SIST EN 16603-32-11:2014

Space engineering - Modal survey assessment

This Standard specifies the basic requirements to be imposed on the performance and assessment of modal survey tests in space programmes. It defines the terminology for the activities involved and includes provisions for the requirement implementation.
This Standard specifies the tasks to be performed when preparing, executing and evaluating a modal survey test, in order to ensure that the objectives of the test are satisfied and valid data is obtained to identify the dynamic characteristics of the test article.
This standard may be tailored for the specific characteristics and constrains of a space project in conformance with ECSS-S-ST-00.

Raumfahrttechnik - Modale Prüfungsbewertung

Ingénierie spatiale - Evaluation des modes vibratoires

Vesoljska tehnika - Ocenjevanje modalnega pregleda

Standard EN 16603-32-11 določa osnovne zahteve za učinkovitost in ocenjevanje modalnega pregleda na področju vesoljskih programov. Določa terminologijo za zajete dejavnosti in vključuje določbe za izvajanje zahtev. Ta standard določa naloge, ki jih je treba opraviti pri pripravi, izvedbi in vrednotenju ocenjevanja modalnega pregleda, da bi zagotovili, da so cilji preskusa izpolnjeni in da so pridobljeni veljavni podatki za identifikacijo dinamičnih značilnosti preskusnih izdelkov. Ta standard se lahko prilagodi posameznim lastnostim in omejitvam vesoljskega projekta v skladu s standardom ECSS-S-ST-00.

General Information

• Status: Published
• Publication Date: 15-Oct-2014
• ICS: 49.140 - Space systems and operations
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 05-Sep-2014
• Due Date: 10-Nov-2014
• Completion Date: 16-Oct-2014
• Mandate: M/496 - Mandate addressed to CEN, CENELEC and ETSI to develop standardisation regarding space industry (Phase 3 of the process)
• Ref Project: EN 16603-32-11:2014 - Space engineering - Modal survey assessment

Overview

SIST EN 16603-32-11:2014 - Space engineering - Modal survey assessment - defines baseline requirements for planning, performing and assessing modal survey tests in space programmes. Published by SIST as the national adoption of EN 16603-32-11:2014 (originating from ECSS‑E‑ST‑32‑11C), the standard sets terminology, test objectives and procedural requirements to ensure valid dynamic characterization of spacecraft structures. It can be tailored to project constraints in conformance with ECSS‑S‑ST‑00.

Key topics and technical requirements

The standard covers the full modal survey lifecycle and includes prescriptive and informative material on:

• Objectives and general requirements

  • Verification of design natural frequencies, mathematical model validation, troubleshooting, verification of design modifications and failure detection.
  • Definition of test success criteria, boundary and environmental conditions, test facility certification and safety.

• Test planning and procedures

  • Activities for pre-test analysis, test execution and post-test evaluation.
  • Development of a Test Analysis Model (TAM), measurement point plan (MPP) and finite element model (FEM) reduction guidance.

• Test set-up, instrumentation and excitation

  • Requirements for test set-up definition, boundary conditions, instrumentation selection and excitation plans (including guidance on excitation signals and systems).

• Data quality, modal identification and parameter estimation

  • Procedures for coherence checks, mode identification, estimation methods (time- and frequency-domain), effective mass calculations, and data storage/delivery.

• Test‑analysis correlation

  • Criteria and techniques for correlating test results with mathematical models, with quality metrics and checklists to assess model fidelity.

• Annexes and supporting material

  • Informative annexes on excitation signals, modal parameter estimation methods, and a mathematical model verification checklist.

Practical applications

This standard is practical for any activity requiring accurate modal testing and model validation in the space domain:

• Verifying spacecraft and payload structural dynamics before environmental testing (e.g., vibration qualification).
• Validating and updating FEMs used for load and margin analysis.
• Root‑causing vibration anomalies and verifying the dynamic impact of design changes.
• Establishing repeatable modal survey procedures and data delivery formats for project verification.

Who should use this standard

• Structural dynamics and vibration test engineers
• Spacecraft systems and verification engineers
• Test laboratories and facilities performing modal surveys
• FEM analysts and model validation specialists
• Program managers defining verification requirements

Related standards

• EN 16601-00-01 / ECSS‑S‑ST‑00‑01 (System glossary)
• EN 16603-10-03 (Space engineering - Testing)
• EN 16603-32 (Space engineering - Structural general requirements)

Keywords: modal survey, modal testing, modal analysis, space engineering, modal survey assessment, test-analysis correlation, FEM validation, Test Analysis Model (TAM), spacecraft structural dynamics.

