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8/11/2019 Frequency Domain Analysis in LS-DYNA_Yun Huang_Jan-2013
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LS-DYNA
Frequency Domain Analysis
in LS-DYNA®
Yun Huang, Zhe Cui
Livermore Software Technology Corporation
16 January, 2013
Oasys LS-DYNA UK Users’ Meeting, Solihull
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LS-DYNA
2
Outline
1. Introduction
2. Frequency response functions
3. Steady state dynamics
4. Random vibration and fatigue5. Response spectrum analysis
6. Acoustic analysis by BEM and FEM
7. Conclusion and future developments
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LS-DYNA
INTRODUCTION
1.
3
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LS-DYNA
4
*FREQUENCY_DOMAIN_FRF
*FREQUENCY_DOMAIN_SSD
*FREQUENCY_DOMAIN_RANDOM_VIBRATION_ {OPTION}
*FREQUENCY_DOMAIN_ACOUSTIC_BEM_ {OPTION}
*FREQUENCY_DOMAIN_ACOUSTIC_FEM*FREQUENCY_DOMAIN_RESPONSE_SPECTRUM
Frequency Domain Features in LS-DYNA
New keywo rds for frequency domain analysis
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LS-DYNA
5
Frequency domain v s. t ime domain
A time-domain graph shows how a signal changes over time
A frequency-domain graph shows the distribution of the energy
(magnitude, etc.) of a signal over a range of frequencies
Time domain analysis
Transient analysis (penetration)
Impact (crash simulation) Large deformation (fracture)
Non-linearity (contact)
Frequency domain analysis
Harmonic (steady state vibration)
Resonance Linear dynamics
Long history (fatigue testing)
Non-deterministic load (random analysis)
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LS-DYNA
6
Time domain excitation Frequency domain excitation
Fourier Transform
A given function or signal can be converted between the time and frequency
domains with a pair of mathematical operators called a transform.
dt et h H t i )()(
d e H t h t i)(2
1)(
Inverse Fourier
Transform
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LS-DYNA
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Vehicle NVH• Interior noise
• Exterior radiated noise
• Vibration
Vehicle Durability
• Cumulative damage ratio• Expected life (mileage)
Aircraft / rocket / spacecraft vibro-acoustics
Durability analysis of machines and electronic devices
Acoustic design of athletic products
Civil Engineering• Architectural acoustics (auditorium, concert hall)
• Earthquake resistance
Off-shore platforms, wind turbine, etc.• Random vibration
• Random fatigue
App l icat ions o f the frequency domain features
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LS-DYNA
8
App l icat ion of LS-DYNA in automot ive industry
In automotive, one model for crash, durability, NVHshared and maintained across analysis groups
Manufacturing simulation results from LS-DYNA
used in crash, durability, and NVH modeling.
Crashworthiness
Occupant Safety
NVH
Durability
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LS-DYNA
9
New Databases in Frequency Domain
Keyword *DATABASE_FREQUENCY_BINARY _{OPTION}
Database lspcode used for
D3SSD 21 Steady state dynamics
D3SPCM 22 Response spectrum analysis
D3PSD 23 Random vibration
D3RMS 24 Random vibration
D3FTG 25 Random fatigue
D3ACS 26 FEM acoustics
ASCII databases
FRF: frf_amplitude, frf_angle, frf_real, frf_imag
BEM acoustics: Press_Pa, Press_dB, bepres, fringe_*,
panel_contribution_NID,
SSD: elout_ssd, nodout_ssd, …
BINARY databases
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LS-DYNA
FREQUENCY RESPONSE FUNCTIONS
2
10
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LS-DYNA
o The concept of Frequency Response Function is the foundation of modern
experimental system analysis and experimental modal analysis
o Keyword *FREQUENCY_DOMAIN_FRF
o Express structural response due to unit load as a function of frequency
o Shows the property of the structure system
o Is a complex function, with real and imaginary components. They mayalso be represented in terms of magnitude and phase angle
o Result files: frf_amplitude, frf_angle
o Support efficient restart
11
Transfer functionH(ω)
Input force
F(ω)
Displacement response
X(ω)
Introduction: FRF
ωFωHωX
ωF
ωXωH
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LS-DYNA
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Accelerance, Inertance Acceleration
Force
Effective MassForce
Acceleration
Mobility VelocityForce
ImpedanceForce
Velocity
Dynamic Compliance,
Admittance, Receptance
Displacement
Force
Dynamic StiffnessForce
Displacement
FRF formulat ions
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LS-DYNA
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Point A
Point B
Mode Damping ratio (0.01)
1 0.450
2 0.713
3 0.386
4 0.328
5 0.3406 0.624
7 0.072
8 0.083
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LS-DYNA
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Example: nodal force/resul tant force
Left end of the beam is fixed and subjected
to z-directional unit acceleration
Nodal force and resultant force FRF at the
left end can be obtained
Resultant force FRF
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LS-DYNA
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Nodal force applied and
displacement measuredExample: FRF for a tr immed BIW
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LS-DYNA
STEADY STATE DYNAMICS
3
17
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LS-DYNA
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Harmonic excitation is often encountered in engineering systems. It is
commonly produced by the unbalance in rotating machinery.
