ISO 7626-2:2015

INTERNATIONAL ISO
STANDARD 7626-2
Second edition
2015-04-01
Mechanical vibration and shock —
Experimental determination of
mechanical mobility —
Part 2:
Measurements using single-point
translation excitation with an attached
vibration exciter
Vibrations et chocs — Détermination expérimentale de la mobilité
mécanique —
Partie 2: Mesurages avec utilisation d’une excitation de translation en
un seul point, au moyen d’un générateur de vibrations solidaire de ce
point
Reference number
ISO 7626-2:2015(E)
©
ISO 2015

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ISO 7626-2:2015(E)

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ISO 7626-2:2015(E)

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Overall configuration of the measurement system . 2
5 Support of the structure under test . 3
5.1 General . 3
5.2 Grounded measurements . 3
5.3 Ungrounded measurements . 3
6 Excitation . 4
6.1 General . 4
6.2 Excitation waveforms . 4
6.2.1 General. 4
6.2.2 Discretely dwelled sinusoidal excitation . 4
6.2.3 Slowly swept sinusoidal excitation . 5
6.2.4 Stationary random excitation . 5
6.2.5 Other excitation waveforms . 5
6.3 Vibration exciters . 5
6.4 Avoidance of spurious forces and moments . 8
6.4.1 General. 8
6.4.2 Transducer mass loading . 8
6.4.3 Transducer rotational inertia loading . 8
6.4.4 Exciter attachment restraints . 8
7 Measurement of the exciting force and resulting motion response .9
7.1 General . 9
7.2 Attachment of transducers . 9
7.3 Mass loading and mass cancellation .10
7.4 Signal amplifiers .10
7.5 Calibrations .11
7.5.1 General.11
7.5.2 Operational calibration .11
8 Processing of the transducer signals .14
8.1 Determination of the frequency-response function .14
8.1.1 General.14
8.1.2 Sinusoidal excitation .14
8.1.3 Random excitation .14
8.2 Filtering .14
8.2.1 Sinusoidal excitation .14
8.2.2 Random excitation .14
8.3 Avoidance of saturation .15
8.4 Frequency resolution.15
8.4.1 General.15
8.4.2 Sinusoidal excitation .15
8.4.3 Random excitation .15
8.4.4 Periodic excitation .15
9 Control of the excitation .16
9.1 General .16
9.2 Time required for sinusoidal excitation .16
9.2.1 General.16
9.2.2 Discretely dwelled sinusoidal excitation .16
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ISO 7626-2:2015(E)

9.2.3 Slowly swept sinusoidal excitation .17
9.3 Time required for random excitation .17
9.4 Dynamic range.18
9.4.1 General.18
9.4.2 Sinusoidal excitation .18
9.4.3 Random excitation .18
10 Tests for valid data .18
11 Modal parameter identification .19
Annex A (normative) Tests for validity of measurement results .20
Annex B (normative) Requirements for excitation frequency increments and duration .23
Annex C (informative) Modal parameter identification .25
Bibliography .26
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ISO 7626-2:2015(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
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of any
patent rights identified during the development of the document will be in the Introduction and/or on
the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT), see the following URL: Foreword — Supplementary information.
The committee responsible for this document is ISO/TC 108, Mechanical vibration, shock and condition
monitoring.
This second edition cancels and replaces the first edition (ISO 7626-2:1990), which has been technically
revised.
ISO 7626 consists of the following parts, under the general title Mechanical vibration and shock —
Experimental determination of mechanical mobility:
— Part 1: Basic terms and definitions, and transducer specifications
— Part 2: Measurements using single-point translational excitation with an attached vibration exciter
— Part 5: Measurements using impact excitation with an exciter which is not attached to the structure
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ISO 7626-2:2015(E)

