examples of early use of statistical energy analysis (sea...
TRANSCRIPT
ABSTRACT: Statistical Energy Analysis (SEA) has some special benefits in product concept evaluation, especially
when many relatively radical ideas have to be benchmarked against e.g. a proven design. The lack of detailed geo-
metry and CAE models are typical at this early development stage of a product. SEA models are simple and quick to
build to follow even rapid generation of ideas. SEA models only need a minimum of geometry parameters and reaso-
nable assumptions of basic material parameters to provide physically reasonable, quantitative relative predictions of
the different concept ideas. The major uncertainties at this stage are often the internal damping estimates for the
different parts. Alternatively SEA models may pinpoint the need to use high enough damping for certain parts.
This paper presents some relatively simple examples from the automotive, off-shore and shipbuilding industry. The
most comprehensive example is from radical concept development for light-weight cars. The other examples illust-
rate how SEA can be used successfully for early “risk assessment” and explanation of e.g. increased sound radiation
to interior spaces even at relatively low frequencies when rib-stiffened structures are redesigned to meet e.g. lower
weight demands.
KEY WORDS: Statistical Energy Analysis; SEA; Concept Development; Product development.
1 INTRODUCTION
There are examples of engineering challenges that require
radical rethinking in product concept development. For
example, to reach expected legal limits for road vehicle CO2-
emissions around 2020-2025, weight reductions of 30-40 %
may be necessary at least for conventional combustion engine
powered cars, to reach these goals without major increase of
cost and obtain as good NVH comfort as presently for
vehicles in the premium (luxury) segment.
Road noise (structure-borne and airborne) as well as wind
noise will determine the interior sound comfort also for cars
with electric powertrains (plug-in hybrids, EVs with range
extenders, fuel-cells etc.). Road- and wind noise issues may
therefore be even more pronounced unless addressed during
the conceptual design of new low weight hybrid/electric
vehicles.
Offshore structures and ships are other examples where
weight optimisation is prioritized. Structure-borne sound
sources with high levels are often situated close to accommo-
dation or office spaces. Use of dynamic solution of detailed
FE-models is usually restricted to low frequency of economic
reasons. They are also produced late in the engineering
process when CAD geometry is mostly determined. A couple
of examples are given where SEA-modelling can illustrate
noise radiation consequences of weight optimisation of rib
stiffened plate or shell structures when only strength is
considered.
2 STATISTICAL ENERGY ANALYSIS (SEA)
The Statistical Energy Analysis (SEA) was first developed
about 50-60 years ago to deal with prediction of noise and
vibration transmission in complex structures with multi-modal
response, the fundamental theory is given in [1, 2].
The name SEA was established in the early 1960's and
means:
Statistical, since the systems being studied are members
of populations of similar design having distributions of
their dynamical parameters.
Energy is the primary variable of interest. Dynamic
variables such as displacement, pressure, etc., are derived
from the energy of vibration.
Analysis is used to say that SEA is a framework of
dynamic analysis, rather than a particular technique.
Resonance frequencies and mode shapes of higher order
modes show great sensitivity even to small variations of
geometry, construction and material properties. Modal overlap
results in high variability of frequency response functions
(FRFs) for such variations [3].
Also, FEM/BEM computer programs used for calculating
mode shapes and frequencies are rather inaccurate for higher
order modes. A statistical model of the modal parameters is
therefore natural and appropriate when the number of modes
becomes high in the frequency intervals considered.
SEA has been successfully used a long time for a number of
applications such as ships [4], buildings [5] and vehicles [6].
The SEA prediction procedure has four basic steps:
1) Modelling of the dynamic system into subsystems and
connections (junctions).
2) Determination of SEA-parameters for the model
3) Calculation of energy distribution between subsystems
4) Calculation of average response levels for subsystems
The energy storage elements are called subsystems, and
should be parts of the modelled system with similar vibratio-
nal modes. The modes are usually of the same type (flexural,
torsional, acoustical etc.) that exist in some section of the sys-
tem (an acoustic volume, a beam, a bulkhead etc.) separated
Examples of early use of Statistical Energy Analysis (SEA) for concept development
evaluation
Juha Plunt
Müller-BBM Scandinavia AB, Box 1054, SE-405 22 Gothenburg, Sweden
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)ISSN: 2311-9020; ISBN: 978-972-752-165-4
3313
by discontinuities from the rest of the structure. Subsystems
are often reasonably easy to identify also in complex mech-
anical or acoustical systems.