The load may also come from periodical load, e.g. in fatigue test.
The excitation may also come from uneven base, e.g. the force on tires
running on a zig-zag road.
May be called as o Harmonic vibration
o Steady state vibration
o Steady state dynamics
Keyword *FREQUENCY_DOMAIN_SSD
Binary plot file d3ssd
)(sin)( 0 t F t F
Background
Introduction: SSD
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LS-DYNA
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Example: a rectangular plate under pressure
X-Stress
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LS-DYNA
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Enforced Motion
Relat ive disp lacement method
o base acceleration loading is applied through
inertial force.
o total displacement (velocity, acceleration) is
obtained by adding the relative displacement
(velocity, acceleration) to the base
displacement (velocity, acceleration).
baserelative
baserelative
baserelative
uuu
uuu
uuu
Large mass method
o a very large mass mL, which is usually 105-107
times of the mass of the entire structure, is
attached to the nodes under excitation
o a very large nodal force pL is applied to the
excitation dof to produce the desired enforced
motion. um p
umi p
um p
L L
L L
L L
2
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LS-DYNA
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o the rectangular plate is excited by z -
direction acceleration at one end
o
steady state response at the other endis desired
o the excitation points are fixed inloading dof
o the resulted response is added
with base motion to get total
response
o a large mass with 106 times the originalmass is added to excitation points using
keyword *element_mass_node_set
o to produce desired acceleration, nodal
force is applied to the nodes in loading dof
o
the excitation points are free in loading dof
Relat ive disp . method Large mass method
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LS-DYNA
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Example: auto model subjected to base acl.
Modal information
Number of nodes: 290k
Number of shells: 532k
Number of solids: 3k
Base acceleration spectrum is applied to
shaker table. 500 modes up to 211 Hz are
used in the simulation. The response is
computed up to 100 Hz.
Point A Point B
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LS-DYNA
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Freq = 15 Hz Freq =25 Hz
Freq = 35 Hz
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LS-DYNA
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o The loading on a structure is not known in a definite sense
oMany vibration environments are not related to a specific driving frequency
(may have input from multiple sources)
oProvide input data for random fatigue and durability analysis
oExamples:
Fatigue
Wind-turbine
Air flow over a wing or past a car body
Acoustic input from jet engine exhaust
Earthquake ground motion Wheels running over a rough road
Ocean wave loads on offshore platforms
Freq (Hz)
A c c e l e r a t i o n P S D
( g ^ 2 / H z )
Freq (Hz)
S P L ( d B )
Loading: PSD or SPL
Why we need random vibration analysis?
2,
2
df f
df f
Introduction: Random Vibration
Based on Boeing’s N -FEARA package
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LS-DYNA
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Card 5 1 2 3 4 5 6 7 8
Variable SID STYPE DOF LDPSD LDVEL LDFLW LDSPN CID
Type I I I I I I I I
Default
Keyword
*FREQUENCY_DOMAIN_RANDOM_VIBRATION
The multiple excitations on structure can be
• uncorrelated
• partially correlated
• fully correlated
(cross PSD function needed)
When SID and STYPE are both < 0, they give the IDs of correlated
excitations
Correlat ion of m ult ip le exci tat ions
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LS-DYNA
The model is a simple pipe with 83700 elements and 105480 nodes. It is subjected to base
acceleration PSD 1) in x, y and z-directions uncorrelated; 2) in x, y and z-directions correlated.
