1. INTRODUCTION
1.1. Energy-Based Methods
There are many methods to solve the vibration and acoustic problems in these days.
The choice of the right method is very important for finding a required result with
minimum effort and cost. Today, energy based methods are the best ones of all the
other methods because of their techniques of using energy quantities (energy, energy
density, power ...) unlike the classical analysis of vibration that is based on quantities
such as force and displacement. Energy-based methods may have some advantages
while having applications [7].
Finite Element Analysis and Boundary Element Analysis, which are the best ones of
all the CAE tools, do a good job describing noise and vibration behavior in the lower
frequency ranges. At the same time, while using energy -based methods, there are
some problems about frequencies. These methods can not achieve to predict high
frequency vibration problems effectively. But, also it is not a good idea to use the
other classical testing and modeling methods. It is the biggest problem to deal with
structure-borne and airborne noise transmission at mid to high frequencies (typically
15 – 15,000 Hz) for noise and vibration in computer aided engineering because if the
frequency increases, wavelengths get smaller and the complexity of the system
dynamics increases. For example, there is increasing of the accumulation of modes
an acoustic cavity as the third power of frequency [5, 6].
One possible CAE solution to solve these challenges is Statistical Energy Analysis
(SEA). And it has the capability to solve this problem and to identify how vibrations
are distributed in the structure of a system described as a set of subsystems. Today, in
university laboratories, there are still studies to develop this approach [5, 6].
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Figure 1. Typical noise or vibration response spectrum of a structural-acoustic system, showing
frequency range of applicability for Finite Element Analysis (FEA); Boundary Element Method
(BEM) and Statistical Energy Analysis (SEA) [6]
1.2. Definition of Sea (Statistical Energy Analysis)
SEA is a sub-structuring analysis method where one seeks to predict only the
statistically meaningful “band limited energy level” of multi-modal noise or
vibration response in each sub-structure region or “subsystem”. The energy level is
defined by the space-averaged, mean-squared vibration or acoustic response and is a
good estimator when there are many interacting modes and the local response
approaches a “reverberant” condition, commonly observed in room acoustics [6].
In SEA no attempt is made to recover the detailed displacement pattern of the
structure, but rather the structure is modeled as an assembly of “subsystems” and the
aim is to predict the vibrational energy level of each subsystem. This is done by
establishing a set of power balance equations which are based on the key assumption
that the energy flow between two connected subsystems is proportional to the
difference in the subsystem modal energies. While SEA has been applied with
considerable success to a wide range of structures, there is a continuing debate over
the theoretical validity of the method [8-10].
1.3. The Development of Sea
In these days, the most famous energy-based method is the statistical energy analysis
(SEA). Statistical means that all results are expected values after the variables are
drawn from statistical population. Energy Analysis denotes that it is more a general
approach rather than a particular technique which use energy variables. Similar
2
approaches of SEA were used in room acoustics, before the actual development of
SEA. It was first used in 1959 by R.H. Lyon and P.W. Smith. Then it was used in the
early 1960 with the application to vibro-acoustic problems in aerospace engineering
.In these years, there were some studies about determining of the vibration energy
and rocket noises. But, while studying, first some modes were taken into
consideration because of insufficiency of the methods using like their slowness. For
instance, it was impossible to solve the problems of the Saturn vehicle, which has
500.000 nature frequencies between 0-2000 Hz frequency bands, existing methods.
Other words, the main matter are the high frequency problems. So, in 1970s, solution
was improved as separating the main system to inferior systems. After 1980s the
method was put into practice [7].
In last few years, this method is mostly used in automotive industry and aerospace
engineering. At the same time, it is started to use in commercial software like the
other analysis methods.
1.4. Where Sea Is Used
Today, it is very common to use for interior noise design of automobiles, air- and
motor-craft, ships, rail cars and other transport vehicles. The space industry uses
SEA to predict random vibration response of sensitive equipment on space structures
subjected to harsh vibro-acoustic launch loads [6].
Figure 2. Geometry read from a finite element model file and used to create a curved side glass shell
subsystem in AutoSEA2. Typical plate, shell and beam subsystems used to model automobile body
structure in the 3D SEA software. [6]
3
Figure 3. Automobile interior acoustic field modeled with eight acoustic cavity subsystems in the 3D
SEA software. Red arrow symbols - correctly oriented in 3D space – are the iconic representation for
suspension vibration loads on the body and chassis subsystems [6]
Figure 4. Thermo gram display using color to denote the modal energy distribution under the applied
structural and acoustic loads. [6]
It is also used in automobile, ship, aircraft, space, architecture, rail and sonar
industries[15].
