ChapterPDF Available

On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’

Authors:
Chapter 14
On the Problem of Describing the Coupling Interface Between
Sub-structures: An Experimental Test for ‘Completeness’
J. W. R. Meggitt, A. T. Moorhouse, and A. S. Elliott
Abstract The implementation of both vibration source characterisation and sub-structure coupling/decoupling procedures
rely on the complete description of a coupling interface, that is, the inclusion of coupling forces in all significant degrees
of freedom (DoFs). However, it is not straight-forward to establish which DoFs are required in the description. E.g. is it
necessary to include moments and/or in-plane forces? This is an important question as an incomplete description will lead
to an erroneous representation of the dynamics. However, there are currently no methods of quantifying the completeness of
an interface description. In this paper an experimental procedure is described for the assessment of interface completeness.
Based on the theoretical blocking of DoF subsets, a relation is presented that allows for the contribution of an unknown DoF
to be established. Further, a coherence style criterion is proposed to estimate the completeness of a given interface description.
This criterion may be used to check whether sufficient coupling DoFs have been included in both source characterisation and
sub-structure coupling/decoupling procedures. Numerical and experimental examples are provided to illustrate the concept.
Keywords Interface · Completeness · Characterisation · Sub-structure · Coupling
14.1 Introduction
Interface dynamics play an essential role in the coupling of a built up structures. The complete description of an interface
(i.e. the correct number, position and orientation of coupling DoFs) is key when attempting to experimentally characterise
a structural assembly and/or its constituent components. This paper is concerned with the development of an ‘Interface
Completeness Criterion’ that quantitatively assesses the degree to which an interface has been correctly described.1
In general, the interface DoFs of a point connected structure are able to move in 6 coordinate DoFs. In theory, a
complete interface description must account for all of these. Experimentally, however, this is typically not possible, nor
is it often warranted.2In any practical scenario access to the coupling interface is likely to be restricted. This complicates
the measurement of coupling DoFs. Furthermore, the experimental challenges associated with the measurement of rotational
and in-plane DoFs has led to their near constant neglect. For this reason, incomplete interface descriptions are routinely
encountered in practice. Whilst considerable research has focused on the importance of rotational DoFs [15], in-plane
DoFs have received far less attention. According to Moorhouse and Elliott [6], however, their importance in the coupling
of structural elements should not be understated. With this in mind, the ability to assess the importance of a particular DoF,
perhaps unknown, would clearly be advantageous.
In the analysis of a continuous interface it is standard practice to approximate the interface in terms of a finite number of
point-like DoFs so as to acquire an approximate description of its dynamics [7,8]. Such an approximation is often based on
1Although we will refer to the proposed quantity as a criterion, given its definition, the authors are undecided as to whether ‘coefficient’ may be a
more appropriate term.
2Whilst a complete interface description is required from a theoretical basis, it is often the case that their exists a subset of DoFs that are of
particular importance, and themselves provide a satisfactory description of the interface. In such a case the remaining DoFs may not need to be
accounted for.
J. W. R. Meggitt () · A. T. Moorhouse · A. S. Elliott
Acoustics Research Centre, University of Salford, Greater Manchester, UK
e-mail: j.w.r.meggitt1@salford.ac.uk
© The Society for Experimental Mechanics, Inc. 2018
A. Linderholt et al. (eds.), Dynamics of Coupled Structures, Volume 4, Conference Proceedings of the Society
for Experimental Mechanics Series, https://doi.org/10.1007/978-3-319-74654- 8_14
171
172 J. W. R. Meggitt et al.
a points per wavelength argument, although the completeness of this description remains unclear. Alternatively, a continuous
interface may be approximated in terms of a truncated orthonormal series expansion [9]. Similarly, however, it is unclear the
degree to which this expansion suitably describes the interface.
In the analysis of both discrete and continuous interfaces, an indication as to whether sufficient DoFs have been accounted
for would clearly benefit the experimenter, and aid in avoiding the potential problems associated with an incomplete
interface description. Based on the mathematical blocking of known interface DoFs, theory is developed that allows for
the contribution of unknown interface DoFs to be established. This contribution is used as part of a coherence style criterion
to assess the completeness of an interface description. The proposed criterion may be used to indicate missing DoFs, weigh
up the potential benefits of including additional DoFs, or provide a level of uncertainty in a given interface description.
