ISO 18437-5:2011

Mechanical vibration and shock — Characterization of the dynamic mechanical properties of visco-elastic materials — Part 5: Poisson ratio based on comparison between measurements and finite element analysis

ISO 18437-5:2011 specifies two methods for estimating Poisson ratio or/and elastic modulus for isotropic visco-elastic or porous-elastic materials for use in linear finite element method (FEM) computer programs or other numerical approaches to vibrational or acoustic problems in visco-elastic structures of complicated geometry. The method is based on comparison between measurements of force-deflection or stiffness characteristics for disc-shaped specimens, with bonded boundary conditions at both ends, and FEM calculations of those conditions as a function of Poisson ratio. The choice of the single-sample or two-sample measurement method depends on whether the Poisson ratio is to be determined alone or together with the elastic modulus. Sometimes these materials are considered to be incompressible and behave non-linearly especially in large static deformations. Many commercial codes are available to solve such problems. This is not the case in ISO 18437-5:2011, where only small deformations observed in typical vibration problems are considered and, hence, linear FEM codes are adequate and more convenient. For the purposes of ISO 18437-5:2011, and within the framework of ISO/TC 108, the term dynamic mechanical properties refers to the determination of the fundamental elastic properties, e.g. the complex Young modulus and Poisson ratio, as a function of temperature and frequency. ISO 18437-5:2011 is applicable to resilient materials that are used in vibration isolators in order to reduce: a) transmission of audio frequency vibrations to a structure, e.g. radiating fluid-borne sound (airborne, structure-borne, or other); b) transmission of low-frequency vibrations which can, for example, act upon humans or cause damage to structures or equipment when the vibration is too severe. The data obtained with the measurement methods that are outlined in ISO 18437-5:2011 and further detailed in ISO 18437-2 to ISO 18437-4 can be used for: 1) design of efficient vibration isolators; 2) selection of an optimum resilient material for a given design; 3) theoretical computation of the transfer of vibrations through isolators; 4) information during product development; 5) product information provided by manufacturers and suppliers; 6) quality control.

Vibrations et chocs mécaniques — Caractérisation des propriétés mécaniques dynamiques des matériaux visco-élastiques — Partie 5: Nombre de Poisson obtenu par comparaison entre les mesures et l'analyse par éléments finis

General Information

• Status: Published
• Publication Date: 13-Apr-2011
• ICS: 17.160 - Vibrations, shock and vibration measurements
• Technical Committee: ISO/TC 108 - Mechanical vibration, shock and condition monitoring
• Drafting Committee: ISO/TC 108/WG 28 - Vibration materials
• Current Stage: 9093 - International Standard confirmed
• Completion Date: 14-Feb-2023

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 18437-5
First edition
2011-04-15


Mechanical vibration and shock —
Characterization of the dynamic
mechanical properties of visco-elastic
materials —
Part 5:
Poisson ratio based on comparison
between measurements and finite
element analysis
Vibrations et chocs mécaniques — Caractérisation des propriétés
mécaniques dynamiques des matériaux visco-élastiques —
Partie 5: Nombre de Poisson obtenu par comparaison entre les
mesures et l'analyse par éléments finis




Reference number
ISO 18437-5:2011(E)
©
ISO 2011

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ISO 18437-5:2011(E)

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©  ISO 2011
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ii © ISO 2011 – All rights reserved

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ISO 18437-5:2011(E)
Contents Page
Foreword . iv
Introduction . v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions . 2
4 Background and measurement principles . 3
[8]
5 Single-sample measurement method . 4
5.1 Introduction . 4
5.2 Basic theory . 4
5.3 Specimen geometry and frequency range . 4
5.4 Stiffness measurement . 7
5.5 Data acquisition . 7
[5]
6 Two-sample measurement method . 8
6.1 Introduction . 8
6.2 Basic theory . 8
6.3 Determining Poisson ratio . 9
6.4 Specimen geometry and frequency range . 9
6.4.1 General . 9
6.4.2 Data acquisition . 10
7 Test equipment . 10
8 Sample preparation and mounting . 11
9 Sample conditioning . 11
10 Main sources of uncertainty . 11
11 Time-temperature superposition . 11
Annex A (informative) Linearity of resilient materials . 12
Bibliography . 13