Automotive: Design for interior sound quality, body structural acoustics and
weight/cost optimization of interior sound package in automobiles, trucks, buses, etc.
Ship: Design for full system-level prediction of shipboard noise and underwater
acoustic signature in ships, luxury yachts, and submarines.
Aircraft: Design for interior noise, for new material/construction, and for faster flight
speed in commercial, executive and military aircraft.
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Space: Design for acoustic, random vibration and shock environment specifications
for primary structure, payload and flight equipment in spacecraft and launch
vehicles.
Architecture: Design for building and HVAC system models that produce N&V
performance specifications on fans, motors, and other noisy components in office
buildings, hotels, etc.
Rail: Design for interior sound quality for wheel/rail interaction noise, engine and
aerodynamic noise and for predicting the exterior community noise impact for
commuter and high speed trains.
Sonar: Design for reduction of hydrodynamic and mechanical flow contributors to
"self noise" for Navy projects and sonar systems.
Figure 5. Graphical representation of an SEA model of a car body shell: plate (top) and beam
(bottom) subsystems [8]
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2. SEA FUNDAMENTALS
2.1. Power Balance Equation
The assumption of conservation of energy between coupling subsystems is the main
idea of SEA. The calculations are based on this assumption.
The time averaged kinetic energy EK is equal to the time averaged potential energy
EP for resonant vibration. So, the total energy in the given band, [11]
F 2 N
Etot 2EK
2M
Where F2Dw is mean-squared force, M is mass, g is modal damping, n (w) = DN/Dw is
modal density. N is number of modes. In SEA time averaged input power is said to
be co spectrum of velocity and the force.
Pin, Re F xi , v* xi , d
where star means complex conjugate. For band limited modal energy, the band
limited power input PDw is,
F 2 N
Pin,
2M
and from the conservation of energy input power is equal to dissipated power: [11]
Pin
Pdiss
Etot (2)
2.2. Modal Energy
To understand the idea behind the modal energy, it will be meaningful to give a
simple example to calculate the power balance equation in an SEA model. Let us
consider a subsystem (Figure 6). If power input is injected into the subsystem, it
keeps vibrational energy E. There is also power loss from the subsystem because of
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dissipation. Power loss is associated with vibrational energy by the damping loss
factor hi. So, this formula is the same one equation 2 [7]:
Pi i E (3)
Figure 6 [7] Figure 7 [7]
If we have two coupled subsystems, we must add coupling loss factor into the
equation (3). As seen in figure 7, there is power exchanging among the coupled
subsystems. These are energy loss from vibrational energy. Although a subsystem
lost its vibrational energy, it gain energy from the other subsystem connected with.
For this situation, new general equation may be formed like this, [7]
Pij ij Ei (4)
The above equation can be solved for the two coupled subsystem. Power balance
equation for figure 7 can be written as
Pi ii Ei ij Ei ji E j
Pj jj E j ji E j ij Ei
If the power input Pj of the second subsystem is taken zero, the result of equation can
be written as,
0 jj E j ji E j ij Ei
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Ej ij
Ei jj ji (5)
In equation 5, if coupling loss factor too large comparing with damping loss factor
(hji>>hjj), it may be said that E1/h1 = E2/h2. It is practically difficult to get this
condition, but it makes a great ease for the response of the system. “E/h” is called
modal energy .When modal energy is used in the equation 4, the equation can be
written as follows:
E Ej
Pij ij i [7]
n n
i j
2.3. Modal Density
In SEA, modal density is an important variable. It means the number of modes per
frequency bandwidth. When it is concern a simple supported plate, modal densities
can be found from the grid patterns in figure 3. Each grid patterns represent a wave
numbers of resonance. To estimate modal density for plates, it is an efficient way to
use simple supported plate due to reducing of effects of boundary conditions for
higher-order modes. From the figure, the number of modes between two frequencies
w1 and w2 can be counted simply. For this, two circles which their radiuses are equal
to the freely propagating wave number of lower and upper frequencies are drawn.
Then the modes are counted between these circles.
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Figure 8. Illustration of wave number plot for estimating
modal density of a simply supported plate [12]
If the lower frequency is taken to be zero, sum of the numbers of modes, represents
N, can be estimated below the given frequency. So the modal density is
[12]
2.4. Damping and Coupling Loss Factors
As seen before damping loss factor is a variable of energy dissipated from vibrational
energy.