28
RMS of Von Mises stress(the pipe is subject to x, y, z excitations, uncorrelated)
Example: pipe under base acceleration
Model provided by Parker Hannifin Corp.
ANSYS LS-DYNA
Freq
(Hz)
Acceleration
psd (g^2/Hz)
5 0.01
40 0.01
100 0.04
500 0.041000 0.0065
2000 0.001
Max Von Mises RMS stress (MPa)
ANSYS LS-DYNA
99.4 100.7
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LS-DYNA
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RMS of Von Mises stress(the pipe is subject to x, y, z excitations, correlated)
ANSYS LS-DYNA
Max Von Mises RMS stress (MPa)
ANSYS LS-DYNA
140.3 142.4
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LS-DYNA
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The tube was fixed to the shaker tables using
aluminum blocks which surrounded the tube
and were tightened using screws.
Shaker table A Shaker table B
CH 6
CH 3 CH 7 CH 5CH 1
x
y
z
CH 1
Tube thickness = 3.3 mm
Example: shaker table
Cou rtesy of Rafael, Israel.
Base accelerat ion PSD load
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LS-DYNA
31
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LS-DYNA
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GRMS=1.63 g^2/Hz
Hz g^2/Hz
10 0.001
20 0.003
40 0.003
80 0.02
120 0.02
200 0.0015
500 0.0015
Input PSD
A cluster server is analyzed
by LS-DYNA to understandthe location of vibration
damage under standard
random vibration condition.
Example: cluster server
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LS-DYNA
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1σ 3σ
U (mm) 0.78 2.34
Sv-m (MPa) 41.2 123.6
D i s p l a c e m e n t
S t r e s s
It is found that the 3
Von-Mises stress is less
than the yield stress of
the material (176 Mpa).
Maximum values
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LS-DYNA
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Nodes: 800k
Elements: 660k
Modes: 1000
Model courtesy of Predict ive Engineering
MPP Random Vibration Analysis
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LS-DYNA
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• Keyword *FREQUENCY_DOMAIN_RANDOM_VIBRATION_FATIGUE
• Calculate fatigue life of structures under random vibration• Based on S-N fatigue curve
• Based on probability distribution & Miner’s Rule of Cumulative DamageRatio
• Schemes:
Steinberg’s Three-band technique considering the number of stress cyclesat the 1 , 2 , and 3 levels.
Dirlik method based on the 4 Moments of PSD.
Narrow band method
Wirsching method
…
Introduction: Random Fatigue
i i
i N
n R
PDF( probability density function)
Typical SN (or Wöhler) curve
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LS-DYNA
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S-N fatigue curve definition
• By *define_curve
• By equation
aS N m
)log()log( N baS
SNLIMT Fatigue life for stress lower than the lowest stress on S-N curve.
EQ.0: use the life at the last point on S-N curve
EQ.1: extrapolation from the last two points on S-N curve
EQ.2: infinity.
• Fatigue life of stress below fatigue threshold
Source of information: http://www.efunda.com
N: number of cycles for fatigue failure
S: stress
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LS-DYNA
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Steinberg’s Three Band Technique
Standard Deviation Percentage of Occurrence Number of cycles for failure
1σ stress 68.3% N1
2σ stress 27.1% N2
3σ stress 4.33% N3
3
3
2
2
1
1][ N n
N n
N n D E
0433.0)0(
271.0)0(
683.0)0(
3
2
1
T E n
T E n
T E n E(0): Zero-crossing frequency with
positive slope
Reference
Steinberg, D.S., Vibration Analysis for Electronic Equipment (2nd edition), John Wiley & Sons, New
York, 1988.