The remainder of this paper will be organised as follows: In Sect. 14.2 the interface completeness problem will be
demonstrated mathematically by considering the independent characterisation of a vibration source. Having introduced the
problem, Sect. 14.3 will describe the relevant theory, before Sect. 14.4 outlines the proposed Interface Completeness Criterion
(ICC). Section 14.5 will provide a numerical and experimental case study. Lastly, Sect. 14.6 will present some concluding
remarks.
14.2 The Interface Completeness Problem
The interface completeness problem is illustrated here with reference to the inverse determination of blocked forces using
the in-situ approach presented in [1012]. A similar problem is encountered in the coupling (or decoupling) of sub-structures
through dynamic sub-structure coupling procedures.
It was shown by Moorhouse et al. [13] that the blocked force, which represents an independent property of a structural
source, may be acquired through an inverse procedure similar to that used in operational force identification and standard
transfer path analysis (TPA) procedures [14]. The relation of note is given by,
vbDYbcN
fc(14.1)
where Ybc 2CNNis the measured mobility matrix of a coupled assembly, vb2CNis a measured operational velocity vector,
and N
fc2CNis the vector of unknown blocked forces. Here subscripts fbgand fcgrepresent complete sets of remote receiver
and coupling interface DoFs, respectively. Variables are given in the frequency domain, with explicit notation omitted for
clarity.
To illustrate the interface problem we begin by considering the in-situ blocked force relation in the form,
vbDYbciN
fciCYbcjN
fcj:(14.2)
where the velocity contributions from known and unknown DoFs are separated. Here, fcicgrepresents the set of coupling
interface DoFs that are known and considered measurable, whilst fcjcjcj6 cigrepresents the set of interface DoFs that
are unknown, or known but can not be measured. An illustrative example of such an assembly is given in Fig.14.1a.
In the determination of the blocked force one pre-multiplies the operational velocity vector by the inverse of a mobility
matrix pertaining to the known DoFs, Ybci. Pre-multiplication of Eq. 14.2 by Y1
bcithus yields,
Y1
bcivbDQ
N
fciDN
fciCY1
bciYbcjN
fcj:(14.3)
The acquired blocked force, Q
N
fci, although correct in its own respect,3is not the true blocked force at the DoFs ci,N
fci.The
neglect of the DoFs cjhas resulted in the additional term, Y1
bciYbcjN
fcj. This term is a property of the coupled assembly and thus
the acquired blocked force is no longer an independent property of the source. This loss of independence may have severe
implications when the acquired blocked force is transferred to a secondary assembly and used to predict the operational
response, for example in the construction of a Virtual Acoustic Prototype [15]. This is demonstrated below.
3The blocked force Q
N
fcirepresents the reaction forces due to a source that is blocked in ciDoFs but unrestrained in the remaining cjDoFs. It is
therefore by definition a blocked force, albeit not the true blocked force.
14 On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’ 173
ab
Fig. 14.1 Diagrammatic illustration of the constrained and unconstrained assemblies corresponding to Eqs. 14.7 and 14.8, respectively. (a)
Unconstrained assembly. (b) Constrained assembly
We are interested in the prediction of the remote receiver velocity, v0
b, on a secondary assembly (denoted by the prime
symbol, 0). The true velocity, that we are aiming to predict, may be expressed in terms of the true blocked force as,
v0
bDY0
bci
N
fciCY0
bcj
N
fcj:(14.4)
To predict the remote velocity the acquired blocked force, Q
N
fci, is pre-multiplied by the coupled transfer mobility of the
secondary assembly that corresponds to the known and measurable DoFs, Y0
bci.