These subsystems represent an entire ensemble of structures
with the same main geometry and material parameters
(volume, area, thickness, Young’s modulus, density etc.) but
no details about shape, boundary conditions etc. This can be
illustrated by Figure 1, showing an ensemble of plates that are
represented by a subsystem with exactly the same parameters!
All represented by the
same plate subsystem:
E, S and t are equal
ENSEMBLE
Figure 1. An ensemble of plates with varying shape is the
same SEA subsystem (this is the S in SEA!)
This makes SEA especially interesting for analysis of sound
and vibration properties during the development of a new
product concept, well before any detailed geometry has been
decided. This is exemplified in this paper.
The SEA parameters determined for the subsystems and
junctions by a SEA software are the following:
1) Input powers Wi to the i-th subsystem
2) Modal densities ni for the i-th subsystem
3) Internal loss factors i for the i-th subsystem.
4) Coupling loss factors ij between the i-th and the j-th
subsystems
When the SEA-parameters for all subsystems and junctions
have been determined, the set of energy balance equations
will be completely defined. This may be written as the
following matrix equation
1 1 1 12 1 1 1 1
2 21 2 2 2 2 2 2
1 2
tot N m in
tot N m in
N N N N N Ntot mN inN
n n n E W
n n n E Wf
n n n E W
(1)
or in matrix notation
m inf A E W (22a)
The matrix [A] is real, symmetric and positive definite of size
NxN where N is the number of subsystems. By appropriate
numbering of subsystems, the matrix become significantly
banded which improves the calculation speed.
.
3 LOW WEIGHT VEHICLE CONCEPT DESIGN EXAMPLE
A lightweight research project - “Collaboration as enabler for
light weight vehicles” - involving around twenty Swedish
automotive suppliers, an automotive OEM and a number of
universities developed new vehicle and system concepts that
may be able to fulfill the abovementioned targets of 30-40 %
weight reduction. The main project concepts are presented at
www.sanatt.se.
It was expected that new system and complete vehicle archi-
tectures may be necessary in order to reach 30-40% weight
reduction, while also targeting excellent performance with
respect to safety and comfort without substantially increased
cost. Optimization by change to lightweight materials within
the same conventional body and interior structure would lead
to unacceptable cost increase if both NVH and weight targets
should be reached.
The concept development process [7, 8] used in this project
was open to any new ideas while based on a number of
defined properties, their weighted importance and targeted
performance 2020-2025. Those properties were transformed
into a list of necessary functionalities, which in turn resulted
in a large matrix of “brainstormed” ideas from specialized
working groups for complete vehicle and critical systems, see
Figure 2.
Low interior noise and vibration level, which will be
discussed in this paper, is a prioritized functionality next to
low weight and passive safety. The underbody system is used
to exemplify the concept generation and analysis process used
in the project.
Fig. 3 – The idea matrix where each function for the under-
body results in a row of the matrix. The ideas are evaluated
against the property diagram and for synergies. The best
combination is used to define a possible concept design.
Combustion engines with higher energy efficiency (diesels,
direct-injection gasoline) tend to radiate more airborne sound
in the mid and high frequency range which requires improved
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
3314
airborne sound insulation between the engine bay and the
interior. This may be in direct physical conflict with weight
reduction for the critical sound insulating partitions, see
Figure 3 [9]. Structure-borne transmission is generally much
more complex to analyze and design for but is not necessarily
in direct conflict with weight reduction.
Sound- and
vibration sources
Structure-
borne sound
transmission
Airborne
sound
transmission
Passenger interior
compartment
•Direct weight - NVH conflict
•Few panels contribute
•Moderate functional complexity
•No direct weight - NVH conflict
•Many panels contribute
•Considerable functional complexity
Figure 3. The relative complexity of airborne and structure-
borne sound transmission in cars is shown. Airborne sound
insulation is in a direct conflict with low weight.
Early in the concept generation process, some basic floor/
firewall ideas were compared [8] and it became obvious that a
basic, double floor/firewall concept was necessary to balance
airborne sound insulation requirements with low weight and
vehicle packaging efficiency. A summary of these SEA ana-
lysis results were presented in [8] and will not be repeated
here.
The final underbody concept is illustrated in Figure 4. It
consists of a bottom panel structure made of a stiff, light-
weight Hybrix™ [10] panel and an upper carbon-fiber reinfor-
ced composite beam and panel structure.
Figure 4. The final SåNätt underbody concept illustration
model. Upper structure of carbon-fibre reinforced composite
with different thickness for panels and beams. Lower structure
made of a stiff Hybrix™ panel and door sills of aluminium or
high strength steel.
