SIST EN ISO 11688-2:2001

Acoustics - Recommended practice for the design of low-noise machinery and equipment - Part 2: Introduction to the physics of low-noise design (ISO/TR 11688-2:1998)

Migrated from Progress Sheet (TC Comment) (2000-07-10): BC/CEN/88/13.212 is covered by WI 36 and 37. ++ Selected as type'B' (comparison) in the one language experiment ++ The TC Secretary want to publish a European Standard based on a published Inter- ++ national Technical Report ISO/TR 11688-2:1998 (TA/981012)

Akustik - Richtlinien für die Gestaltung lärmarmer Maschinen und Geräte - Teil 2: Einführung in die Physik der Lärmminderung durch konstruktive Maßnahmen (ISO/TR 11688-2:1998)

Dieser Teil von ISO/TR 11688 stellt den physikalischen Hintergrund zu den in Teil 1 wiedergegebenen Konstruktionsregeln und Beispielen dar. Darüber hinaus wird die Anwendung umfangreicher Fachliteratur gefördert. Die beabsichtigten Anwender sind Maschinen- und Gerätekonstrukteure ebenso wie deren Nutzer und/oder Käufer von Maschinen sowie Behörden im Bereich der Gesetzgebung und Überwachung. Die in dieser Norm wiedergegebenen Gleichungen fördern das allgemeine Verständnis der Lärmminderung und erlauben in vielen Fällen den Vergleich unterschiedlicher Konstruktionsvarianten.

Acoustique - Pratique recommandée pour la conception de machines et équipements a bruit réduit - Partie 2: Introduction a la physique de la conception a bruit réduit (ISO/TR 11688- 2:1998)

L'ISO/TR 11688-2:2002 traite du contexte physique, des règles et des exemples de conception à bruit réduit donnés dans l'ISO/TR 11688-1 et vient à l'appui d'une importante documentation spécialisée.
Elle est destinée à être utilisée par les concepteurs de machines et d'équipements ainsi que par les utilisateurs et/ou acheteurs de machines et les autorités agissant dans le domaine de la législation, ou de l'inspection.
Les équations indiquées dans l'ISO/TR 11688-2:2002 sont destinées à faciliter la compréhension générale de la réduction du bruit. Dans de nombreux cas, elles permettent une comparaison entre différentes versions d'une conception, mais ne sont pas utilisables pour la prévision de valeurs absolues d'émission sonore.
Les informations sur les sources sonores internes, les chemins de transmission et les parties d'une machine rayonnant du bruit constituent les données de base pour la réduction du bruit des machines. C'est pourquoi, des méthodes de mesurage et des méthodes de calcul appropriées pour obtenir ces informations sont décrites aux articles 7 et 8 et à l'annexe A.

Akustika - Priporočila za konstruiranje tihih strojev in naprav - 2. del: Fizikalne osnove za načrtovanje (ISO/TR 11688-2:1998)

General Information

• Status: Published
• Publication Date: 31-Aug-2001
• ICS: 17.140.20 - Noise emitted by machines and equipment
• ICS: 21.020 - Characteristics and design of machines, apparatus, equipment
• Technical Committee: AKU - Acoustics
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Sep-2001
• Due Date: 01-Sep-2001
• Completion Date: 01-Sep-2001
• Directive: 98/37/EC - Machinery
• Mandate: M/BC/CEN/88/13 - Standardization request to CEN/CENELEC relating to machinery
• Ref Project: EN ISO 11688-2:2000 - Acoustics - Recommended practice for the design of low-noise machinery and equipment - Part 2: Introduction to the physics of low-noise design (ISO/TR 11688-2:1998)

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 11688-2:2001
01-september-2001
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RVQRYH]DQDþUWRYDQMH,6275
Acoustics - Recommended practice for the design of low-noise machinery and
equipment - Part 2: Introduction to the physics of low-noise design (ISO/TR 11688-
2:1998)
Akustik - Richtlinien für die Gestaltung lärmarmer Maschinen und Geräte - Teil 2:
Einführung in die Physik der Lärmminderung durch konstruktive Maßnahmen (ISO/TR
11688-2:1998)
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EUXLWUpGXLW3DUWLH,QWURGXFWLRQDODSK\VLTXHGHODFRQFHSWLRQDEUXLWUpGXLW,6275