Standards Content (Sample)

SLOVENSKI STANDARD
01-november-2014
Vesoljska tehnika - Ocenjevanje modalnega pregleda
Space engineering - Modal survey assessment
Raumfahrttechnik - Modale Prüfungsbewertung
Ingénierie spatiale - Evaluation des modes vibratoires
Ta slovenski standard je istoveten z: EN 16603-32-11:2014
ICS:
49.140 Vesoljski sistemi in operacije Space systems and
operations
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN 16603-32-11
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2014
ICS 49.140
English version
Space engineering - Modal survey assessment
Ingénierie spatiale - Evaluation des modes vibratoires Raumfahrttechnik - Modale Prüfungsbewertung
This European Standard was approved by CEN on 23 February 2014.

CEN and CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving
this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning
such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN and CENELEC
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN and CENELEC member into its own language and notified to the CEN-CENELEC Management Centre
has the same status as the official versions.

CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia,
Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.

CEN-CENELEC Management Centre:
Avenue Marnix 17, B-1000 Brussels
© 2014 CEN/CENELEC All rights of exploitation in any form and by any means reserved Ref. No. EN 16603-32-11:2014 E
worldwide for CEN national Members and for CENELEC
Members.
Table of contents
Foreword . 5
1 Scope . 6
2 Normative references . 7
3 Terms, definitions and abbreviated terms . 8
3.1 Terms from other standards . 8
3.2 Terms specific to the present standard . 8
3.3 Abbreviated terms. 22
3.4 Notation . 23
4 General objectives and requirements . 25
4.1 Modal survey test objectives . 25
4.1.1 Overview . 25
4.1.2 General . 25
4.1.3 Verification of design frequency . 25
4.1.4 Mathematical model validation . 26
4.1.5 Troubleshooting vibration problems . 26
4.1.6 Verification of design modifications . 26
4.1.7 Failure detection . 27
4.2 Modal survey test general requirements . 27
4.2.1 Test set-up . 27
4.2.2 Boundary conditions . 28
4.2.3 Environmental conditions . 28
4.2.4 Test facility certification . 28
4.2.5 Safety. 29
4.2.6 Test success criteria . 29
5 Modal survey test procedures . 31
5.1 General . 31
5.2 Test planning . 31
5.2.1 Test planning . 31
5.2.2 Pre-test activities . 33
5.2.3 Test activities . 33
5.2.4 Post-test activities . 34
5.3 Test set-up . 34
5.3.1 Definition of the test set-up . 34
5.3.2 Test boundary conditions . 34
5.3.3 Test instrumentation . 36
5.3.4 Excitation plan . 37
5.3.5 Test hardware and software . 38
5.4 Test performance. 38
5.4.1 Test . 38
5.4.2 Excitation system . 38
5.4.3 Excitation signal . 39
5.4.4 Linearity and structural integrity. 40
5.4.5 Measurement errors . 40
5.5 Modal identification methods . 41
5.6 Modal parameter estimation methods . 42
5.7 Test data . 42
5.7.1 Quality checks . 42
5.7.2 Generalized parameters . 44
5.7.3 Effective masses . 44
5.7.4 Data storage and delivery . 45
5.8 Test-analysis correlation . 46
5.8.1 Purpose . 46
5.8.2 Criteria for mathematical model quality . 47
6 Pre-test analysis . 49
6.1 Purpose . 49
6.2 Modal survey test FEM . 49
6.2.1 Purpose . 49
6.2.2 Reduction of the detailed FEM . 50
6.3 Test analysis model (TAM) . 52
6.3.1 Purpose . 52
6.3.2 TAM accuracy . 53
6.3.3 Measurement point plan (MPP) . 53
6.3.4 Test predictions . 54
6.3.5 Test fixture participation . 54
6.4 Documentation . 55
6.4.1 FEM documentation . 55
6.4.2 TAM documentation . 55
Annex A (informative) Excitation signals . 57
A.1 Overview . 57
A.2 Purpose and classification . 57
A.3 Excitation methods . 58
Annex B (informative) Estimation methods for modal parameters . 61
B.1 Overview . 61
B.2 Theoretical background and overview. 61
B.3 Frequency domain methods . 67
B.4 Time domain methods . 71
Annex C (informative) Modal test - mathematical model verification
checklist . 74
Annex D (informative) References . 76
Bibliography . 77

Figures
Figure 5-1: Test planning activities . 32
Figure 5-2: Comparison of mode indicator functions (MIF)
according to Breitbach and Hunt . 43
Figure 6-1: Modal survey pre-test analysis activities . 50