Q
v0
bDY0
bci
Q
N
fciDY0
bci.N
fciCY1
bciYbcjN
fcj/(14.5)
Expanding the above we arrive at,
Q
v0
bDY0
bci
N
f0
ciCY0
bciY1
bciYbcjN
fcj:(14.6)
From the above it is clear that the true velocity, v0
b, and the predicted velocity, Q
v0
b, are not equal. Hence the blocked force is
no longer transferable. Here, the unknown blocked force, N
fcj, contributes to the predicted velocity response through the
propagating transfer function, Y0
bciY1
bciYbcj. So, whilst the response prediction still accounts for the unknown blocked
force, its contribution to the response of a secondary assembly is incorrect. This discrepancy is clearly a consequence of
an incomplete interface description. Had all coupling DoFs been accounted for the true blocked force would have been
acquired, and subsequently transferred to the secondary assembly with no problems.4The uncertainty introduced as a result
of an incomplete interface description is referred to here as model uncertainty.
In this paper we are interested in establishing an experimental procedure to minimize, or identify the severity/cause of,
this source of model uncertainty through the development of an Interface Completeness Criterion (ICC).
14.3 Theoretical Development
In this section we will develop the theory required to formulate the proposed Interface Completeness Criterion.
Consider the assembly depicted in Fig. 14.1a, where a source and receiver sub-structure are coupled via two sets of
interface DoFs. Denoted ciand cj, these DoFs form subsets of the complete coupling interface c, such that fcicgand
4A similar problem is encountered in the application of sub-structure coupling and decoupling procedures. The neglect of coupling interface DoFs
results in an erroneous representation of the assembly/substructure dynamics.
174 J. W. R. Meggitt et al.
fcjcjcj6 cig. Also included are two sets of remote measurement DoFs on the source and receiver. These are referred
to as aand b, respectively. The equations that govern the behaviour of the coupled source-receiver assembly (as depicted in
Fig. 14.1a) are given generally by,
0
B
B
@
va
vci
vcj
vb
1
C
C
A
D
2
6
6
4
Yaa YaciYacjYab
YciaYciciYccjYcib
YcjaYcjciYcjcjYcjb
Yba YbciYbcjYbb
3
7
7
5
0
B
B
@
fa
fci
fcj
fb
1
C
C
A
:(14.7)
We begin by considering the case where only two external forces are applied, i.e. fcjDfbD0. The first is an arbitrary force
at the remote source DoFs a,fa. The second is a constraint force at the coupling interface DoFs ci,N
fci. This second force is
the blocking force required to constrain the velocity vcito 0. The constrained assembly may be represented by the following
set of equations,
0
B
B
@
va
0
vcj
vb
1
C
C
A
D
2
6
6
4
Yaa YaciYacjYab
YciaYciciYcicjYcib
YcjaYcjciYcjcjYcjb
Yba YbciYbcjYbb
3
7
7
5
0
B
B
@
fa
N
fci
0
0
1
C
C
A
:(14.8)
The above describes an assembly that is excited by an arbitrary force at a, whilst the coupling interface, c,ispartially
constrained. This constrained assembly is shown diagrammatically in Fig. 14.1b. Taking the second line of Eq.14.8,
0DYciafaCYciciN
fci:(14.9)
and solving for the blocked force, we arrive at,
N
fciDY1
ciciYciafa:(14.10)
The above relation is a force transmissibility that relates the externally applied force at a, to the resultant blocked force at ci.
Taking the 4th line of Eq. 14.8, whilst introducing the notation v.cj/
bto describe the velocity of the constrained assembly, i.e.
the contribution through the coupling DoFs cjonly,
v.cj/
bDYbafaCYbciN
fci:(14.11)
The first RHS term describes the velocity at bdue an applied force at aon the unconstrained assembly, i.e. v.c/
bDYbafa.
The second RHS term describes an added contribution to this velocity due to the blocking force required to constrain the
interface ci. The blocked force may be eliminated by expressing it in terms fa, as per Eq. 14.10,
v.cj/
bDYbafaYbciY1
ciciYciafa(14.12)
or equivalently,
v.cj/
bDYba YbciY1
ciciYciafa:(14.13)
Equation 14.13 relates an externally applied force at ato the resultant velocity at bon the constrained assembly depicted
in Fig. 14.1b.5The bracketed mobility term therefore represents the transfer mobility through the constrained assembly.