Ta slovenski standard je istoveten z: EN ISO 11688-2:2000
ICS:
17.140.20 Emisija hrupa naprav in Noise emitted by machines
opreme and equipment
21.020 =QDþLOQRVWLLQQDþUWRYDQMH Characteristics and design of
VWURMHYDSDUDWRYRSUHPH machines, apparatus,
equipment
SIST EN ISO 11688-2:2001 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 11688-2:2001

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SIST EN ISO 11688-2:2001

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SIST EN ISO 11688-2:2001

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SIST EN ISO 11688-2:2001
TECHNICAL ISO/TR
REPORT 11688-2
First edition
1998-09-01
Acoustics — Recommended practice for
the design of low-noise machinery and
equipment —
Part 2:
Introduction to the physics of low-noise design
Acoustique — Pratique recommandée pour la conception de machines et
équipements à bruit réduit —
Partie 2: Introduction à la physique de la conception à bruit réduit
A
Reference number
ISO/TR 11688-2:1998(E)

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SIST EN ISO 11688-2:2001
ISO/TR 11688-2:1998(E)
Contents
1  Scope . 1
2  References. 1
3  Definitions . 1
4  Acoustical modelling. 1
5  Control of airborne and liquid-borne noise. 2
5.1 Generation of fluid-dynamic noise. 2
5.2 Noise control measures . 8
6  Control of structure-borne sound. 10
6.1 Model of sound generation. 10
6.2 Internal sources . 15
6.3 Transmission of structure-borne sound . 18
6.4 Control of structure-borne sound transmission
by damping . 28
6.5 Radiation. 30
7  Analysis by measurement methods . 35
7.1 Purpose of the analysis. 35
7.2 Internal sources . 36
7.3 Transmission paths. 36
7.4 Radiation. 36
7.5 Summary of procedures for the analysis of existing
machinery by measurement methods. 37
8  Analysis by computational methods . 39
8.1 Purpose of the analysis. 39
8.2 Deterministic methods . 39
8.3 Statistical methods. 39
8.4 Applicability of computational methods . 39
Annex A Example of the estimation of airborne sound emission
of a machine caused by structure-borne and airborne sound
emission from a component . 41
Annex B Glossary. 44
Bibliography. 46
©  ISO 1998
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced
or utilized in any form or by any means, electronic or mechanical, including photocopying and
microfilm, without permission in writing from the publisher.
International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet [e-mail]
Printed in Switzerland
ii

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SIST EN ISO 11688-2:2001
©
ISO ISO/TR 11688-2:1998(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide
federation of national standards bodies (ISO member bodies). The work of
preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which
a technical committee has been established has the right to be represented
on that committee. International organisations, governmental and non-
governmental, in liaison with ISO, also take part in the work. ISO
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
The main task of technical committees is to prepare International
Standards, but in exceptional circumstances a technical committee may
propose the publication of a Technical Report of one of the following types:
— type 1, when the required support cannot be obtained for the
publication of an International Standard, despite repeated efforts;
— type 2, when the subject is still under technical development or where
for any other reason there is the future but not immediate possibility
of an agreement on an International Standard;
— type 3, when a technical committee has collected data of a different
kind from that which is normally published as an International
Standard ("state of the art", for example)
Technical Reports of types 1 and 2 are subject to review within three years
of publication, to decide whether they can be transformed into International
Standards. Technical Reports of type 3 do not necessarily have to be
reviewed until the data they provide are considered to be no longer valid or
useful.
ISO/TR 11688-2, which is a Technical Report of type 3, was prepared by
Technical Committee ISO/TC 43, Acoustics, Subcommittee SC 1, Noise.
ISO 11688 consists of the following parts, under the general title Acoustics
— Recommended practice for the design of low-noise machinery and
equipment:
— Part 1: Planning
— Part 2: Introduction to the physics of low-noise design
iii