The main concern was if the relatively stiff CF-structure
(compared to present day heavy layer mats) would result in
higher sound radiation efficiency of the firewall and foot-well
panels. The weight reduction compared to a present, conven-
tional underbody structure for a midsize premium car with all
its trim is approximately 45%.
3.1 The SEA-models
A commercially available SEA program, GSSEA-Light, was
used [11], allowing modeling with components connected in a
2D network since no 3D geometry was available anyway until
the end of the project. It has sufficient capabilities for this
type of relatively crude concept evaluation.
A SEA project defined in GSSEA-Light can also use and
compare results across multiple SEA models, making it
suitable for fast modeling and comparison of very different
concepts. The SEA model in Figure 5 is for the conventional,
present day underbody used as reference, and Figure 6 shows
the model for the final underbody concept of the SåNätt
project as shown in Figure 4.
The input data used for the baseline reference concept was
0.7 mm steel plate, 30 mm soft foam as distance holder and a
2 mm thick heavy layer mat with 2000 kg/m3 density.
The main input data for the lightweight concept were, for
the upper CFR-structure:
Carbon fiber compound AMC 8590
Front seat cross beam and tunnel 4 mm
Horizontal floor panels and firewall 2 mm
For the lower structure a Hybrix composite plate with a
bending stiffness corresponding to 1 mm steel plate but with
50% lower surface weight was used.
The initial “baseline” internal loss factors used were 5% for
the Hybrix and 2% for the CFR composite. Additional dam-
ping with loss factor of 5% for the thicker CFR composite
panels and 10% for the thinner panels were then introduced in
the SEA model to improve the structure-borne sound
transmission properties. The door sills in aluminum were
approximated by an equivalent rectangular, hollow profile.
.Figure 5. SEA-model for the baseline underbody structure.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
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The average separation distance between the two floor/fire-
wall surfaces was set to 100 mm and airborne sound transmis-
sion was calculated for this double wall structure.
Figure 6. The SEA-model for the SåNätt lightweight
underbody concept.
The models use excitation from three power sources, one air-
borne sound source in the engine compartment, one airborne
sound source under the floor and a structure-borne point force
acting on one of the longitudinal beams, simulating input from
an engine mount or a wheel suspension bushing.
The corresponding transfer functions in 1/3rd
octaves are
calculated from these sources to the car interior compartment
and compared between both models. The target was to obtain
lower or equal transfer functions for the low-weight under-
body concept as for the conventional reference design.
3.2 The SEA-results
In summary, the comparable performance, shown in Figures 7
to 9 was obtained for airborne and structure-borne sound
transmission between the present conventional reference
design and the SåNätt underbody concept for different
amounts of damping in the CFR panels.
Figure 7 shows the estimated sound pressure level in the
interior compartment relative to conventional baseline design
for the same excitation sound pressure level in the engine
compartment. Values above zero means deterioration while
negative values means improvement of sound insulation by
the SåNätt concept. The lightweight concept is better above
approximately 250 Hz but is slightly worse for lower frequen-
cies. Airborne sound insulation is normally most important
over a few hundred Hz so this may be fully acceptable. As
expected, the additional damping of the CFR panels did not
influence the airborne sound transmission and the two curves
are perfectly overlaid.
Worse
Better
Figure 7. The predicted interior airborne sound pressure level
for the SåNätt concept (blue) relative to present baseline (red)
for airborne sound excitation in the engine compartment.
Figure 8 shows the estimated sound pressure level in the
interior compartment relative to the conventional reference for
the same sound pressure level excitation below the floor.
Worse
Better
Figure 8. The predicted interior airborne sound pressure level
for the SåNätt concept (blue and green) relative to present ba-
seline (red) for airborne sound excitation below the floor.
Figure 9 shows the estimated sound pressure level in the inte-
rior compartment relative to present, conventional “baseline”
for the same force in Z-direction on a point on the left
longitudinal beam. The case with moderately damped CFR-
panels (Baseline) seems to be much more sensitive (higher
NTF:s) in the entire frequency range than the present day
design. A “what if” case with damping added to the CFR
panels, as mentioned in Section 3.1 above, makes the concept
perform equal below 2 kHz but still worse at higher frequen-
cies. Structure borne sound contributions to interior vehicle
sound are expected to dominate at low frequencies, so this
may still be acceptable, except when higher frequency issues
like whine, clonks or rattle are of concern.