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LS-DYNA
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Time of exposure: 4 hours
Frequency (Hz)
P S D (
g 2 / H z
)
Z-acceleration PSD
PSD = 2 g2/Hz
100.0 2000.0
Example: Aluminum bracket
0
5
10
15
20
25
30
35
40
45
50
1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
No. of cycles
S t r e s s ( K s i )
S-N fatigue curve
Nodes constrained to
shaker table
Aluminum 2014 T6
= 2800 Kg/m3
E = 72,400 MPa
= 0.33
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LS-DYNA
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Accumulative damage ratio(by Steinberg’s method)
RMS of Von-Mises stress (unit: GPa)
(given in d3ftg) (given in d3rms)
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LS-DYNA
40Model cou rtesy of CIMES France
Aluminum alloy 5754
= 2700 Kg/m3
E = 70,000 MPa
= 0.33
Base acceleration is applied at the edge of the hole
Acceleration PSD(exposure time: 1800 seconds)
Example: beam with predefined notch
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LS-DYNA
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RMS Sx = 35.0 MPa at critical point
Analysis method Expected life Damage ratio
Experiment 7mn 25s -
Steinberg 4mn 10s 7.19
Dirlik 5mn 25s 5.54
Narrow Band 2mn 05s 14.41Wirsching 5mn 45s 5.08
Chaudhury & Dover 6mn 03s 6.03
Tunna 4mn 06s 7.31
Hancock 22mn 18s 1.35
CODE RMS Sxx
ANSYS 33.5 MPa
RADIOSS® BULK 35.7 MPa
LS-DYNA 35.0 MPa
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LS-DYNA
42Cumulative damage ratio by Dirlik method
Cumulative damage ratio by Steinberg’s method
Damage ratio = 5.540
Damage ratio = 7.188
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LS-DYNA
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Experiment setup
Failure at the notched point in experiment
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LS-DYNA
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Initial failure area
A model from railway application
The structure is subjected to base acceleration defined by the International Standard
IEC61373 to simulate the long-life test. This standard intends to highlight any weakness
which may result in problem as a consequence of operation under environment where
vibrations are known to occur in service on a railway vehicle.
Example: support antenna
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LS-DYNA
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Area 1 - damage ratio = 25.5
Area 2 - damage ratio = 3.45
Area 1
Area 2
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LS-DYNA
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Initial Damage Ratio
Card1 1 2 3 4 5 6 7 8
Variable MDMIN MDMAX FNMIM FNMAX RESTRT MFTG RESTRM INFTG
Type I I F F I I I I
Default 1 0.0 0 0 0 0
*FREQUENCY_DOMAIN_RANDOM_VIBRATION_ FATIGUE
Card7 1 2 3 4 5 6 7 8
Variable FILENAME
Type C
Default d3ftg
Define Card 7 if option FATIGUE is used and INFTG=1.
INFTG Flag for including initial damage ratio.
EQ.0: no initial damage ratio,
EQ.1: read existing d3ftg file to get initial damage ratio.
FILENAME Path and name of existing binary database (by default, D3FTG) for
initial damage ratio.
VARIABLE DESCRIPTION
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LS-DYNA
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Time of exposure: 4 hours
0
5
10
15
20
25
30
35
40
45
50
1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09
No. of cycles
S t r e s s ( K s i )
S-N fatigue curve
Edge fixed toshaker table.
Acceleration
PSD = 1g2/Hz
for 1-2000 Hz
RMS - von mises for x-acl PSD RMS -von mises for z-acl PSD
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LS-DYNA
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Damage ratio for x-load only
Damage ratio for z-load only
Damage ratio for x+z load
Dirlik method is used (MFTG = 2).
1.152e-01
6.019e-01
7.171e-01
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LS-DYNA
RESPONSE SPECTRUM ANALYSIS
5
49
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LS-DYNA
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Introduction: Response Spectrum
*FREQUENCY_DOMAIN_RESPONSE_SPECTRUM Use various mode combination methods to evaluate peak
response of structure due to input spectrum.
The input spectrum is the peak response (acceleration, velocity
or displacement) of single degree freedom system with different
natural frequencies. The input spectrum is dependent on damping (using
*DEFINE_TABLE to define the series of excitation spectrum
corresponding to each damping ratio).
Output binary database: d3spcm (accessible by LS-PREPOST).
It is an approximate method. It has important application in earthquake engineering, nuclear
power plants design etc.