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SIST EN ISO 11688-2:2001
©
ISO/TR 11688-2:1998(E) ISO
Introduction
The objective of this part of ISO/TR 11688 is noise reduction in existing
machinery and noise control at the design stage of new machinery.
It is important that non-acoustic engineers are engaged in noise control
practice. It is of great importance for these engineers to have a basic
knowledge of noise generation and propagation characteristics and to
understand the principles of noise control measures.
iv

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SIST EN ISO 11688-2:2001
TECHNICAL REPORT  © ISO ISO/TR 11688-2:1998(E)
Acoustics — Recommended practice for the design of low-noise
machinery and equipment —
Part 2:
Introduction to the physics of low-noise design
1 Scope
This part of ISO/TR 11688 provides the physical background for the low-noise design rules and examples given in
1)
ISO/TR 11688-1 and supports the use of extensive special literature.
It is intended for use by designers of machinery and equipment as well as users and/or buyers of machines and
authorities in the field of legislation, supervision or inspection.
Equations given in this Technical Report will improve the general understanding of noise control. In many cases
they allow a comparison of different versions of design, but they are not useful for the prediction of absolute noise
emission values.
Information on internal sound sources, transmission paths and sound radiating parts of a machine is the basis for
noise control in machines. Therefore measurement methods and computational methods suitable to obtain this
information are described in clauses 7 and 8 and annex A.
2 References
See ISO/TR 11688-1 and the bibliography.
3 Definitions
See ISO/TR 11688-1 and annex A.
4 Acoustical modelling
In order to facilitate the understanding of complex sound generation and propagation mechanisms in machinery and
equipment or vehicles (the latter are also called "machines" in this part of ISO/TR 11688), it is necessary to create
simple acoustical models. The models provide a basis for noise control measures at the design stage.

1)
ISO/TR 11688-1:1995, Acoustics — Recommended practice for the design of low-noise machinery and equipment — Part 1:
Planning.
1

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SIST EN ISO 11688-2:2001
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A universal approach is to distinguish between
 internal sources;
 transmission paths inside the machine;
 radiation from its boundaries.
The internal sources and the transmission paths can each be assigned to three categories according to the media
used:
 airborne;
 liquid-borne;
 structure-borne.
Radiation is considered for air only.
Figures 1 and 2 serve to illustrate the principle of acoustical modelling. Figure 1 shows a simplified machine
consisting of an electric motor and a housing with an opening in it.
The motor is the only internal source. It generates airborne and structure-borne sound.
There are three internal transmission paths:
 through the air inside the housing to the opening;
 through the air inside the housing to the walls of the housing;
 through the fastenings to the walls of the housing.
Radiation occurs from the opening and from the walls of the housing.
Figure 2 illustrates this in a block diagram.
The total sound power emitted from the machine is the sum of the three contributions.
A systematic approach starts with an assessment of the relative importance of these contributions. The next step is
examining the blocks in Figure 2 looking for possibilities to reduce source strength, transmission and/or radiation
(see also following clauses). This should be done in relation to the various aspects of the design process (see
ISO/TR 11688-1:1995, Figure 1).
5 Control of airborne and liquid-borne noise
The basic principles of generation, transmission and radiation of sound in air (or other gases) and liquids are
basically identical and are therefore considered together in this clause. There is only one important exception:
cavitation. Occurring in liquids only, this phenomenon is considered separately in 5.1.3.
5.1 Generation of fluid-dynamic noise
Important noise-generating phenomena in gases and liquids are turbulence, pulsation and shock. Fluid-dynamic
processes generate noise if flow rate and pressure vary over time in a limited volume of a liquid or a gas, for
example in a turbulent flow. This leads to the transmission of sound from the disturbed volume of the fluid to the
surrounding medium. A classic example of this is the escape of compressed air from a nozzle.
2