Consequently, let us define,
Y.cj/
ba ,Yba YbciY1
ciciYcia(14.14)
as the transfer mobility from ato b, through the DoFs cj, whilst the DoFs ciare blocked.
5Although not discussed in any further detail here, for jcjjD1,Eq.14.13 may be considered the velocity at bdue to the contribution of a
single path, i.e. whilst all other paths are blocked. This is a similar concept to that used by Margans [17] in the formulation of the GTDT TPA
procedure [18].
14 On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’ 175
Noting that the left hand term in the bracket of Eq. 14.13 is the transfer mobility of the unconstrained assembly, let us
redefine this as,
Y.c/
ba ,Yba (14.15)
that is, the transfer mobility from ato bthrough all coupling DoFs (ciand cj). Lastly, the right hand term in the bracket of
Eq. 14.13 can be seen to form a round trip identity [16] for a mobility similar to Yba. It is interesting to note that for the case
whereby only a single set of coupling DoFs exist, i.e. jcjjD0, this round trip identity is equal exactly to the unconstrained
mobility, Yba [16].6For the constrained interface considered, however, the mobility product YbciY1
ciciYciacorresponds to a
transfer mobility between aand bwhilst accounting for only the coupling DoFs ci. As such, let us define,
Y.ci/
ba ,YbciY1
ciciYcia:(14.16)
Using the above definitions Eq. 14.14 may be rewritten as,
Y.cj/
ba DY.c/
ba Y.ci/
ba (14.17)
or alternatively,
Y.c/
ba DY.ci/
ba CY.cj/
ba :(14.18)
Equation 14.18 states that the transfer mobility from ato bthrough the unconstrained interface, Y.c/
ba , may be represented as
the sum of two mobility terms. These correspond to; the transfer mobility from ato bwhilst the DoFs ciare constrained,
Y.cj/
ba ; and transfer mobility from ato bwhilst the DoFs cjare in some way neglected, Y.ci/
ba .
Experimentally we are able to measure Y.c/
ba directly, simply through the excitation of a, and response measurement of b,
since the physical assembly is not constrained. Similarly, we are able to compute Y.ci/
ba through the direct measurement of its
associated mobilities, Ybci,Y1
cici, and Ycia. We are therefore able to calculate the contribution of the DoFs cjwithout having
access to them directly.
We note here that if the DoF subset cicontains all DoFs, ciDc, then jcjjD0and Y.c/
ba DY.ci/
ba . Experimentally this
would mean that all of the interface DoFs have been included and the interface description is complete.7This final remark
will be used in the formulation of an Interface Completeness Criterion. This criteria may be used to provide a quantitative
assessment of an interface’s ‘completeness’, that is, whether sufficient DoFs have been accounted for.
14.4 Interface Completeness Criterion
In the field of modal analysis there exist a number of criteria to assess confidence in acquired modal parameters. For example,
the modal assurance criterion (MAC), the coordinate modal assurance criterion (COMAC), and the frequency response
assurance criterion (FRAC), to name but a few [19].
The aim here is to establish a similar criterion for the ‘completeness’ of an interface description. Here ‘completeness’
refers to the degree to which the coupling interface DoFs are accounted for by the coupling interface mobility matrix, Ycc.A
complete interface is defined as one whose DoFs are completely described by Ycc.
A suitable criteria should be bound between 0 and 1 such that the degree of completeness may be assessed with ease. An
assessment is proposed in the same form as the well established modal assurance criterion (MAC). The proposed criteria will
be referred to as the Interface Completeness Criterion (ICC).
6Consequently, Y.cj/
ba D0since the DoF subset cjdoes not exist.
7Alternatively, if one considers Eq. 14.14, a complete interface description would block entirely the coupling interface, resulting in a velocity of 0
at the remote source DoFs b.