Coupling loss factor means energy transfer between the coupled subsystems. There
are two way to produce expressions of coupling loss factors for structures; the modal
and wave ways. In the modal method, the coupling between individual modes is
calculated and averaged the modes in each frequency band. In the wave method, the
coupling loss factor may be connected to the power transmissibility for semi-infinite
structures, which is often easier to estimate than the average of the couplings
between modes of finite structures [12].
2.5. The Statistics in SEA
For the simple theoretical approach taken here, statistical operations consist of a
threefold average that is more implicit. First, calculation is done always for a
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frequency band (octave, third-octave ...), but only at the centre frequency which
means average of frequency. Second, only one variable is used to characterize the
energy in one subsystem. This corresponds to a spatial average of the subsystem.
Lastly, by using very few parameters to characterize a subsystem there is no
possibility to restore all information from these parameters that is necessary to
describe the vibrational behavior in detail. For example, only area, thickness,
material parameters are used as input parameters for a plate. Consequently, as long as
these parameters remain the same, the shape of the plate does not matter in SEA. A
circular, a quadratic or a trapezoidal plate map are all to the same SEA model. This
kind of average is called ensemble average. In modal space, all three averages are
included in the average over a group of modes. It shall be noted in passing that
besides the estimation of mean or expected values from the averages the estimation
of variance is also possible, but is not straightforward. Generally, the variance is
acceptable only at mid to high frequencies. That is why SEA is often referred to as a
high-frequency method [7].
3. SEA MODELING PROCEDURES
First of all, structure is converted to a SEA model. In SEA, system is divided into
subsystems. After modeling SEA, the interactions between subsystems, input powers
and subsystem energies are defined. These statements are concerned in power
balance equations. Coupling and damping loss factors are important parameters in
this equation and generally estimated in experimental methods. When power balance
equations solved for the unknowns within it, energies of subsystem are found [14].
3.1. Sub-structuring
A subsystem is a physical element of the structure that is to be analyzed. Due to this
definition, an element must be capable of vibrating quite independently from other
elements. The word “quite” is emphasized here because as long as the element is not
separated from the rest of the structure its vibration is not truly independent. Then,
for a subsystem it is required to vibrate in resonant mode. That means, if the
excitation is suddenly cut, the vibrational energy collected in the subsystem will lose
its energy rather then fall into zero immediately (a point mass for instance is no
suitable candidate for a subsystem). So, a reverberant sound field exists within the
subsystem. If different wave types exist in the element, each of the corresponding
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sound fields is modeled by one subsystem. A subsystem is a group of “similar”
energy storage modes.
To illustrate this, some examples of vibro/acoustic elements that may be treated as
subsystems shall be given here together with the necessary input data to characterize
them:
• an acoustic cavity (a room): longitudinal waves –only one subsystem needed,
characterized by volume, fluid parameters, absorption
• a plate: bending, compression and shear waves modeled by three subsystems,
characterized by area, thickness, material parameters, damping
• a beam: four wave types – four subsystems, characterized by length, shape of cross-
section, material parameters, damping
• shells, non-isotropic plates, ...
As seen above, the energy stored in the subsystem is related to measurable quantities
such as sound pressure level. This fact enables the practical application of the purely
energy-based SEA equations [2].
3.2. Subsystem Selection
The best approach to the definition of subsystems is to start with subsystems that
extend to junctions that cause significant reflections. Bear in mind that different
wave types often require subsystems of differing physical sizes. For example, since
longitudinal wavelengths are larger than bending wavelengths, longitudinal
subsystems may extend over a number of bending subsystems. If the coupling loss
factors between two subsystems are such that they are strongly coupled in both
directions, then these subsystems can be combined into one subsystem without loss
of accuracy. Smaller models of the most complex part of the structure can sometimes
aid in checking for strong coupling and simplification of the overall model.
For a first pass, it is useful to hypothesize strong coupling. The relationship between
the assumed damping and coupling loss factors should be reviewed as the model is
developed. The user not familiar with coupling loss factors should consider bounding
these factors as a starting point for the power balance equations, and refining them as
additional information becomes available and as the model is exercised and
compared to measurements of predictions for similar systems.
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Larger structures will contain more modes, allowing for a more accurate analysis at
lower frequencies. The results for smaller structures will only be valid when there are
several modes present, which may be limited to mid- to high- frequency ranges [3].