Tables
Table 5-1: Test objectives and associated requirements for the test boundary
conditions . 35
Table 5-2: Most commonly used correlation techniques . 46
Table 5-3: Test-analysis correlation quality criteria . 48
Table 5-4: Reduced mathematical model quality criteria . 48
Table 6-1: Advantages and disadvantages of model reduction techniques . 52
Table B-1 : Overview and classification of commonly used modal parameter estimation
methods . 64
Table B-2 : Advantages and disadvantages of the time and frequency domain methods. 65
Table B-3 : Advantages and disadvantages of single and multiple degree of freedom
methods . 66
Table B-4 : Other aspects of selecting a modal parameter estimation method . 67
Table C-1 : Verification checklist for mathematical models supporting modal survey
tests . 75

Foreword
This document (EN 16603-32-11:2014) has been prepared by Technical
Committee CEN/CLC/TC 5 “Space”, the secretariat of which is held by DIN.
This standard (EN 16603-32-11:2014) originates from ECSS-E-ST-32-11C.
This European Standard shall be given the status of a national standard, either
by publication of an identical text or by endorsement, at the latest by February
2015, and conflicting national standards shall be withdrawn at the latest by
February 2015.
Attention is drawn to the possibility that some of the elements of this document
may be the subject of patent rights. CEN [and/or CENELEC] shall not be held
responsible for identifying any or all such patent rights.
This document has been prepared under a mandate given to CEN by the
European Commission and the European Free Trade Association.
This document has been developed to cover specifically space systems and has
therefore precedence over any EN covering the same scope but with a wider
domain of applicability (e.g. : aerospace).
According to the CEN-CENELEC Internal Regulations, the national standards
organizations of the following countries are bound to implement this European
Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic,
Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,
Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United
Kingdom.
Scope
This Standard specifies the basic requirements to be imposed on the
performance and assessment of modal survey tests in space programmes. It
defines the terminology for the activities involved and includes provisions for
the requirement implementation.
This Standard specifies the tasks to be performed when preparing, executing
and evaluating a modal survey test, in order to ensure that the objectives of the
test are satisfied and valid data is obtained to identify the dynamic
characteristics of the test article.
This standard may be tailored for the specific characteristics and constrains of a
space project in conformance with ECSS-S-ST-00.

Normative references
The following normative documents contain provisions which, through
reference in this text, constitute provisions of this ECSS Standard. For dated
references, subsequent amendments to, or revision of any of these publications,
do not apply. However, parties to agreements based on this ECSS Standard are
encouraged to investigate the possibility of applying the more recent editions of
the normative documents indicated below. For undated references, the latest
edition of the publication referred to applies.

EN reference Reference in text Title
EN 16601-00-01 ECSS-S-ST-00-01 ECSS system — Glossary of terms
EN 16603-10-03 ECSS-E-ST-10-03 Space engineering — Testing
EN 16603-32 ECSS-E-ST-32 Space engineering — Structural general requirements

Terms, definitions and abbreviated terms
3.1 Terms from other standards
For the purpose of this Standard, the terms and definitions from
ECSS-S-ST-00-01 apply.
3.2 Terms specific to the present standard
3.2.1 accelerance
ratio of the output acceleration spectrum to the input force spectrum
NOTE 1 Accelerance is computed as follows:
• •
X (ω)
A(ω) =
F(ω)
where
• •
is the output acceleration spectrum;
X (ω)
is the input force spectrum.
F(ω)
NOTE 2 The accelerance is also called “inertance” and it is
the inverse of the apparent mass (see 3.2.2).
3.2.2 apparent mass
ratio of the input force spectrum to the output acceleration spectrum
NOTE 1 Apparent mass is computed as follows:
F(ω)
M (ω) =
• •
X (ω)
where
is the input force spectrum;
F(ω)
• •
is the output acceleration spectrum.
X (ω)
NOTE 2 The apparent mass is also called “dynamic mass”,
and it is the inverse of the accelerance (see 3.2.1).
3.2.3 auto modal assurance criterion
AutoMAC
measure of the degree of correlation between two mode shapes of the same
mode shape set
NOTE 1 For example, test mode shapes or analysis mode
shapes.
NOTE 2 The AutoMAC is a specific case of the MAC
(see 3.2.26); the AutoMAC matrix is symmetric.
NOTE 3 The AutoMAC is particularly useful for assessing
whether a given selection of DOFs is adequate for
MAC evaluations employing two different sets of
mode shapes (e.g. test and analysis).
3.2.4 coherence function
measure of the degree of linear, noise-free relationship between the measured
system input and output signals at each frequency
NOTE 1 The coherence function is defined as
S (ω)
xf
γ (ω) =
S (ω) S (ω)
xx f f
where
ω is the frequency;
Sff (ω) is the power spectrum of the input signal;
Sxx (ω) is the power spectrum of the output signal;
Sxf (ω) is the input-output cross spectrum.
NOTE 2 γ (ω)=1 indicates a linear, noise-free relationship
between input and output.
NOTE 3 γ (ω)=0 indicates a non causal relationship
between input and output.
3.2.5 complex mode shape
modal vector of a non-proportionally damped system
NOTE 1 For complex mode shapes, any phase relationship
can exits between different parts of the structure.
NOTE 2 Complex mode shapes can be considered to be
propagating waves with no stationary node lines.
3.2.6 complex mode indicator function
indicator of the existence of real or complex modes and their relative
magnitudes
NOTE The complex mode indicator function has
extended functionality to estimate approximate
modal parameters.
3.2.7 co-ordinate modal assurance criterion
CoMAC
measure of the correlation of the a given DOF of two different sets of mode
shapes over a number of comparable-paired mode shapes
NOTE 1 The coordinate modal assurance criterion for DOF
j is defined as:
m
 
