 Analysis complete 0

Log, Modal solution


24/47

$TITLE = FLUID WITH ACOUSTIC SOURCE 1$SUBTITLE= 2

$LABEL = 3

$DISPLACEMENTS 4


$SUBCASE ID = 1 6

$FREQUENCY = 2.0000000E+01 7

10224 S -1.427161E-11 0.000000E+00 0.000000E+00 8

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 9

-CONT- 3.049356E-15 0.000000E+00 0.000000E+00 10

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 11

10235 S -1.423625E-11 0.000000E+00 0.000000E+00 12

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 13

-CONT- 1.270832E-15 0.000000E+00 0.000000E+00 14

Head of punch file


-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 15

10243 S -1.415010E-11 0.000000E+00 0.000000E+00 16-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 17

-CONT- -3.049356E-15 0.000000E+00 0.000000E+00 18

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 19

10251 S -1.407545E-11 0.000000E+00 0.000000E+00 20

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 21

-CONT- -6.788064E-15 0.000000E+00 0.000000E+00 22

-CONT- 0.000000E+00 0.000000E+00 0.000000E+00 23$TITLE = FLUID WITH ACOUSTIC SOURCE 24

$SUBTITLE= 25

$LABEL = 26

$DISPLACEMENTS 27


$SUBCASE ID = 1 29

$FREQUENCY = 3.0000000E+01 30


25/47

Industrial Case Studies, Verification and Validation of FEM

alternative models or methods of

compuation.

comparison to physical experiment

Do we solve the problem right Do we solve the right problem

J. Tinsley Oden

= check computational results by


Verification

Fluid Modes (with A. Mller, Audi AG)

Validation

Fluid Modes (with S. Wegner, A. Kropp, R.

Stryczek, BMW)

Radiation of Sound (cooperation with BMW,Dept. EA)


26/47

Influence of mesh quality on eigenfrequencies of fluid cavity


Manually generated mesh


27/47

Manual Mesh, high quality


!"ID #$%&'

C(E)* $+&-

C.E."* -#&


28/47

Automatic mesh generator, fine mesh


!"ID #/-

C(E)* %'$0&

C.E."* %%#+/

1uerschnitt


29/47

Automatic mesh generator, coarse mesh


!"ID -&%'

C(E)* '&-

C.E."* '&'%1uerschnitt


30/47

Results of modal analysis

Mode

Manual Automatic

Division 13

Automatic,

Division 20

1 79.088 79.441 79.130

2 111.468 112.310 111.553

3 126.683 127.626 126.838

4 138.213 139.105 138.828

Fluid Mesh


5 146.984 147.717 147.287

6 174.515 175.425 174.774

7 179.815 180.877 180.150

8 189.041 189.921 189.218

9 195.605 196.792 196.107

10 223.470 224.691 224.293


31/47

Validation

Fluid Modes


Coupled Response of an automotive body to harmonicexcitation of hatch cover (constant pressure on whole area)


32/47

Excitation

Setup


Experiment:loudspeaker, pink noiseFEM:harmonic excitation of hatch door

Microphone Positions


33/47

Methodical question

Which interior parts should be in themodel?



34/47

Pipe Eigenmodes

Compare: First three Eigenmodes of Car



35/47

Var 1: Vollausstattung( mit / ohne Luftspalt bei Hutablage)

Var 2: ohne Hutablage

f1=38.4 / 76 Hz f1=52.0 Hz

Variants


Var 3: ohne Hutablage, ohne Rcksitz Var 4: ohne Hutablage, ohne Sitze

f1=64.4 Hz f1=70.1 Hz

Eff t


36/47

Effects

pipe

Helmholtz

resonator



37/47

Modes for model with four seats, no trunk cover

52Hzf =


96Hzf =

Details


38/47

Details


Variant: four seats no hatrack


39/47

Rechnung

ung

Variant: four seats, no hatrack

Pressure level at microphone positions

Computation


Messung

gute

berseinstimm

Measurement

Variant: hatrack as sound barrier in cabin model


40/47

Rechnung

Variant: hatrack as sound barrier in cabin model

e ung


Messung

schlechter

berseins

tim

Validation


41/47

Validation

Radiation of engine vibrations

Setup

Microphone positions

open top

microphones


Concrete socket

Reflecting walls

Engine block

35cm

FE Model


42/47

FE Model

Fluid Cavity with absorbingBC above reflecting walls

Structural Model

Fluid model: detail

Simulation: excitation ofstructure, full structure-fluid

compling, evaluation atmicrophone positions in fluid


Adaptive Approach


43/47

Parameter 1: Size of fluid domain

a = 57.5cm

Adaptive Approach


.

cm

Parameter 2: Order of radiation condition (1,2)

Adaptive Approach: fluid domains


44/47

h = 39.1 cm

h = 57.5 cm

h = 77.9cm

dapt e pp oac u d do a s


Computational Result: Frequency Response at Fluid


45/47

Computational Result: Frequency Response at FluidMP

HAW/M+P, Ihlenburg, CompA Acoustics with FEM 4545F. Ihlenburg/

La CoruniaVerification and Validation

Structural modes

Computational Result: Fluid Operational Shape @ 724Hz


46/47

p p p

HAW/M+P, Ihlenburg, CompA Acoustics with FEM 4646F. Ihlenburg/

La CoruniaVerification and Validation


47/47

acoustic simulation with fem

Documents