3.3. Experimental SEA
Experimental SEA based on determining all quantities in equation (1) by experiment.
To do this firstly, power is injected to each subsystem in the structure in turn. This
may be done for example by means of a hammer, a shaker or a loudspeaker. Then,
each time the energy in each subsystem is measured (by accelerometers or
microphones). As illustrated in Figure 3, for each subsystem a set of energies is
ready and the equation (2) can be set up using equation (1):
(1)
[7]
[7]
(2)
[7]
The colors in equation (2) refer the order of power injected in Figure 3. By inverting
the matrix of energies, this system may be solved to get the coupling and damping
loss factors. In practice the matrix of energies is often bad conditioned but a number
of methods have been developed to cope with that. Knowing now the matrix of loss
factors, main paths of power may be identified, the effect of modifications may be
12
assessed and a sensitivity analysis may be performed to find those factors that are
most important for a given transmission scenario [7].
3.4. Predictive SEA
Theoretically, the basic idea of predictive SEA is to assess the coupling loss factors.
So, it is possible to predict the behavior of a structure even in an early stage of its
design without requirements of any measurement after built. This procedure firstly
starts with estimating of the damping loss factors either from measurement, from
tables, calculations or simply” experience”. Then, the input power is determined (by
experiment or calculation). Alternatively, the input power is set to unity, if only
transmission loss is of interest and not absolute response values. The coupling loss
factors may be estimated by lots of different methods:
• From radiation or transmission efficiencies (wave approach)
• using modal approaches
• using numerical methods (e.g. Finite Element Method)
• coupling power proportionality hij = hjihj/hi (hi, hj are the modal densities of
subsystems i and j)
• ...
With all necessary input parameters available, the SEA equations may be solved and
the response of the structure may be predicted. As in experimental SEA this enables
lots of useful possibilities for analysis [7].
4. MODELING SOFTWARES
Nearly all of the industries have started to use SEA as a CAE tool and some of the
organizations have prepared SEA computer codes. Three of these codes have been
developed commercially. SEAM developed by Cambridge Colloborative Inc., was
the first SEA computer code to become commercially available. Recently, AutoSEA
developed by Vibro- Acoustic Sciences Ltd., has been made commercially available.
AARCSEA which has been used in several naval vehicle and architectural designs is
available on an application basis to end user customers [6].
4.1. Seam Acoustic and Vibration Prediction Software
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Dynamic response of complex structures at mid and high frequencies can be
measured by SEAM software. Anyway it is a complete implementation of statistical
energy analysis. SEAM is used to predict interior noise and vibration in automobiles,
aircraft, shipbuilding and construction equipment cabs as well as the radiated noise
from ships and the vibro-acoustic environments for spacecraft. The complex dynamic
system being analyzed is divided into a set of substructures and acoustic elements.
The modes of each substructure and acoustic element are grouped into SEA
subsystems. The flow of energy between the different subsystems is proportional to
the modal energies of the subsystems and the coupling factors. The SEAM program
calculates all required coupling factors and performs a power balance for each
subsystem. The resulting equations are solved for the modal energy and response of
each subsystem. SEAM software was developed in 1980 to study structure-borne
noise in submarines, and was made commercially available in 1983. Since that time
SEAM has become an accepted analysis procedure by automobile manufacturers and
suppliers, major shipyards, Navy research establishments, and aerospace companies.
Cambridge Collaborative continues to advance the state of the art in statistical energy
analysis (SEA) through software development and research [1].
4.1.1. Seam Technical Features
Vibrational and acoustic energy flow techniques can be used in statistical energy
analysis while solving problems with the SEAM software package, which is the only
commercially-available software that provides a complete statistical representation of
the SEA response.
There are many of the standard features that come with SEAM on the following list
[1].
- Ability to develop very large models with thousands of SEA subsystems - Bending
and in plane subsystems for all structural elements
- Calculation of coupling loss factors and modal densities
- Transverse shear deformation corrections for bending of all structural elements
- Frequency dependent damping and material properties
- Octave, one-third-octave, narrowband and percentage bandwidth analysis
- Fast sparse matrix solution routines
- Prediction of input power and response mean and variance
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- Acoustic duct, layer, and space elements with one, two and three-dimensional
modal densities
- Design sensitivity analysis
- Transient analysis
- Interface to structural optimization programs
- Automatic calculation of properties for beam, plate and shell elements from cross-
section dimensions and materials
- Readable ASCII input and output files
- Choice of several different metric and English units, including mixed units
- Automatic generation of SEA subsystems from structural and acoustic elements
- Automatic generation of SEA junctions for each degree of freedom from structural
and acoustic point, line and area connections
- Parameter studies using symbolic constants and algebraic equations for input
parameters
- On-line context sensitive help
- Quick-look plotting for subsystem SEA parameters: modal energy, energy flow,
response, transfer functions, acoustic noise reduction, vibration reduction, and sound
transmission loss
- Acoustic damping using loss factors, absorption coefficients, or reverberation times
- Algebraic expressions for input parameters
4.1.2. Application Platforms
SEAM and visiSEAM are appropriate for both UNIX and PC-compatible computers.