X A
Φ Φ
∑ jr jr
 
r=1 
CoMAC(j) =
m m
2 2
X A
(Φ ) (Φ )
∑ jr ∑ jr
r=1 r=1
where
A
Φ is the mode shape coefficient for DOF j for mode r
jr
of set A;
X
Φ is the mode shape coefficient for DOF j for mode r
jr
of set X;
r is the index of the correlated mode pairs.
For example, mode shapes X and A are test and
analysis mode shapes, respectively.
NOTE 2 CoMAC = 1 indicates perfect correlation.
NOTE 3 The results can be considered to be meaningful
only when the CoMAC is applied to matched
modes, i.e. for correlated mode pairs.
3.2.8 damping
dissipation of oscillatory or vibratory energy with motion or with time
3.2.9 damped natural frequency
frequency of free vibrations of a damped linear mechanical system
3.2.10 driving point residue
calculated quantity that defines the most appropriate exciter positions
NOTE The magnitude of the driving point residue for a
location is defined as:
v
jr
r =
jr
2m ω
r dr
where
rjr is the driving point residue of DOF j for mode r;
vjr is the mode shape coefficient of DOF j for mode r;
mr is the modal mass for mode r;
ωdr is the damped natural frequency for mode r.
3.2.11 dynamic compliance
ratio of the output displacement spectrum to the input force spectrum
NOTE 1 Dynamic compliance is computed as follows:
X (ω)
H (ω) =
F(ω)
where
X(ω) is the output displacement spectrum;
F(ω) is the input force spectrum.
NOTE 2 The dynamic compliance is also called dynamic
flexibility, and it is the inverse of the dynamic
stiffness (see 3.2.12).
3.2.12 dynamic stiffness
ratio of the input force spectrum to the output displacement spectrum
NOTE 1 Dynamic stiffness is computed as follows:
F(ω)
K(ω) =
X (ω)
where
F(ω) is the input force spectrum;
X(ω) is the output displacement spectrum.
NOTE 2 The dynamic stiffness is the inverse of the
dynamic compliance (see 3.2.11).
3.2.13 effective modal mass
measure of the mass portion associated to the mode shape with respect to a
reference support point
NOTE 1 The six effective masses for a normal mode, {Φ}r,
are the diagonal values of the modal mass matrix.
T
{L} {L}
r r
[M ] =
r
m
r
where
{L}r is the modal participation factor:
T
;
{L} = {Φ } [M ]{φ}
r RB r
mr is the generalised mass:
T
m = {Φ} [m] {φ} ;
r r r
{Φ}r, is the elastic mode r;
{Φ }, is the rigid body mode.
ΡΒ
NOTE 2 The sum of the effective masses provides an
indication of the completeness of the measured
modes, since the accumulated effective mass
contributions from all modes equal the total
structural mass and inertia for each of the six
translatory and rotatory DOFs, respectively.
3.2.14 eigenfrequency
See natural frequency
3.2.15 finite element model
FEM
mathematical representation of a physical structure or system where the
distributed physical properties are represented by a discrete model consisting
of a finite number of idealized elements which are interconnected at a finite
number of nodal points
NOTE The FEM contains only a finite number of degrees
of freedom compared to the infinite number of
degrees of freedom for the physical structure or
system.
3.2.16 forced vibration
vibratory motion of a system that is caused by mechanical excitation
3.2.17 free vibration
vibratory motion of a system without forcing
3.2.18 frequency response assurance criterion
FRAC
measure of the similarity between an analytical and experimental frequency
response function
NOTE 1 The frequency response assurance criterion is a
degree of freedom correlation tool. It is the FRF
equivalent to the CoMAC (see 3.2.7).
NOTE 2 The frequency response assurance criterion is
defined as
T
{ H (ω)} { H (ω)}
X jk A jk
FRAC(j,k) =
T T
({ H (ω)} { H (ω)}) ({ H (ω)} { H (ω)})
X jk X jk A jk A jk
where
AHjk(ω) is the analytical frequency response
function of a response at DOF j due to
an excitation at DOF k;
XHjk(ω) is the corresponding experimental
frequency response function.
NOTE 3 FRAC = 1 indicates a perfect correlation of the two
frequency response functions.
NOTE 4 FRAC = 0 indicates a non correlation of the two
frequency response functions.
3.2.19 frequency response function
FRF
descriptor of a linear system in the frequency domain that relates the output motion
spectrum (displacement, velocity or acceleration) to the input force spectrum
NOTE 1 The frequency response function is generally
defined as:
X (ω)
H (ω) =
F(ω)
NOTE 2 H(ω) is a complex function containing magnitude
and phase information.
NOTE 3 Common definitions of standard and inverse FRF are:
• accelerance or inertance (see 3.2.1);
• apparent or dynamic mass (see 3.2.2);
• dynamic compliance or flexibility (see 3.2.11);
• dynamic stiffness (see 3.2.12).
• impedance (see 3.2.22);
• mobility (see 3.2.24).
3.2.20 fundamental resonance
first major significant resonance as observed during the modal survey test
NOTE 1 For unconstrained mechanical systems, the
fundamental resonance is the lowest natural
frequency with motions of the whole test article.
NOTE 2 For clamped mechanical systems, the fundamental
resonance is the mode with the largest effective
mass.
3.2.21 impact
single collision between masses where at least one of the masses is in motion
3.2.22 impedance
ratio of the input force spectrum to the output velocity spectrum
NOTE 1 Impedance is computed as follows:
F(ω)
Z(ω) =
•
X (ω)
where
F(ω) is the input force spectrum;
•
is the output velocity spectrum.
X (ω)
NOTE 2 The impedance is the inverse of the mobility
(see 3.2.24).
3.2.23 linear system
system whose response is directly proportional to the excitation for every part
of the system
3.2.24 mobility
ratio of the output velocity spectrum to the input force spectrum
NOTE 1 Mobility is computed as follows:
•
X (ω)
Y (ω) =
F(ω)
where
•
is the output velocity spectrum;
X (ω)
F(ω) is the input force spectrum.
NOTE 2 The mobility is the inverse of the impedance
(see 3.2.22).
3.2.25 modal analysis
process of determining the modal parameters of a structure within the
frequency range of interest
NOTE For the frequency range of interest, see 4.1.2.
3.2.26 modal assurance criterion
MAC
measure of the degree of correlation between two mode shapes
NOTE 1 The modal assurance criterion is defined as:
T
[{Φ} {Φ} ]
r s
MAC =
rs
T T
[{Φ} {Φ} ][{Φ} {Φ} ]
r r s s
where and are the two mode shapes.
{Φ} {Φ}
r s
NOTE 2 MAC = 1 indicates perfect correlation of the two
mode shapes.
NOTE 3 MAC = 0 indicates no correlation of the two mode
shapes.
3.2.27 modal confidence factor
MCF
indicator of computational noise modes in time domain parameter estimation
methods
NOTE 1 The modal confidence factor for mode r is given as
~
T  
{Φ} Φ
 