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LS-DYNA
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Capabilities
o
SRSS methodoNRC Grouping method
oCQC method
oDouble Sum methods Rosenblueth-Elorduy coefficient
Gupta-Cordero coefficient
Modified Gupta-Cordero coefficient
oNRL SUM method
oRosenblueth method
Mode comb inat ion
oBase velocityoBase acceleration
oBase displacement
oNodal force
oPressure
Input sp ectrum
o
LogarithmicoSemi-logarithmic
o Linear
Frequenc y interpolat ion
oBINARY plot file: d3spcm
o ASCII files: nodout_spcm, elout_spcm
Results
oCivil and hydraulic buildings Hydraulic dams
Bridges
High buildings
oNuclear power plants
Appl icat ions
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Example: multi story tower
60 m /15 story towerLoading conditionsBase acceleration input spectrum
Mode combination method
SRSS
Damping = 1%
Frequency (Hz) Acceleration (m/s2)
0.1 19.4
5.0 22.23
10.0 24.10
15.0 25.5
20.0 26.6
6 0 m
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Z displacement results
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Von Mises stress results
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Example: arch dam
o 464.88 feet high
o Rigid foundation
o Subjected to x -directional ground acceleration
spectrum
The pseudo-acceleration spectrum of El
Centro earthquake ground motion (=5%)
The 1940 El Centro earthquake (or 1940 Imperial
Valley earthquake) occurred on May 18 in the
Imperial Valley in Southern California near the
border of the United States and Mexico. It had a
magnitude of 6.9.
X-directional acceleration
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LS-DYNA
ACOUSTIC ANALYSIS BY BEM/FEM
6
56
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*FREQUENCY_DOMAIN_ACOUSTIC_BEM_ {OPTION}
Available options include:
PANEL_CONTRIBUTION
HALF_SPACE
Introduction: BEM Acoustics
SSD
Structure loading
V (P) in time domain
V (P) in frequency domain
Acoustic pressure and SPL (dB) at field points
FFT
FEM transient analysis
BEM acoustic analysis
User data
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BEM (accurate)
Indirect variational boundary element method
Collocation boundary element method
They used to be time consuming
A fast solver based on domain decomposition MPP version
Approximate (simplified) methods
Rayleigh method
Kirchhoff method Assumptions and simplification in formulation
Very fast since no equation system to solve
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N
j
j
j
N
j
P p
d n
G pn
pG P p
j
1
1
)(
)(
real
i m a g i n a r y
p p
j
O
Projection in the direction
of the total pressure
Acoustic Panel Contribution
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Freq = 11Hz
Freq = 101 Hz
6 m
3 m
The plate is 0.2 m away from the vehicle
Sound Pressure Level distribution (dB)
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Half-space Problem
r eG
ikr
4
r
e R
r
eG
r ik
H
ikr
H
44
Free space Green’s function
Half space Green’s function
pr
r’
S
H H n ds
n
G pGvi P )()(
Helmholtz integral equation
R H = 1: rigid reflection plane, zero velocity
-1: soft reflection plane, zero sound pressure (water-air interface in
underwater acoustics)
The reflection plane is defined by *DEFINE_PLANE.
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Muffler Transmission Loss Analysis
W i
W t
t
i
W
W TL 10log10
TL (Transmission loss) is the difference in the sound power level
between the incident wave entering and the transmitted wave
exiting the muffler when the muffler termination is anechoic (no
reflection of sound).
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pi
pr
P 1 P 2 P 3
Muffler
Anechoic
Termination (Z=c)
po
Muffler P 2
v2
P 1
v1
Three-point method Four-pole method
Incoming wave is given as
1
21
12
2
)](sin[2
1 ikxikx
i e pe p x xk i
p
o
i
o
i
s
s
p
pTL 1010 log10log20
2
2
1
1
v
p
DC
B A
v
p
o
i
s
s
DcC c
B ATL
10
10
log10
1
2
1log20
Where, si and so are the inlet and outlet tube
areas, respectively
21
21
21
21
/
/
/
/
vv D
pvC
v p B
p p A
1,0|
1,0|
1,0|
1,0|
12
12
12
12
v p
vv
v p
vv
The four pole parameters A, B, C, D, can
be obtained from
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1. F. Fahy, Foundations of Engineering Acoustics. Elsevier Academic Press, 2001.