Sun, Silicon Graphics, and Hewlett Packard workstations are supported [1].
4.2. AutoSEA2
Statistical Energy Analysis (SEA), which is called an analytical method, is used in
AutoSEA2 to approach noise and vibration reduction in design. With AutoSEA2,
noise and vibration problems can be modeled earlier in the design process,
eliminating costly mistakes before they go too far. AutoSEA2 is designed to work
closely with existing noise and vibration test processes, to build confidence in the
SEA results [2].
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[2]
4.2.1. Using of AutoSEA2
AutoSEA2 is applied to predict interior noise levels in automobiles, trucks, trains,
aircraft, ships, construction and agricultural equipment, and even the Space Station
Freedom! Prediction of noise radiated by the product under design is also possible
(consumer appliances, automobile pass-by noise, submarine radiated noise, etc.) as
well as prediction of vibration levels (launch acoustics, microgravity, and survival of
sensitive electronic equipment). The excitation mechanisms may include complex
acoustic fields, which is essential to treat problems such as propeller noise or
aerodynamic noise. New applications are under study in a number of companies [4].
4.2.2. Features [4]
4.2.2.1. Dimensional Modeling
All structural and acoustic subsystems are created
directly from design geometry and rendered as shaded
solids with AutoSEA2
-Models built faster
-Time saved and errors avoided updating models
-Avoids guestimation of radius, area, volume
[4]
-Eliminates error prone definition of junction angles & beam orientations
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-Immediate model verification- visually
-Improved communication of N&V design opportunities to management
4.2.2.2. Computation Engine
AutoSEA2 have been made the most widely used code in its
field by unique capabilities for aero-acoustic loads, ribbed-
shells and layered materials.
-Reliability of the proven industry standard
-Accuracy of full wave transmission theory
[4] -Intuitive – less dependence on user skill
-Confidence in results of Q.A.-tested code
4.2.2.3. Open-Architecture
AutoSEA2 is built on an open-architecture platform
designed with flexibility and expandability in mind
allowing users and third-party vendors to further expand
its functionality using Extension Modules.
[4]
4.2.2.4. Auto-Connect
Common boundary geometry is shared by point, line
and area junctions between all structural and acoustic
subsystems and, the junction is automatically detected
and computed.
[4]
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4.2.2.5. Multi-Model Integration
Team of designers or group of companies can develop
component parts of a large N&V design model by
AutoSEA2.
[4]
5. SEA IN SHIP INDUSTRY
The usage of SEA has begun to spread over the ship industry for last years. The most
crucial reason of this, undoubtedly, is the importance of preliminary calculations of
vibrations caused by main diesel engines and their auxiliary machines (Electric
Generators) and pumps. Great noise problems, which are the reason of the vibration
of machines, affect the living places on ship negatively. So, for ship design, these
calculations -made before- are important.
It is same with yacht industry. Especially, motor-yachts use high speed engines –
diesel or water jet. These machines make great noise and passengers may be
disturbed. SEA is used to predict this noise before and comfort of passengers can be
supplied. The following section is an example of an SEA usage in motor-yacht.
5.1. Sample of SEA Usage in a Yacht Design [13]
In yacht design, noise comfort must be revised because of being best in design race.
This sample of SEA model’s aim is to predict the airborne and structure-borne
transmission of noise from the source to saloon and cabin of a large luxury yacht. To
show the target reductions and effects of distinctive changes on the noise levels,
LMS-SEADS software is used for modeling. For this model, 150 elements, 10
onboard spaces, and nearly 400 subsystems are used. Figure 9 shows an example of
graphic network for a SEA model.
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Figure 9. Graphic network for a SEA model [6]
Getting good source data is among the most critical issues for providing a reasonable
prediction of expected absolute noise levels in the different interior spaces. The
structure-borne source strength for the resiliently mounted engines is expressed as
velocity levels in octaves on the engine feet in three directions and the data can
mostly be obtained from the engine manufacturer or eventually from measurements
made onboard existing craft.