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ISO 18437-5:2011(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 organizations, 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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 18437-5 was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and condition
monitoring.
ISO 18437 consists of the following parts, under the general title Mechanical vibration and shock —
Characterization of the dynamic mechanical properties of visco-elastic materials:
 Part 2: Resonance method
 Part 3: Cantilever shear beam method
 Part 4: Dynamic stiffness method
 Part 5: Poisson ratio based on comparison between measurements and finite element analysis
The following part is under preparation:
 Part 1: Principles and guidelines
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ISO 18437-5:2011(E)
Introduction
Visco-elastic materials are used extensively to reduce vibrations in structural systems through dissipation of
energy (damping) or isolation of components and noise levels in acoustical applications through modification
of reflection, transmission, or absorption of acoustic energy. It is often required to have specific dynamic
mechanical properties in order for such materials to function in an optimum manner. Energy dissipation is due
to interactions on the molecular scale and can be measured in terms of the lag between stress and strain in
the material. The dynamic mechanical properties, such as Young modulus, loss factor and Poisson ratio, of
most visco-elastic materials depend on frequency, temperature, pre-strain and strain amplitude. The choice of
a specific material for a given application determines the system performance. The goal of this part of
ISO 18437 is to provide brief descriptions of several methods, the details in construction of each apparatus,
measurement range, and the limitations of each apparatus. This part of ISO 18437 applies to the linear
behaviour observed at small strain amplitudes.

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INTERNATIONAL STANDARD ISO 18437-5:2011(E)