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Figure 1 — Simplified machine for the illustration of acoustical modelling
Figure 2 — Block diagram for the illustration of generation, transmission and radiation of sound in the
"machine" of Figure 1
Mechanisms of fluid-dynamic sound generation can be related to properties of elementary sound sources with
known characteristics:
 monopoles;
 dipoles;
 quadrupoles.
5.1.1 Elementary model sources
A monopole
source is an in-phase volume change, such as a pulsating volume of any shape or a piston in a large
rigid surface. In the far field, monopoles have a spherical radiation pattern. The sound radiated from a monopole
source can be reduced by reducing the temporal variation in the volume flow rate.
EXAMPLE 1: Outlets of internal combustion engines, rotary piston fans, multi-cell compressors, piston pumps, piston
compressors, flares.
A dipole source arises as a result of external time-variable forces acting on a fluid without volume change, such as
in an oscillating rigid body of any shape. The dipole source can be replaced by two monopole sources of equal
strength and opposite phase situated very closely together. The far-field directivity pattern of a dipole is shown in
Table 1. Radiation from a dipole can be reduced by reducing the temporal variation of the forces acting on the fluid.
EXAMPLE 2: Vibrating rigid parts of machinery, parts of machinery running out of balance, ducts, propellers and fans.
A quadrupole source can be represented by a time-variable deformation of a body without change of its volume or
position. It can be replaced by two dipole sources of equal strength and opposite phase situated very closely
3

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SIST EN ISO 11688-2:2001
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together. The far-field directivity pattern is shown in Table 1. Radiation from a quadrupole is reduced when the time-
variable deformation is reduced.
EXAMPLE 3: Free turbulent flow as in safety valves, compressed-air nozzles, pipe fittings.
Most sound sources encountered in machinery contain aspects of more than one elementary source.
NOTE  Because of the stochastic nature of turbulence the sound spectrum is broad-band. An example is the turbulent flow in
the mixing zone of a free jet, particularly for Mach numbers Ma > 0,8. The definition of the Mach number is:
u
Ma = (1)
c
where
u is the flow velocity;
c is the speed of sound.
Table 1 summarizes and illustrates the information on the properties of the elementary sources.
Table 1 — Properties of elementary model sources
Type of source Schematic illustration Example(s) Far-field directivity
Monopole Siren, piston compressor
or pump, exhaust of
"Breathing"
internal combustion
sphere
engine, cavitation
phenomena,
compressed air engine,
gas burner
Dipole Slow machines (axial
and centrifugal fans),
Oscillating
obstacles in the flow
sphere
(flow separation),
ventilating or air-
conditioning systems,
ducts with flow
Quadrupole Turbulent flow (mixing
zone of a free jet),
Two oscillating
compressed-air nozzles,
spheres with an
steam jet equipment,
opposite
safety valves
phaseshift (two
dipole sources)
5.1.2 Influence of main parameters
The sound power radiated by aerodynamic sound sources (e.g. the elementary source models monopole, dipole,
quadrupole) can be approximated by (see reference [17]):
k
u
  k
23 23
WD=rru = Du Ma (2)
  ()
 