Introduction
General introduction to the ISO 7626- series on mobility measurement
Dynamic characteristics of structures can be determined as a function of frequency from mobility
measurements or measurements of the related frequency-response functions, known as accelerance and
dynamic compliance. Each of these frequency-response functions is the phasor of the motion response
at a point on a structure due to a unit force (or moment) excitation. The magnitude and the phase of
these functions are frequency-dependent.
Accelerance and dynamic compliance differ from mobility only in that the motion response is expressed
in terms of acceleration and displacement, respectively, instead of in terms of velocity. In order to
simplify the various parts of ISO 7626, only the term “mobility” is used. It is understood that all test
procedures and requirements described are also applicable to the determination of accelerance and
dynamic compliance.
Typical applications for mobility measurements are for:
a) predicting the dynamic response of structures to known or assumed input excitation;
b) determining the modal properties of a structure (natural frequencies, damping ratios and mode
shapes);
c) predicting the dynamic interaction of interconnected structures;
d) checking the validity and improving the accuracy of mathematical models of structures;
e) determining dynamic properties (i.e. the complex modulus of elasticity) of materials in pure or
composite forms.
For some applications, a complete description of the dynamic characteristics can be required using
measurements of translational forces and motions along three mutually perpendicular axes as well as
measurements of moments and rotational motions about these three axes. This set of measurements
results in a 6 × 6 mobility matrix for each location of interest. For N locations on a structure, the system
thus has an overall mobility matrix of size 6N × 6N.
For most practical applications, it is not necessary to know the entire 6N × 6N matrix. Often it is
sufficient to measure the driving-point mobility and a few transfer mobilities by exciting with a force at
a single point in a single direction and measuring the translational response motions at key points on
the structure. In other applications, only rotational mobilities might be of interest.
Mechanical mobility is defined as the frequency-response function formed by the ratio of the phasor
of the translational or rotational response velocity to the phasor of the applied force or moment
excitation. If the response is measured with an accelerometer, conversion to velocity is required to
obtain the mobility. Alternatively, the ratio of acceleration to force, known as accelerance, can be used
to characterize a structure. In other cases, dynamic compliance, the ratio of displacement to force, can
be used.
NOTE Historically, frequency-response functions of structures have often been expressed in terms of the
reciprocal of one of the above-named dynamic characteristics. The arithmetic reciprocal of mechanical mobility
has often been called mechanical impedance. It should be noted, however, that this is misleading because the
arithmetic reciprocal of mobility does not, in general, represent any of the elements of the impedance matrix of
a structure. Rather, conversion of mobility to impedance requires an inversion of the full mobility matrix. This
point is elaborated upon in ISO 7626-1.
Mobility test data cannot be used directly as part of an impedance model of the structure. In order to
achieve compatibility of the data and the model, the impedance matrix of the model is converted to
mobility or vice versa (see ISO 7626-1 for limitations).
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ISO 7626-2:2015(E)

Introduction to this part of ISO 7626
For many applications of mechanical mobility data, it is sufficient to determine the driving-point
mobility and a few transfer mobilities by exciting the structure at a single location in a single direction
and measuring the translational response motions at key points on the structure. The translational
excitation force can be applied either by vibration exciters attached to the structure under test or by
devices that are not attached.
Categorization of excitation devices as “attached” or “unattached” has significance in terms of the ease
of moving the excitation point to a new position. It is much easier, for example, to change the location of
an impulse applied by an instrumented hammer than it is to relocate an attached vibration exciter to a
new point on the structure. Both methods of excitation have applications to which they are best suited.
This part of ISO 7626 deals with measurements using a single attached exciter; measurements made by
impact excitation without the use of attached exciters are covered by ISO 7626-5.
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INTERNATIONAL STANDARD ISO 7626-2:2015(E)
Mechanical vibration and shock — Experimental
determination of mechanical mobility —
Part 2:
Measurements using single-point translation excitation
with an attached vibration exciter
1 Scope
This part of ISO 7626 specifies procedures for measuring linear mechanical mobility and other frequency-
response functions of structures, such as buildings, machines and vehicles, using a single-point
translational vibration exciter attached to the structure under test for the duration of the measurement.
It is applicable to measurements of mobility, accelerance, or dynamic compliance, either as a driving-
point measurement or as a transfer measurement. It also applies to the determination of the arithmetic
reciprocals of those ratios, such as free effective mass. Although excitation is applied at a single point,
there is no limit on the number of points at which simultaneous measurements of the motion response
may be made. Multiple-response measurements are required, for example, for modal analyses.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 2041, Mechanical vibration, shock and condition monitoring — Vocabulary
ISO 7626-1, Mechanical vibration and shock — Experimental determination of mechanical mobility —
Part 1: Basic terms and definitions, and transducer specifications
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 7626-1 and ISO 2041 and the
following apply.
Note As this part of ISO 7626 deals with mechanical mobility, the notes to the definitions below provide
more detail than is given in ISO 2041.
3.1
frequency-response function
frequency dependent ratio of complex motion response to complex excitation force for a linear system
Note 1 to entry: Excitation may be harmonic, random or transient functions of time. The frequency-response
function does not depend on the type of excitation function if the tested structure can be considered a linear
system in a certain range of the excitation or response. In such a case, the test results obtained with one type of
excitation may be used for estimating the response of the system to any other type of excitation. Phasors and their
equivalents for random and transient excitation are discussed in Annex B.
Note 2 to entry: Linearity of the system is a condition which, in practice, is met only approximately, depending on
the type of system and on the magnitude of the input. Care has to be taken to avoid nonlinear effects, particularly
when applying impulse excitation. Structures which are known to be nonlinear (e.g. structures with fluid
elements) should not be tested with impulse excitation and great care is required when using random excitation
for testing of such structures.
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ISO 7626-2:2015(E)