r
−λ ∆τ
r
 
r
MCF = e
r
T
{Φ} {Φ}
r r
where
~
 
is a computed mode;
Φ
 
 
r
λr is a complex eigenvalue, or system pole for
mode r;
{Φ} is a mass-normalized mode shape;
r
∆τ is the time interval.
NOTE 2 MCFr ≈ 1 indicates a physical mode, and in such
case:
−λ ∆τ
~
r
 
Φ = {Φ} e
 
r
 
r
NOTE 3 MCFr << 1 indicates a computational noise mode.
3.2.28 modal identification
technique to determine the inherent modal properties of a mechanical system
3.2.29 modal parameters
collection of natural frequency, modal damping, mode shape and (generalized)
modal mass for each mode of a mechanical system
NOTE 1 The modal parameters of all modes, within the
frequency range of interest (see 4.1.2), constitute a
complete dynamic description of the structure.
NOTE 2 Common definitions relating to modal parameters are:
• damped equations of motion
.. .
 
   
;
[M ] x (t) +[C] x (t) +[K] x (t) = {f (t)}
     
   
 
• inertia force
..
 
[M ] x (t)
 
 
• elastic force
 
[K] x (t)
 
 
• damping force (proportional with velocity)
.
 
;
[C] x(t)
 
 
• external dynamic force
{f (t)}
• undamped eigenvalue problem
([K] − ω [M ]){Ψ} = {0}
r r
• natural or eigenfrequency
ω
r
;
ω (rads /s), f = (Hz)
r r
2π
• general mode shape
{Ψ}
r
• (generalized) modal mass
T
{Ψ} [M ]{Ψ} =m
r r r
• (generalized) modal damping
T
{Ψ} [C]{Ψ} = 2m ξ ω
r r r r r
• generalized stiffness
T
{Ψ} [K ]{Ψ} =m ω
r r r r
• mass-normalized mode shape
{Φ}
r
• mass-normalized modal mass
T
{Φ} [M ]{Φ} = 1
r r
• mass-normalized modal damping
T
{Φ} [C]{Φ} = 2ξ ω
r r r r
• mass-normalized modal stiffness
T 2
{Φ} [K ]{Φ} = ω
r r r
• modal matrix
{Ψ}, {Φ}
NOTE 3 For non-proportional damping, the generalized
damping matrix is not a diagonal matrix.
3.2.30 modal participation factor
measure of the efficiency of the excitation at each degree of freedom of the
supporting point
NOTE 1 The modal participation factor is a measure of the
reaction force at the supported reference point.
NOTE 2 See also 3.2.13.
3.2.31 modal scale factor
MSF
least squares difference of two mode shapes, where one mode shape is
projected on the other and scaled to the length of the latter
NOTE The modal scale factor is given as
T
{Φ} [W ]{Φ}
r s
MSF =
rs
T
{Φ} [W ]{Φ}
s s
where
{Φ} and {Φ} are the two mode shapes;
r s
[W] is a weighting matrix (most often the unity
matrix).
3.2.32 modal survey test
MST
test that identifies a set of modal properties of a mechanical system
3.2.33 mode indicator function
MIF
measure for phase purity of the measured mode shapes using a single reference
NOTE 1 The most common definitions applied by different
modal analysis systems are:
M x' x
∑ jj j j
• Breitbach (1972):
MIF =1 −
M x
∑ jj j
M x'
∑
jj j
• Hunt (1984):
MIF =1 −
M x
∑ jj j
th
where xj is the complex valued response at the j
structural point:
2 2
,
x = x' +ix" x = x' +x"
j j j
j j j
NOTE 2 MIF = 1 indicates a perfectly excited mode shape.
NOTE 3 MIF << 1 indicates either no resonances in the
frequency range or inappropriately excited modes.
NOTE 4 The mass weighting is often neglected.
NOTE 5 The MIF is a special case of the MMIF (see 3.2.35).
3.2.34 mode shape
characteristic shape of motion of an elastic structure when vibrating at its