2. Z. Tao and A.F. Seybert, a Review of Current Techniques for Measuring Muffler Transmission Loss.
SAE International , 2003
0
10
20
30
40
0 1000 2000 3000
T r a n s
m i s s i o n
L o s s ( d B )
Frequency (Hz)
Plane Wave theory [1]
Experiment [2]
LS-DYNA (Three-Point Method)
LS-DYNA (Four-Pole Method)
Cutoff frequency for plane wave theory f =1119 Hz
Muffler transmission loss by different methods
References
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Double expansion chamber
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Z. Tao and A.F. Seybert, a Review of Current Techniques for Measuring Muffler Transmission
Loss. SAE International , 2003
References
LS DYNA
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*BOUNDARY_ACOUSTIC_MAPPING
VARIABLE DESCRIPTION
SSID Set or part ID
STYP Set type:
EQ.0: part set ID, see *SET_PART,EQ.1: part ID, see *PART,
EQ.2: segment set ID, see *SET_SEGMENT.
Card 1 2 3 4 5 6 7 8
Variable SSID STYP
Type I I
Default none 0
*BOUNDARY_ACOUSTIC_MAPPING
Purpose: Define a set of elements or segments on structure for mapping structural nodal velocity to boundary of acoustic volume.
LS DYNA
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Mesh A: 20 30 (600) Mesh B: 15 20 (300) Mesh C: 7 11 (77)
Mesh A 16 min 34 sec
Mesh B 10 min 10 sec
Mesh C 6 min 49 sec
CPU time (Intel Xeon 1.6 GHz)
Also mesh for structure surface
LS DYNA*FREQUENCY DOMAIN ACOUSTIC BEM ATV
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*FREQUENCY_DOMAIN_ACOUSTIC_BEM_ ATV
Acoustic Transfer Vector can be obtained by including the option ATV in the keyword. It calculates acoustic pressure (and sound pressure level) at field points due to unit
normal velocity of each surface node.
ATV is dependent on structure model, properties of acoustic fluid as well as location
of field points.
When ATV option is included, the structure does not need any external excitation,
and the curve IDs LC1 and LC2 are ignored.
ATV_DB_FIELD_PT_* (decibel due to unit vn at each node)
ATV_FIELD_PT_* (complex pressure due to unit vn at each node) ATV_DB_FIELD_PT_FRINGE_* (user fringe plot file for decibel due to unit vn at
each node)
Output files
LS DYNA
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ATV is useful if the same structure needs to be studied under multiple
load cases.
n
j
nmnm jmmm
ni jiii
n j
n j
m
i
V
V
V V
P
P
P P
2
1
,,2,1,
,,2,1,
,2,22,21,2
,1,12,11,1
2
1
Need to be computed only once
ATV at field points 1-m, due to unit normal velocity at node j
Change from case to case
1 2 m
LS DYNAA i FRF
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Acoustic FRF
Unit force excitation
Driver ear position
A simplified auto body model without any inside details
Analysis steps:
1.Modal analysis2.Steady state dynamics
3.Boundary element acoustics
All done in one run
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LS DYNA
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LS-DYNAPressu re distr ibu t ion
f =100 Hz
f =400 Hz
f =200 Hz
f =500 Hz
75
LS DYNAE l li d
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Introduction
Nodal force 0.01N is applied for frequency range of 10-20000 Hz.
Diameter 10mm, length 31.4mmThis edge is
fixed in x, y, z
translation dof.
To solve an interior acoustic problem by variational indirect BEM,collocation BEM and FEM. The cylinder duct is excited by harmonic nodal
force at one end.
*FREQUENCY_DOMAIN_SSD
*FREQUENCY_DOMAIN_ACOUSTIC_BEM
*FREQUENCY_DOMAIN_ACOUSTIC_FEM
or
Example: cylinder
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LS DYNA
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78f =20000 Hz
f =5000 Hz
f =15000 Hz
f =10000 Hz
Acoust ic pressure dist r ibut ion(by d3acs)
LS-DYNA
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CONCLUSION &FUTURE DEVELOPMENTS
7
79
LS-DYNA
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LS-DYNA
A set of frequency domain features have been imp lemented,
towards NVH, durabi l i ty analys is of vehicles and other vibrat ion
and acous t ic analysis
Frequency Response Function
Steady State Dynamics
Random Vibration and Fatigue
BEM & FEM Acoustics Response spectrum analysis
Future wo rk
SEA method for high frequency acoustics
Fast multi-pole BEM for acoustics
Infinite FEM
Fatigue analysis with strains
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