Note 3 to entry: Motion may be expressed in terms of velocity, acceleration or displacement; the corresponding
frequency response function designations are mobility, accelerance and dynamic compliance, respectively. In
some publications, these quantities are alternately referred to (in whole or in part) as mechanical admittance,
inertance and receptance, respectively. These alternate terms are avoided herein, and are provided only for
reference.
[SOURCE: ISO 2041:2009, 1.53, modified]
3.2
mobility
mechanical mobility
complex ratio of the velocity, taken at a point in a mechanical system, to the excitation force, taken at the
same or other point in the system
Note 1 to entry: Mobility is the ratio of the complex velocity-response at point i to the complex excitation force
at point j with all other measurement points on the structure allowed to respond freely without any constraints
other than those constraints which represent the normal support of the structure in its intended application.
Note 2 to entry: The term “point”, as used here, designates both a location and a direction. The terms “coordinate”
and “degree-of-freedom” have also been used with the same meaning as “point”.
Note 3 to entry: The velocity response can be either translational or rotational, and the excitation force can be
either a rectilinear force or a moment.
Note 4 to entry: If the velocity response measured is a translational one and if the excitation force applied is a
rectilinear one, the units of the mobility term are m/(N · s) in the SI system.
Note 5 to entry: Mechanical mobility is an element of the inverse of mechanical impedance matrix.
[SOURCE: ISO 2041:2009, 1.54, modified]
3.3
driving-point mobility
Y
jj
frequency-response function formed by the complex velocity-response at point j to the complex excitation
force applied at the same point with all other measurement points on the structure allowed to respond
freely without any constraint other than those constraints which represent the normal support of the
structure in its intended application
[SOURCE: ISO 2041:2009, Note to 1.55, modified]
3.4
transfer mobility
Y
ij
frequency-response function formed by the complex velocity-response at point i to the complex excitation
force applied at point j with all points on the structure, other than j, allowed to respond freely without
any constraint other than those constraints which represent the normal support of the structure in its
intended application
[SOURCE: ISO 2041:2009, 1.56, modified]
3.5
frequency range of interest
span between the lowest frequency to the highest frequency at which mobility data are to be obtained
in a given test series
[SOURCE: ISO 7626-1:2011, 3.1.5, modified]
4 Overall configuration of the measurement system
Individual components of the system used for mobility measurements carried out in accordance with
this part of ISO 7626 shall be selected to suit each particular application.
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ISO 7626-2:2015(E)

However, all such systems should include certain basic components arranged as shown in Figure 1.
Requirements for the characteristics and usage of those components are given in the relevant clauses.
Key
1 basic feature 8 structure under test
2 optional feature 9 motion response transducer(s)
3 signal generator 10 signal conditioners
4 power amplifier 11 monitoring oscilloscope
5 vibration exciter 12 analyser
6 drive rod 13 plotter or other output device
7 force transducer
Figure 1 — Block diagram of mobility measurement system
5 Support of the structure under test
5.1 General
Mobility measurements are performed on structures either in an ungrounded condition (freely
suspended) or in a grounded condition (attached to one or more supports), depending on the purpose
of the test. The restraints on the structure induced by the application of the vibration exciter are dealt
with in 6.4.
5.2 Grounded measurements
The support of the test structure shall be representative of its support in typical applications unless it
has been specified otherwise. A description of the support should be included in the test report.
5.3 Ungrounded measurements
A compliant suspension of the test structure shall be used. The magnitude of driving-point mobility
of the suspension at each point of attachment to the structure under test should be at least 10 times
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ISO 7626-2:2015(E)

greater than that of the structure at the same attachment point, within the frequency range of interest.
Details of the suspension system used shall be included in the test report.
In the absence of quantitative information, design of the suspension is largely a matter of judgment
depending on the frequency range of interest. As a minimum requirement, all resonance frequencies of
the rigid-body modes of the suspended structure shall be less than half the lowest frequency of interest.
Items commonly used to provide compliant suspension include shock cords and resilient pads of
material such as foam and rubber. Since some suspension systems have mass but little damping, care
shall be taken to ensure that the frequencies of the suspension resonances are well away from the
modal frequencies of the test structure itself. The masses of any suspension components, such as hooks
and turnbuckles, located close to the structure under test shall also be less than one-tenth of the free
effective mass of the structure at each frequency of interest.
Preliminary testing should be performed to identify locations for the attachment of the suspension
with the minimum possible effect on the intended measurements. Suspension near nodal points of
the structure under test will minimize the interaction of the suspension system with the structure.
Suspensio
...