The resilient mounts determine the exciting forces to the foundation, and reliable
dynamic transfer stiffness data for these are also important. These are however
harder to obtain from some manufacturers, also on demand.
It is essential that data for all directions is obtained as is shown by the example in
Figure 2, which shows the predicted vibration power input from a resiliently
mounted engine at full speed and load to the different subsystems of the foundation
bedplate.
This shows that the longitudinal wave power input to the foundation bedplate may
dominate in some cases, even without the use of a thrust bearing at the engine. The
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conversion to bending wave energy may be quite effective already in the near
vicinity of the engine bed structure due to many perpendicularly coupled plates.
The GRP-sandwich hull and deck sections are known to be efficient sound radiators
and proper modeling of these at least in the frequency range up to 1-2 kHz is
essential for reliable noise level predictions. Also the added mass effects of water
loading of the hull are large and important for the lightweight and stiff GRP
structure. The non-resonant mass-law transmission through partitions should as well
be accounted for by the software used.
[6]
The predictions of structure-borne sound and airborne sound levels for a new design
were compared to measurements from a reasonably similar but smaller yacht. The
measurements comprised airborne sound spectra for all compartments as well as a
reasonable number of vibration measurements at beds, propeller region and on
different parts of the hull at different cruising speeds as well as at harbor idle.
Airborne sound levels in cabins and saloon was also measured for airborne sound
excitation from the engine compartment.
The predicted sound pressure spectra as well as bedplate vibration levels for the new
design agreed generally within 5-8 dB with the measured levels in the existing
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smaller craft. The data are restricted and can not be published here. This gave us a
certain level of confidence for the reliability of the model.
An example of typical predicted A-weighted SPLs for different speed conditions and
separated between overall and airborne sound contribution only for one space is
shown in Figure 3. Typically, the airborne sound transmission dominates at mid and
higher frequencies for spaces close to the engine compartment, but the structure-
borne sound generated sound levels at lower frequency, especially around the diesel
engine firing frequency, are also too high for the original design.
The simulation of different reasonable noise reducing modifications to the hull
design and the airborne sound isolation of the partitions were investigated. Primarily,
reduction of the input vibration power to the engine foundation was investigated.
This may be achieved by reducing the mobility of the beds by e.g. introducing
substantial stiffening and eventually some additional damping to the bed structure to
reduce resonance peaks in the real part of these mobilities. Figure 4 shows a
preliminary and rough SEA prediction of the impact of additional stiffness to the bed
structure. Since this part of the boat is not very well suited for reliable SEA modeling
due to its stiffness and the resulting low modal density, this study was complemented
by a FEM calculation. A local model of the bottom structure of the engine
compartment was used to estimate the effect of proposed modifications on the
magnitude of the real part of the mobilities.
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[6]
[6]
6. CONCLUSION
In this report, a short overview was given on the basic ideas behind the method,
called Statistical Energy Analysis (SEA), which is based on energy variables. In
particular, theory and application of the most popular of this method was explained.
As seen through the report, SEA is used to predict sound pressure levels with a given
frequency band before the design is done. It works great between middle to high
frequency bandwidth. There was also given an example for usage of SEA in yacht
industry and was given the packet soft wares using SEA.
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[4] http://www.esi-group.com/SimulationSoftware/Vibro_acoustics/faq.html#autosea
[5] http://europa.eu.int/comm/research/brite-eu/thematic/html/2-2-07.html
[6] Kenny, A., April 2002, “Statistical Energy Analysis (SEA)”, Benchmark, p. 8-11
[7] Sarradj, E., 2004, “Energy Based Vibroacoustics: SEA and Beyond“,
CFA/DAGA, Strasbourg
[8] F. J. FAHY 0883 Philosophical Transactions of the Royal Society 235\ 320_336.
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[9] Langey, R. S., “A general derivation of the statistical energy analysis equations
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[13] Plunt, J., 1999, “The Use of Statistical Energy Analysis (SEA) for the Noise
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[14] Kopuz, Ş., 1998 “İstatistik Enerji Analizi (SEA) Yönteminin Otomotivdeki
Uygulamasına Bir Örnek”, 4. Ulusal Akustik Kongresi Bildiri Kitabı, p.147-156,
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[15] http://www.isvr.co.uk/modelling/sea.htm
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