Figure 10 illustrates the response contributions to the car
interior due to radiation from the different panels for the case
with additional damping of the CFR panels. This analysis can
be used to further fine tune the underbody concept. E.g. one
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
3316
can see that the dominating radiators above 1 kHz are the stif-
fer CFR cross beam surfaces.
Worse
Better
Figure 9. Predicted structure-borne NTFs for force excitation
in Z-direction on a point on the left front longitudinal beam to
the interior cavity. Two different damping inputs for the CFR
panels.
Figure 10. SEA “Transfer path analysis” into the interior com-
partment for the SåNätt concept with additional damping.
-90
-85
-80
-75
-70
-65
-60
-55
-50
Mo
bili
ty le
vel,
[dB
re.
1 m
/Ns]
Frequency , Hz
Sånätt
Baseline
Figure 11. Estimated point mobilities at the force excitation
point on the longitudinal beam for the SåNätt concept and the
baseline structure.
Figure 11 exemplifies the point mobility differences for the
longitudinal beams used in the conventional reference
baseline design and the SåNätt concept. Higher mobility
corresponds to higher power input to the structure.
The issues shown above 2 kHz for the SåNätt concept in
Figure 9 are obviously not due to higher mobility in this
frequency range for these beams. A closer comparison reveals
that the main reason is high vibration levels of the CFR cross
beam surfaces. It may also be noted that no cross-beam
structure was included in the conventional reference structure,
making the comparison above 2 kHz a bit unfair. This illustra-
tes the iterative SEA model generation process often used on
an “as needed” basis when dealing with concept comparisons.
A cross beam was introduced to the conventional concept but
results of that comparison is not shown here.
4 OFFSHORE PLATFORM EXAMPLE
A relatively large SEA model was created with the GSSEA-
Light software [11] for a topside structure of a large produc-
tion platform. The SEA model had 124 components joined
with more than 300 connectors and was excited with 4 input
power sources, representing the airborne sound and the
vertical structure-borne sound excitation of the two emer-
gency generator units respectively.
The generator sets were designed with the diesel engine and
the electric generator separately vibration isolated on a com-
mon skid. This generator unit concept may have shaft align-
ment issues, since creep and setting of the isolators may be
uneven, resulting in increased misalignment over time.
Also, since the isolators are loaded with the full torque
transferred from the engine, they cannot be made especially
soft, which limits isolation effectiveness. One may therefore
expect issues at the 1st engine order at 30 Hz due to both the
misalignment and the moderate vibration reduction by the
isolation system.
The appropriate frequency ranges for the SEA model of the
topside structure is approximately 50-60 Hz and above, see
Figure 12 that shows a sharp increase in modal density from
the 50 Hz band to the 63 Hz band. For lower frequencies,
SEA results are only indicative for a risk assessment but will
have large inherent uncertainties.
Figure 12. Number of expected vibration modes for the (sepa-
rate) ESS Generator deck as function of frequency. Note the
jump in modal density at 50-60 Hz.
Worse
Better
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
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The SEA-model can still be used for some risk assessment
of excessive noise at frequencies as low as 30 Hz. One
particularly simple thing is to evaluate the sound radiation
efficiency of the stiffened steel deck and bulkhead structures
used. This is shown in Figure 13, which shows a dramatic
increase in the radiation efficiency at the same frequency
bands as the jump in the modal density.
The reason for this can be found by comparing the bending
wavelength of the stiffened panels with sound wavelength in
the surrounding air; one example is shown in Figure 14. We
have the expected coincidence frequency for the unstiffened
deck plate at 1600 Hz. Since the stiffened panel acts like an
orthotropic panel with smeared out additional stiffness at low
frequency, we get another coincidence frequency for the panel
at 20-25 Hz. The bending wavelength remains larger than the
wavelength in air for frequencies above this until the indivi-
dual subpanels can vibrate independently, resulting in effi-
cient sound radiation.
Figure 13. Sound radiation efficiency levels for decks radia-
ting into different interior spaces.
Sound wavelength in air
Figure 14.Bending wave length for the generator deck as
function of frequency.
Obviously, if noise levels are a concern, the vibration levels of
the deck have to be kept particularly low in this low frequency
region. The usual noise reduction methods, like vibration
insulation, floating deck covering etc. are not very effective in
this frequency range. Proper definition and fulfilment of rigo-
rous source strength requirements become especially critical
in this situation.
It is also seen from Figure 14 that the design of the bending
stiffness of the orthotropic plates may take sound radiation
properties into account to avoid increasing the bending wave-
length above the wavelength of sound. Again, simple SEA-
modeling can be used to compare suggested variants as
exemplified in the next example.