Mechanical vibration and shock — Characterization of the
dynamic mechanical properties of visco-elastic materials —
Part 5:
Poisson ratio based on comparison between measurements
and finite element analysis
1 Scope
This part of ISO 18437 specifies two methods for estimating Poisson ratio or/and elastic modulus for isotropic
visco-elastic or porous-elastic materials for use in linear finite element method (FEM) computer programs or
other numerical approaches to vibrational or acoustic problems in visco-elastic structures of complicated
geometry. The method is based on comparison between measurements of force-deflection or stiffness
characteristics for disc-shaped specimens, with bonded boundary conditions at both ends, and FEM
calculations of those conditions as a function of Poisson ratio. The choice of the single-sample or two-sample
measurement method depends on whether the Poisson ratio is to be determined alone or together with the
elastic modulus. Sometimes these materials are considered to be incompressible and behave non-linearly
especially in large static deformations. Many commercial codes are available to solve such problems. This is
not the case in this part of ISO 18437, where only small deformations observed in typical vibration problems
are considered and, hence, linear FEM codes are adequate and more convenient.
For the purposes of this part of ISO 18437, and within the framework of ISO/TC 108, the term dynamic
mechanical properties refers to the determination of the fundamental elastic properties, e.g. the complex
Young modulus and Poisson ratio, as a function of temperature and frequency.
This part of ISO 18437 is applicable to resilient materials that are used in vibration isolators in order to reduce:
a) transmission of audio frequency vibrations to a structure, e.g. radiating fluid-borne sound (airborne,
structure-borne, or other);
b) transmission of low-frequency vibrations which can, for example, act upon humans or cause damage to
structures or equipment when the vibration is too severe.
The data obtained with the measurement methods that are outlined in this part of ISO 18437 and further
detailed in ISO 18437-2 to ISO 18437-4 can be used for:
 design of efficient vibration isolators;
 selection of an optimum resilient material for a given design;
 theoretical computation of the transfer of vibrations through isolators;
 information during product development;
 product information provided by manufacturers and suppliers;
 quality control.
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ISO 18437-5:2011(E)
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 472, Plastics — Vocabulary
ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
ISO 4664-1, Rubber, vulcanized or thermoplastic — Determination of dynamic properties — Part 1: General
guidance
ISO 6721-1, Plastics — Determination of dynamic mechanical properties — Part 1: General principles
ISO 10846-1, Acoustics and vibration — Laboratory measurement of vibro-acoustic transfer properties of
resilient elements — Part 1: Principles and guidelines
ISO 23529, Rubber — General procedures for preparing and conditioning test pieces for physical test
methods
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 472, ISO 2041, ISO 4664-1,
ISO 6721-1, ISO 10846-1, and ISO 23529 and the following apply.
3.1
dynamic mechanical properties
fundamental elastic properties of a visco-elastic material, i.e. elastic modulus, shear modulus, bulk modulus
and loss factor
3.2
resilient material
visco-elastic material intended to reduce the transmission of vibration, shock or noise
3.3
Young modulus
quotient of normal stress (tensile or compressive) to resulting normal strain or fractional change in length for a
long specimen of resilient material
NOTE 1 The Young modulus is expressed in pascals.
NOTE 2 The Young modulus for visco-elastic materials which are isotropic is a complex quantity with symbol E*,
having a real part E and an imaginary part E.
NOTE 3 Physically, the real component of the Young modulus is related to the stored mechanical energy. The
imaginary component is a measure of mechanical energy loss.
3.4
loss factor
ratio of the imaginary part of the Young modulus of a material to the real part of the Young modulus (the
tangent of the argument of the complex Young modulus)
NOTE When there is energy loss in a material, the strain lags the stress by a phase angle, . The loss factor is equal
to tan .
[ISO 18437-2, 3.2]
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ISO 18437-5:2011(E)
3.5
linearity
property of the dynamic behaviour of a resilient material if it satisfies the principle of superposition
NOTE 1 The principle of superposition can be stated as follows: if an input x (t) produces an output y (t) and in a
1 1
separate test an input x (t) produces an output y (t), superposition holds if the input x (t)  x (t) produces the output
2 2 1 2
y (t)  y (t). This holds for all values of ,  and x (t), x (t);  and  are arbitrary constants.
1 2 1 2
NOTE 2 In practice the above test for linearity is impractical and measuring the dynamic modulus for a range of input
levels does a limited check of linearity. For a specific preload, if the dynamic transfer modulus is nominally invariant, the
system measurement can be considered linear. In effect this procedure checks for a proportional relationship between the
response and the excitation.
[ISO 18437-2, 3.7]
3.6
Poisson ratio
ratio of transverse strain to the corresponding axial strain resulting from uniformly distributed axial stress
below the proportional limit of the material
[11]
[ISO 17561:2002 , 3.1.1]
3.7
shape factor
ratio of the area of one loaded surface to the total force-free area in a sample for compression or tension test
with bonded ends
4 Background and measurement principles
It is very difficult for numerical analysts to select the Poisson ratio properly in linear FEM analysis. The reason
is that the Poisson ratio of visco-elastic materials, which is known to be close to 0,5, is rarely provided by the
material manufacturers while the computation results are extremely sensitive to the Poisson ratio at values
neighbouring 0,5. This part of ISO 18437 uses a quasi-static method for determining the Poisson ratio of a
visco-elastic material or a porous-elastic material. The method is based on the relationship between the
compressional stiffness, Young modulus, Poisson ratio, and shape factor obtained from axisymmetrical finite
element calculations on a disc-shaped sample under static compression. The relationship accounts for the
fact that the disc sample bulges sideways when compressed between two rigid plates on which it is bonded. A
compression test is used to measure the stiffness of the sample.
The conditions for the validity of the estimation methods are:
a) linearity of the vibrational behaviour of the isolator;
NOTE 1 This includes elastic elements with non-linear static load-deflection characteristics where the elements show
approximate linearity in vibration behaviour at a given static preload.
b) interfaces of the vibration isolator with the adjacent source and receiver structures can be considered as
surface contacts;
c) no interaction between the isolator and the surrounding fluid (usually air) medium.
NOTE 2 This condition is typically fulfilled at frequencies less than 100 Hz for isolators made from open-cell porous-
elastic materials (e.g. foams).
The Poisson ratio may also be determined by measuring other elastic constants such as complex bulk and
[7]
shear modulus . However, experimental difficulties may exist. Alternatively, a direct measurement of Poisson
ratio may be possible using a laser vibrometer to measure the lateral displacement.
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ISO 18437-5:2011(E)
[8]
5 Single-sample measurement method
5.1 Introduction
In this method it is assumed that the Young modulus for the material of interest is determined using other
techniques, such as those specified in ISO 18437-2 to ISO 18437-4. The key idea and practice of this method
is simply to prepare a chart of dimensionless stiffness versus Poisson ratio for a disc-shaped specimen by
FEM computations, to measure the stiffness from an excitation test using a test rig and measurement
equipment such as those in ISO 18437-4, and to select a value of Poisson ratio from the chart corresponding
to the measured stiffness. In this method, the size of the sample is not specified, but a large shape factor is
required.
5.2 Basic theory
Let a circular cylindrical visco-elastic or porous-elastic specimen of thickness, T, cross-sectional area,
2
A  D /4, and Young modulus, E, with bonded boundary conditions at both ends, as shown in Figure 1, be
subject to an axial load, F, and for which a corresponding deflection, , occurs. Then, a factor defined by
FT
R (1)
AE
that may be called dimensionless stiffness, is known to be ideally 1,0 for thick specimens. Numerical
computations for three sample specimens of different geometric shapes, but of one given material in
[2]
Figure 2 show that the factor, R, depends on the Poisson ratio, v, and on the shape factor as a parameter.
For a disc-shaped sample the shape factor, S, is given by
D
S (2)
4T
The ordinate in Figu
...