1、raising standards worldwideNO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBSI Standards PublicationBS ISO 18437-5:2011Mechanical vibration and shock Characterization of thedynamic mechanical propertiesof visco-elastic materialsPart 5: Poisson ratio based on comparisonbetween m
2、easurements and finite elementanalysisBS ISO 18437-5:2011 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of ISO 18437-5:2011.The UK participation in its preparation was entrusted to TechnicalCommittee GME/21, Mechanical vibration, shock and conditionmonitoring.A list
3、 of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its correctapplication. BSI 2011ISBN 978 0 580 69158 4ICS 17.160Compliance with a British Stand
4、ard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strategy Committee on 31 May 2011.Amendments issued since publicationDate Text affectedBS ISO 18437-5:2011Reference numberISO 18437-5:2011(E)ISO 2011INTERNATIONAL STAND
5、ARD ISO18437-5First edition2011-04-15Mechanical 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 mcaniques Caractrisation des proprits mc
6、aniques dynamiques des matriaux visco-lastiques Partie 5: Nombre de Poisson obtenu par comparaison entre les mesures et lanalyse par lments finis BS ISO 18437-5:2011ISO 18437-5:2011(E) COPYRIGHT PROTECTED DOCUMENT ISO 2011 All rights reserved. Unless otherwise specified, no part of this publication
7、may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Te
8、l. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2011 All rights reservedBS ISO 18437-5:2011ISO 18437-5:2011(E) ISO 2011 All rights reserved iiiContents Page Foreword iv Introduction . v 1 Scope 1 2 Normative references 2 3 Terms and
9、definitions . 2 4 Background and measurement principles 3 5 Single-sample measurement method84 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 6 Two-sample measurement method58 6.1 Introduction 8 6.2 Basic the
10、ory . 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 (in
11、formative) Linearity of resilient materials . 12 Bibliography 13 BS ISO 18437-5:2011ISO 18437-5:2011(E) iv ISO 2011 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing I
12、nternational 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
13、 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 tech
14、nical 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 draw
15、n 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
16、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 o
17、n comparison between measurements and finite element analysis The following part is under preparation: Part 1: Principles and guidelines BS ISO 18437-5:2011ISO 18437-5:2011(E) ISO 2011 All rights reserved vIntroduction Visco-elastic materials are used extensively to reduce vibrations in structural s
18、ystems 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
19、 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
20、 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, meas
21、urement range, and the limitations of each apparatus. This part of ISO 18437 applies to the linear behaviour observed at small strain amplitudes. BS ISO 18437-5:2011BS ISO 18437-5:2011INTERNATIONAL STANDARD ISO 18437-5:2011(E) ISO 2011 All rights reserved 1Mechanical vibration and shock Characteriza
22、tion 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 poro
23、us-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 characte
24、ristics 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 t
25、he 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 typ
26、ical 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
27、 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 (a
28、irborne, 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
29、 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 provid
30、ed by manufacturers and suppliers; quality control. BS ISO 18437-5:2011ISO 18437-5:2011(E) 2 ISO 2011 All rights reserved2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated
31、 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 gu
32、idance 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 pre
33、paring 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 ela
34、stic 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 result
35、ing 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. NO
36、TE 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 th
37、e 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 BS ISO 18437-5:2011ISO 18437-5:2011(E) ISO 2011 All rights reserved 33.5 linearity property of the dynamic behaviou
38、r 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 x1(t) produces an output y1(t) and in a separate test an input x2(t) produces an output y2(t), superposition holds if the input x1(t) x2(t) produces th
39、e output y1(t) y2(t). This holds for all values of , and x1(t), x2(t); and are arbitrary constants. 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 t
40、ransfer 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
41、from uniformly distributed axial stress below the proportional limit of the material ISO 17561:200211, 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 i
42、s 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 sensit
43、ive 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
44、, 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 meas
45、ure 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 vib
46、ration 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 fulfil
47、led 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 shear modulus7. However, experimental difficulties may exist. Alternatively, a direct me
48、asurement of Poisson ratio may be possible using a laser vibrometer to measure the lateral displacement. BS ISO 18437-5:2011ISO 18437-5:2011(E) 4 ISO 2011 All rights reserved5 Single-sample measurement method85.1 Introduction In this method it is assumed that the Young modulus for the material of in
49、terest 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 t