corresponding natural frequency
3.2.35 multi-variate mode indicator function
MMIF
measure of the phase purity of the measured mode shapes using a multiple
reference
NOTE 1 The MMIF is given as a frequency dependent
eigenvalue problem:
λ ( [A]+ [B] ){F(ω)}= [A] {F(ω)}
where:
T
[A] = [H (ω)] [M ][H (ω)];
R R
T
[B] = ;
[H (ω)] [M ][H (ω)]
I I
H (ω) is the real part of the FRF;
R
H (ω) is the imaginary part of the FRF;
I
is the force eigenvector;
{F(ω)}
is the mass matrix;
[M ]
λ is an eigenvalue.
NOTE 2 The MMIF comprises the eigenvalues resulting
from the solution of the eigenvalue problem for
each frequency ω.
NOTE 3 MMIF = 0 indicates a perfectly excited mode
shape.
NOTE 4 MMIF >> 0 indicates either no resonances in the
frequency range or inappropriately excited modes.
NOTE 5 The MMIF yields a set of exciter force patterns that
can best excite the real normal modes. It is
therefore a simple but effective method to check
the adequacy of the selected exciter locations.
3.2.36 natural frequency
characteristic frequency of a linear mechanical system at which the system
vibrates when all external excitations are removed or damped out
NOTE 1 This definition refers to both, damped or
undamped natural frequencies.
NOTE 2 The natural frequency is frequently referred to also
as resonant frequency or eigenfrequency (see
3.2.14).
3.2.37 noise
total of all sources of interference in a measurement system, independent of the
presence of a signal
NOTE For example, mechanical background noise,
ambient excitation, electrical noise in the
transducing system, data acquisition noise,
computational noise, and non-linearities.
3.2.38 normal mode shape
mode shapes where all parts of the structure are moving either in phase, or 180°
out of phase with each other
NOTE 1 Normal mode shapes can be considered to be
standing waves with fixed node lines.
NOTE 2 For proportionally damped systems, the normal
mode shapes can be derived from the complex
mode shapes by re-scaling.
3.2.39 orthogonality check
measure of the mathematical orthogonality and linear independence of a set of
mode shapes (analytical or measured) using the mass matrix of the
mathematical model (FEM or TAM) as a weighting factor
NOTE 1 The following are common definitions of the
orthogonality check:
• Auto orthogonality check (AOC)
Measure of the mathematical orthogonality of
mode shapes Φr and Φs taken from the same set
j of analytical or measured mode shapes.
T
{Φ} [M ]{Φ}
r,j s,j
AOC =
rs
T T
{Φ} [M ]{Φ} {Φ} [M ]{Φ}
r,j r,j s,j s,j
Where 0 ≤ AOCrs ≤1.
• Cross orthogonality check (COC)
Measure of the mathematical orthogonality of
mode shapes Φr and Φs taken from two
different sets, j and k, of mode shapes
(analytical and measured, respectively).
T
{Φ} [M ]{Φ}
r,j s,k
COC =
rs
T T
{Φ} [M ]{Φ} {Φ} [M ]{Φ}
r,j r,j s,k s,k
Where 0 ≤ COCrs ≤1.
NOTE 2 The degree of orthogonality is usually assessed by
the magnitude of the off-diagonal elements AOCrs
and COCrs of the orthogonality matrices [AOC] and
[COC], respectively.
NOTE 3 The auto orthogonality check is an indicator of the
accuracy of the assumed mass matrix and the
acquired data. Ideally:
1 for r =s