c
4

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SIST EN ISO 11688-2:2001
© ISO
ISO/TR 11688-2:1998(E)
where
ρ is the density of the liquid,
D is the characteristic dimension of the elementary source,
u is the flow velocity,
k the exponent of the Mach number, which depends on the type of elementary source.
NOTE 1 The following is typical:
 k = 1 for a monopole source;
 k = 3 for a dipole source;
 k = 5 for a quadrupole source.
NOTE 2 Stüber and Heckl [18] have shown that for a three-dimensional sound field and three-dimensional sound
propagation the following relationship applies:
kn=−()32+(e−1) (3)
where
n is the dimension of the flow field and
e is the parameter of elementary sources (monopole: e = 1, dipole: e = 2, quadrupole: e = 3).
Table 2 shows a summary of the influence of flow velocity and flow field dimension on sound power emission.
Table 2 — Summary of functional relationship between the sound power, W, flow velocity, u, and dimension
of flow field, n (see reference [18])
Dimension n of flow field
n = 1 n = 2 n = 3
2 3
Mass flow fluctuation r
4
Wa~ru Wu~r
Wu~
(monopole)
a
Force fluctuation (dipole)
r r r
4 5 6
Wu~ Wu~ Wu~
2 3
a
a a
Turbulence (quadrupole)
r
r r
8
6 7
Wu~
Wu~ Wu~
5
3 4
a
a a
Since the sound power of a fluid-dynamic noise source (in a three-dimensional flow field) increases in proportion to
the fourth power for a monopole source, the sixth power for a dipole source and the eighth power for a quadrupole
source, a reduction in flow velocity leads to a considerable reduction of the sound energy emitted. For machines
with rotors, the demand for lower flow velocities also means that lower rotational speeds, i.e. lower peripheral
velocities, are required.
Figure 3 shows how the sound power level of a source varies along with a variation of the flow rate. If a
characteristic fluid-mechanical value (e.g. mass flow rate, volume flow rate, mechanical power consumption) is to be
conserved, a reduction of flow velocity must be compensated by an increase of the characteristic dimension D.
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SIST EN ISO 11688-2:2001
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Examples of the characteristic dimension are
 duct diameter for duct flow,
 impeller diameter in flow machines,
 smallest dimension of obstacles in flow,
 diameter of inlet or outlet nozzle.
u = given flow rate; u = reduced flow rate
1 2
Figure 3 — Reduction of sound emission by reduction of flow rate
(for three-dimensional sound propagation)
For a simple prediction or estimation of the sound power W of an aeroacoustic sound source mechanism, the
acoustic efficiency is an important value:
W
h = (4)
W
mech
where W is the mechanical or aerodynamic power of the flow.
mech
An empirical estimation for the sound power level is
W
mech
L = 120 dB + 10 lg h dB (5)
W
W
0
where W = 1 W.
0
Examples of acoustic efficiencies in aeroacoustics are summarized in Table 3.
Theoretical methods of high accuracy for predicting or estimating the sound power level or the sound power spectra
of fluid-borne sound are not generally available. Equation (2) can be written in a logarithmic form:
D
LL=+ 20 lg dB+kM⋅10 lga dB (6)
WWsp
D
0
If the specific sound power level L is known, acoustical data measured for certain configurations can be scaled
W
sp
using similarity laws, to apply to other configurations with different geometry, dimensions, flow velocities, static
pressure levels or flowing media.
For the conversion of spectra, a distinction must be made between broad band and tonal components. The
frequency of tonal noise is to be normalized with the Strouhal number St
fD
St = (7)
u
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SIST EN ISO 11688-2:2001
© ISO
ISO/TR 11688-2:1998(E)
Table 3 — Typical values of the acoustic efficiency
Aeroacoustic sound source Type of elementary source Acoustic efficiency η
Piston compressor (radiation in long duct monopole
p′
)
h =  *
system)
Δp
-1
Siren monopole
1 × 10
-2
Trumpet dipole
1 × 10
-3
Propeller aircraft dipole
1 × 10
-4 5
Outlet flow (subsonic flow Ma < 1) mixed
1 × 10 Ma
-4
Diesel engine (outlet flow noise) mixed
1 × 10
-5
Gas turbine mixed
1 × 10
-6
Flow machine (at design point) dipole
1 × 10
-4 5
Free turbulent jet quadrupole
1 × 10 Ma
-7
Propeller of a ship with cavitation monopole
1 × 10
*) p is the maximum value of variable pressure, Δp is the pressure difference.
5.1.3 Cavitation
Cavitation is a special effect occurring exclusively in liquids. Where local pressure drops below the vapour pressure,
cavitation will occur in flowing liquids. Bubbles are generated, which will collapse in a region of higher pressure. This
is illustrated in Figure 4. In a flowing liquid the pressure is determined by the Bernoulli equation
2
up
++ gz= const (8)
2 r
where
u
is the flow velocity
p is the static pressure
ρ is the density of the liquid
2
g 9,81 m/s
z is the height of liquid on top of the region of interest
p gz
NOTE  = ρ .
Equation (8) will allow the determination of low pressure regions where cavitation can occur. When entering a
region where the pressure exceeds the vapour pressure, the bubbles implode.
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SIST EN ISO 11688-2:2001
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ISO/TR 11688-2:1998(E)
Figure 4 — Generation and implosion of cavitation bubbles
Cavitation is avoided by maintaining low flow velocities in the suction line of the system. In low-pressure tubes,
bubbles can continue to exist if no pressure increase takes place after the generation. These bubbles are
transported to the reservoir and will enter the pump which results in sound generation. Separation of the bubbles
can be effected by placing a mesh in the reservoir between the inlet and outlet. To avoid cavitation, increase static
pressure and keep pressure differences low. Cavitation is a monopole source. For further measures to avoid
cavitation, see ISO/TR 11688-1.
5.2 Noise control measures
Some noise control measures and mechanisms for the generation of sound are described hereafter by using
important fluid-borne industrial sound sources as examples.
Obstacles in the flow
The obstacle is characterized in terms of fluid mechanics by the dimensionless drag coefficient ζ , the drag force F ,
w w
which is caused by the flow acting on the body,
F
w
z = (9)
w
r
2
uA
2
where, in general, A is the main cross-sectional area of the body.
An analysis of dimension shows that ζ is a function of the Reynolds number Re
w
uD⋅
Re = (10)
ν
and the length ratio where is the length and is the characteristic dimension of the obstacle. is the
L/D L D n
kinematic viscosity.
For Reynolds numbers > 100 the relation between sound power level and drag coefficient for a dipole source is
Re
A u
LL=+ 10 lg dB+ 30 lgz dB+ 60 lg dB (11)
WWsp w
A u
00
2
with A = 1 m and u = 1 m/s.
0 0
8