5 LIGHTWEIGHT SURFACE VESSEL EXAMPLE
A similar issue at low frequency can be illustrated by an
example of designing a lightweight steel hull for a high speed
surface vessel. The main strategy in order to reduce weight
was to use much thinner hull plating and compensate that by
using a much smaller c/c distance between the longitudinal
stringers in order to retain the static and low frequency stiff-
ness that meet strength requirements.
It was not entirely obvious how this different hull concept
would influence the transmission of structure-borne sound and
the sound radiation properties at low frequencies. For examp-
le, the radiation efficiency at low frequencies was expected to
be influenced considerably by the hull plate thickness, the
stiffener cross-sections and the c/c distances between
stiffeners of the same reasons that were discussed in the
previous section.
Figure 15 illustrates the influence on the radiation efficiency
due to different c/c distance of longitudinal stringers on a 3
mm steel hull plate with 1.2 m between web frames. Clearly
the frequency is strongly affected below which the radiation
efficiency increases rapidly.
Figure 15. Sound radiation efficiency levels for different
stiffener c/c distance. 3 mm steel plate.
Figure 16 illustrates the influence on the radiation efficiency
due to different hull plate thickness using the same 400 mm
c/c distance of the longitudinal stringers for a steel hull plate
with 1.2 m between web frames. Again the influence on low
frequency radiation efficiency is considerable.
The necessary SEA-model for these radiation efficiency
comparisons is very simple, see Figure 17. Subsystem proper-
ties such as wavelengths, mobility’s etc. are directly available
as are the connector properties such as radiation efficiencies.
It is possible using such limited SEA modeling and analysis
to use different stiffening strategies for different parts of the
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
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ship in order to avoid low frequency structure-borne sound
issues.
Stiffer orthotropic plates may be used for hull sections
where vibration sources are acting, e.g. above the propellers
and below engine beds, to obtain lower mobility and thus
reduce vibration power input to the hull. Less stiff panels,
optimized with respect to radiation efficiency, are preferably
used for the main radiating surfaces into cabins etc. to avoid
high sound radiation at critical excitation frequencies.
Figure 16. Sound radiation efficiency levels for different
stiffener c/c distance. 3 mm steel plate.
Figure 17. Simple SEA-model to compare sound radiation
efficiency levels for different stiffener configurations and
plate thicknesses.
6 DISCUSSION AND CONCLUSIONS
Statistical Energy Analysis (SEA) is a computational method
that is especially suitable for early, quantitative sound and
vibration evaluation of crude, competing and very different
system concepts. It can of course also be used for comparative
evaluation of vastly different complete vehicle architectures
resulting in significantly larger SEA models than those shown
here.
The detailed geometry needed for global low frequency
modeling by FEM is not available at early stages when the
sound and vibration performance of radically different product
concepts is compared in order to rank the concepts or illust-
rate main parameters like surface mass, double wall thickness,
internal damping etc. needed for possible target fulfillment.
The lack of both “proper simulation=FEA” and physical
prototypes usually results in sound and vibration experts not
being involved in such early concept generation and to
missing opportunities of influencing the selected concepts in
a proper direction concerning noise and vibration.
The need to communicate target conflicts, e.g. between
weight and sound insulation in a relatively simple and
quantitative manner is imminent when the sound and vibration
expert has the opportunity to participate in early concept gene-
ration. Simplified SEA modeling will be more reliable than
qualitative, “educated” guesses or overly simplified, rough
textbook calculations since topographic complexity of the
structures can be included also in relatively simple SEA
models.
One also needs to be aware of the very limited time frame
of opportunities in most cases to influence the early, but often
decisive and major concept selection process. One has to use
the best possible analysis tools under those circumstances.
Simplified SEA models that can be rapidly built may be quite
well suited for this relatively dynamic and fast development
and selection between radically different competing ideas.
ACKNOWLEDGMENTS
The vehicle case example was developed for the project
“Collaboration as enabler for light weight vehicles” in the FFI
- Strategic Vehicle Research and Innovation program and
partly funded by VINNOVA, the Swedish Governmental
Agency for Innovation Systems.
The offshore and ship examples are extracts from different
company confidential consulting projects. These examples do
not reveal any information about the actual objects or custo-
mers; however I am still grateful for the opportunity to use the
ideas of risk assessment at such low frequencies that the SEA-
models may be considered as unreliable for prediction of
sound and vibration transmission between different parts of
the structure.
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
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