AOC =
rs 
0 for r ≠s

3.2.40 pick-up
See transducer
3.2.41 pre-test analysis
structural analysis activities to prepare for the modal survey test
NOTE Usually, the pre­test analysis employs the
structural mathematical model of the test article.
The test set-up is included if it has a significant
influence on the results.
3.2.42 real mode shape
modal vector of a proportionally damped system where all parts of the
structure vibrate in phase
NOTE Real mode shapes can be considered to be
standing waves with stationary node lines.
3.2.43 reciprocity
structural response at a given point due to an input at another point equals the
response at the input point due to an identical input at the given response point
NOTE This is known as Maxwell’s reciprocity principle:
αpq = αqp.
3.2.44 resonance
maximum amplification of the response of a mechanical system in forced
vibrations
3.2.45 resonance frequency
frequency of a mechanical system where any change, however small, in the
frequency of excitation in either direction causes the system response to
decrease
3.2.46 response
output of a structure at a given point due to an input at another point
NOTE For modal survey tests the structural responses are
usually measured in terms of accelerations.
3.2.47 response vector assurance criterion
RVAC
measure of the similarity between an analytical and experimental response
vector at a particular frequency
NOTE 1 The response vector assurance criterion is a vector
correlation tool. It is the FRF equivalent to the
MAC (see 3.2.26).
NOTE 2 The response vector assurance criterion is defined
as:
T
{ H (ω )} { H (ω )}
X k r A k r
RVAC(ω ,k) =
r
T T
({ H (ω )} { H (ω )})({ H (ω )} { H (ω )})
X k r X k r A k r A k r
where
• H (ω ) is the analytical vector containing
A k r
only the FRF values at all response points due
to an excitation at DOF k for a particular
frequency ωr;
• H (ω ) is the corresponding experimental
X k r
response vector.
NOTE 2 RVAC = 1 indicates perfect correlation of the two
response vectors.
NOTE 3 FRAC = 0 indicates no correlation of the two
response vectors.
3.2.48 signal analysis
process of evaluating the input and output signals of mechanical systems to
describe their characteristics in meaningful and easily interpretable terms in the
time or frequency domain
3.2.49 signal-to-noise ratio
ratio of the power of the desired signal to that of the coexistent noise at a
specified point in a transmission channel under specified conditions
NOTE 1 The signal­to­noise ratio is a measure of the signal
quality.
NOTE 2 It is usually given as the ratio of voltage of a
desired signal to the undesired noise component
measured in corresponding units.
3.2.50 signal conditioner
amplifier placed between a transducer or pick­up and succeeding devices to
make the signal suitable for these devices
NOTE For example, succeeding devices can be amplifiers,
transmitters or read-out instruments.
3.2.51 spectrum control
capability to limit the excitation to the frequency range of interest
NOTE For the frequency range of interest, see 4.1.2.
3.2.52 steady-state vibration
vibration where the amplitude and frequency stay constant over the whole
duration of the vibration
3.2.53 test analysis model
TAM
finite element model of the test set-up in terms of stiffness and mass matrix, for
test purposes reduced to excitation and measurement degrees of freedom
NOTE The test set-up can include the test fixture.
3.2.54 test equipment
collection of hardware to support the test execution
NOTE For example, test adapters.
3.2.55 test set-up
collection of the test article, the test equipment and the test instrumentation
3.2.56 transducer
device to convert a mechanical quantity into an electrical signal
NOTE 1 For example, usually, these mechanical quantities
are force and acceleration.
NOTE 2 The transducer is frequently referred to as pick-up.
3.2.57 transducer sensitivity
ratio between the electrical signal (output) and the mechanical quantity (input)
of a mechanical-to-electrical transducer or pick­up
NOTE For example, transducer sensitivity is given in
(mV)/(m/s ).
3.2.58 transient
finite duration change from one steady-state condition to another
NOTE Usually the initial and the final steady-state
conditions are zero.
3.2.59 transmissibility
relative vibration levels of the same mechanical quantity at two points in terms
of this quantity in the frequency domain
NOTE The transmissibility reaches its maximum at the
resonance frequency.
3.3 Abbreviated terms
For the purpose of this Standard, the abbreviated terms from ECSS-S-ST-00-01
and the following apply:
Abbreviation Meaning
auto orthogonality check
AOC
auto-regressive moving average
ARMA
complex mode indicator function
CMIF
cross orthogonality check
COC
centre of gravity
CoG
coordinate modal assurance criterion
CoMAC
data acquisition system
DAS
degree of freedom
DOF
effective independence
EI
finite element analysis
FEA
finite element model
FEM
frequency response assurance criterion
FRAC
frequency response function
FRF
hardware
H/W
improved reduction system
IRS
kinetic energy
KE
modal assurance criterion
MAC
modal confidence factor
MCF
multiple degree of freedom
MDOF
mode indicator function
MIF
multi-variate MIF
MMIF
multiple input - multiple output system
MIMO
modal survey test
MST
measurement point plan
MPP
pseudo orthogonality check
POC
point drive residue
PDR
root mean square
RMS
response vector assurance criterion
RVAC
single degree of freedom
SDOF
system equivalent reduction expansion process
SEREP
single input - single output system
SISO
software
S/W
test article
TA
test analysis model
TAM
to be defined
TBD
test fixture
TF
3.4 Notation
The following notation, compatible with Ewins, 2000 (see Annex D) is used
within this document:
• Matrices, vectors and scalars
[ ] matrix
{ } vector
T T
[ ] , { } transpose of a matrix, vector
| | modulus of complex number
• Spatial properties
[C] viscous damping matrix
[D] structural damping matrix
{f(t)} force vector (time domain)
{F(ω)} force vector (frequency domain)
h(t) impulse response function (IRF)
H(ω) frequency response function (FRF)
G(ω) estimated frequency response function
[K] stiffness matrix
Mjj mass connected with DOF j
[M] mass matrix
S(ω) coherence function
{x(t)} displacement vector (time domain)
⋅
 