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SIST EN ISO 11688-2:2001
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ISO/TR 11688-2:1998(E)
The specific sound power level L of ventilation grids, for example, is 10 dB.
W
sp
The above equations show that noise reduction is achieved by
 reduction of flow speed (u),
 downscaling of the bodies in the flow (A),
 disturbance of vortex street (A, ζ ),
w
 streamlining of the outer shape of the body (A constant, reduce ζ ).
w
Duct and pipe flow
At ducts and pipes with installations (bends, diffusers, changes of cross-sectional area) sound sources are:
 separation which causes secondary flow regions;
 turbulence due to shear layers of different speed (or density).
Separated flow regions and pulsating secondary flows have a dipole source character.
Flow machines
The rotating pressure field of the impeller is one important sound source in flow machines. In centrifugal fans the
radial gap between the impeller and the casing is the most important value for (discrete) noise emission. In axial
fans the number of impeller and vane blades have a large influence on the sound power level of the blade passing
frequency. The tip clearance ratio (the gap between impeller and casing wall) in axial turbo-machines is also
important for noise emission.
Generally a flow machine with high aerodynamic efficiency has a low noise emission.
The fan installation has an important influence on sound generation, because disturbed inlet flow profiles causes
high pressure fluctuations in addition to the sound of the rotating pressure field.
For Mach numbers Ma < 0,3 the predominant sound generation mechanisms have dipole character.
Measures for noise control are:
 low tip speed of impeller;
 large casing (centrifugal fans);
 small tip clearance (axial fans);
 no blade and vane numbers which are multiples or submultiples (spinning modes generated by the fan cannot
propagate).
Free jets
The noise of a free jet originates in the turbulent mixing region approximately four to five diameters downstream of
the outlet nozzle. That means that the sound is mainly generated in the mixing layer through differences in Mach
numbers.
Noise control is possible by
 reducing flow speed (increasing outlet dimensions);
 avoiding obstacles in the flow;
 reducing differences of Mach numbers between outlet flow and surrounding ambient flow field;
 frequency shift by replacing large openings by smaller ones.
9