x(ω)
  velocity vector (time domain)
 
⋅⋅
 
x(t)
  acceleration vector (time domain)
 
{X(ω)} displacement vector (frequency domain)
⋅
 
X (ω)
  velocity vector (frequency domain)
 
⋅⋅
 
X (t)
  acceleration vector (frequency domain)
 
xj complex valued response of DOF j
x′j real part of xj
x″j imaginary part of xj
∆t time increment
• Modal properties
th
ωr natural or eigenfrequency of r mode (rad/s)
th
λr eigenvalue of r mode
th
{Ψ}r r mode shape or eigenvector
th
{Φ}r r normalized mode shape or eigenvector (normalised
either to mass or maximum displacement)
{Φ } rigid body mode
ΡΒ
th
ζr modal viscous damping (damping ratio) of r mode
th
mr (generalized) modal mass of r mode
E
th
m effective modal mass of r mode (j = 1,…6)
r, j
P
th
m
modal participation factor of r mode (j = 1,…6)
r, j
[m] (generalized) modal mass matrix
[c] (generalized) modal viscous damping matrix
[d] (generalized) modal structural damping matrix
[k] (generalized) modal stiffness matrix
General objectives and requirements
4.1 Modal survey test objectives
4.1.1 Overview
As specified in ECSS-E-ST-32, modal survey tests are performed to identify
dynamic characteristics such as the natural frequency, mode shapes, effective
and generalized mass and modal damping.
The objective is to identify the majority of the test parameters to be acquired,
and the accuracy of the test results.
4.1.2 General
a. Prior to the execution of the test, the frequencies of interest and the mode
shapes of interest shall be identified.
NOTE 1 The “frequencies of interest” and the “mode
shapes of interest” are those identified as being
relevant for achieving the modal survey test
objectives.
NOTE 2 Instead of specific frequencies of interest, a
frequency range of interest can be identified.
NOTE 3 In cases where the test article mathematical model
is employed for accurate response predictions, the
frequency range of interest is usually defined as
being the frequency range in which major dynamic
excitations from the launch vehicle are expected.
4.1.3 Verification of design frequency
a. The modal survey test shall demonstrate that the manufactured
hardware conforms to the design frequency requirements listed in the
test specification.
NOTE 1 For the test specification, see ECSS-E-ST-10-03.
NOTE 2 Frequency requirements are specified for a
structure to avoid coupling with dynamic
excitations during launch or operation which can
result to structural damages or loss of the mission.
4.1.4 Mathematical model validation
a. The modal survey test shall demonstrate that the structural mathematical
model correlates with the hardware characteristics.
NOTE Adequate correlatio
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