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SIST EN ISO 11688-2:2001
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6 Control of structure-borne sound
6.1 Model of sound generation
Structure-borne sound is generated when a structure (e.g. a machine housing) is excited by a time-variable force or
velocity.
The causal chain of the structure-borne sound generation can be described by the model displayed in Figure 5.
According to this model the radiated sound power of a machine can be determined from an excitation function (the
force or velocity spectrum) together with quantities representing the vibrational transmission (h , h ) and radiation
TF T
v
efficiency (σ) of an excited structure
F , V : excitation force and velocity
1 1
, : transmission quantities
h h
TF Tv
V : velocity of the radiating surface
2
s: radiation efficiency
W: radiated sound power
Figure 5 — Mechanical sound generation
The excitational quantities not only include all quantities arising from mechanical processes such as impacts or
unbalances, but all physical processes which can excite vibrations in mechanical structures, such as magnetic flux
(electric motors) or non-stationary forces of fluid flow (pumps, internal combustion engines). Excitation by airborne
sound is not considered.
Machine structures include housings, frames and claddings as well as moving parts insofar as these transmit and/or
radiate sound when the machine is in operation.
For problems of low-noise design, it is convenient to use a simplified model with the following features:
 The excitational quantity is described by the frequency spectrum corresponding to its time function.
 The point of force excitation is characterized by its mechanical impedance or admittance (mobility).
 The passive machine structure is characterized by a frequency-dependent overall transfer function for
frequency-bands.
 Complex machine components are simplified by reduction to basic structural elements (plates, beams etc.).
 The structure-borne sound transmission is described by approximations.
 The radiation behaviour of vibrating structures is described by approximations.
Furthermore the following assumptions are made:
 linearity of the transmission characteristics of the structure; noisy "loose connections" (for example, the rattling
of cladding sheets etc.) in the passive structure have to be treated as new sources;
 point-like and unidirectional excitation;
 incoherence of excitations, i.e. the effect of each excitation can be examined separately and the overall effect
calculated by energetic addition.
On the basis of these assumptions two special cases of structure-borne sound excitation can be distinguished:
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SIST EN ISO 11688-2:2001
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F , V : excitation force or velocity
1 1
h : internal source admittance
a
h : load admittance
p
Figure 6 — Source-receiver model
Figure 7 — Schematic cross-section of diesel engine
Force excitation:
The excitation can be described approximately by force alone, i.e. without the complex values of the frequency-
dependent admittances h and h (see Figure 6). This is allowed if the source admittance is much greater than the
a p
admittance of the excited system (passive noise element). Thus h . h for high admittance sources (force
a p
sources). For mass controlled structures with h = 1/jw m it follows that m . m . Example: Piston pressure excites

a p a
engine structure (see Figure 7).
Velocity excitation:
The velocity at the connection between source and load does not depend upon the respective admittance if h ,, h
a p
m m
(for mass controlled systems . ). This is often true at the periphery of machines. Example: Thick-walled cast
a p
iron housing excites thin sheet metal (see Figure 7).
The decision "force or velocity excitation" is of great practical importance for the choice of effective noise control
measures for machines.
A mathematical description of the model in Figure 5 relies upon the definition of the radiation efficiency σ which is
defined indirectly through the radiated sound power:
2
Wf =rscv f S f (12)
() ( ) ()
where
11

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SIST EN ISO 11688-2:2001
© ISO
ISO/TR 11688-2:1998(E)
ρc is the characteristic impedance;
ρ is the density of air;
c is the speed of sound;
2
v f is the spatially averaged mean square value of the velocity of the radiating surface;
()
σ is the radiation efficiency for a typical frequency characteristic, see Figure 29;
S is the radiating surface area of the structure.
2
v
2 2
For the case of force excitation an energetic model (Figure 8) can be described by hf= , the squared
()
TF
2
F
1
velocity transmission mobility, which is the squared ratio of the mean velocity of the radiating surface and the
exciting force.
2
V
2 2
For velocity excitation refer to Figure 9 with h = the squared velocity transmission. By applying the definition
Tv
2
V
1
of σ the radiated sound power due to force excitation reads
Wf() 1
22
=⋅rsch f f S=rc⋅h f ⋅s fS⋅ (13)
() () () ()
TTF v
2 2
Ff Zf
() ()
1 1
Ff()
1
with = the driving point impedance, i.e. the impedance at the point of force excitation. Thus a reduction
Zf()
1
v f
()
1
of the sound power radiated
...