176 J. W. R. Meggitt et al.
Using an expression identical in form to the MAC, the ICC yields a frequency dependent scalar value bound between 0
and 1, and is defined as,
ICCbaDˇ
ˇ
ˇYc
ba Yci
baHˇ
ˇ
ˇ
2
Yc
ba.Yc
ba/HYci
ba.Yci
ba/H(14.19)
where, Y.ci/
ba DYbciY1
ciciYcia.
Recalling the closing remark of Sect. 14.3, we note that if all coupling DoFs are accounted for, that is, Y.c/
ba DY.ci/
ba ,the
ICCbais equal to one. Similarly, if none of the coupling DoFs are accounted for, that is, Y.ci/
ba D0,theICC
bais equal to zero.
The ICCbais thus related to the degree of completeness, and consequently, the degree of model uncertainty present in a given
interface description.
We note that the ICCbadescribes the degree to which an interface is complete through the blocking of a transfer function
measured between a set of source side DoFs, a, and a single receiver side DoF, b. As such, a different ICCbais obtained for
each remote receiver DoF considered. Furthermore, it should be noted that whilst the above criterion, in theory, yields 1for a
complete interface description this is likely unachievable in an experimental scenario. The measured and predicted mobilities,
Y.c/
ba and Y.ci/
ba , respectively, will be contaminated to some extent by measurement uncertainty and perfect agreement is
unlikely. The question of experimental error is further addressed in the case study of Sect. 14.5.2, although a more thorough
investigation regarding the sensitivity of the ICC is considered beyond the scope of this work.
14.5 Case Studies
In this section the application of the ICC will be demonstrated as part of two case studies. In the first, the discretisation of a
continuous interface between two coupled plates will be considered numerically. In the second, an experimental study will
investigate the completeness of an interface between two sections of steel rod.
14.5.1 Numerical: Continuous Interface
In this study the Interface Completeness Criterion (ICC) is used too assess the completeness of a discrete approximation
to a continuous interface. The interface is considered to be an arbitrary line that separates two sides of a simply supported
rectangular plate, as illustrated in Fig. 14.2. Each side of the interface is considered a separate plate, and are referred as source
(plate 1) and receiver (plate 2). The coupled plate assembly is modelled analytically using a truncated modal summation.
Both translational z, and xyrotational DoFs, ˛and ˇ, are included. The geometric and material properties of the model are
presented in Table 14.1. Five source side DoFs (a) are considered on plate 1 and a single receiver side DoF (b)onplate2.
The coupling interface is represented by an increasing number of positional DoFs, as illustrated in Fig. 14.3. All positional
DoFs, unless otherwise specified, are made up of three coordinate DoFs, relating to z,˛and ˇ. The aim of this study is to
illustrate the use of the ICC in quantitatively assessing the discretisation of a continuous interface. Interfaces of this type are
often encountered in practical scenarios and are typically represented by a series of discrete point like DoFs. The degree to
which this approximation accounts for the continuous nature of the interface is of interest. The ICC between the source side
DoFs and each of the receiver side DoFs are calculated (these are referred to as ICCz,ICC
˛and ICCˇ).
Five interface descriptions are considered here, corresponding to 1, 2, 3, 4 and 5 positional DoFs, evenly spread across
the breadth of the plate, as illustrated through Fig. 14.3a–e. The corresponding ICCs are shown in Fig. 14.4, from top to
bottom, respectively. The ICCs pertaining to translational and rotational (˛and ˇ) receiver DoFs are shown in blue, orange
Table 14.1 Geometry of the coupled plate assembly, plate 1 and plate 2. The material properties of the three plates were; Young’s modulus
ED200 109,densityD9000, Poison’s ratio D0:3, and loss factor D0:1
Plate Dimensions
Coupled 10:8 0:005
Plate 1 0:35 0:8 0:005
Plate 2 0:65 0:8 0:005
14 On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’ 177
Fig. 14.2 Diagrammatic representation of the continuous interface numerical study. Two plates are coupled via a continuous interface (dashed red
line) in the translational zand x=yrotational DoFs, ˛and ˇ
ab
de
c
Fig. 14.3 Diagrammatic representation of the continuous interface numerical study. Two plates are coupled via a continuous interface which is
approximated through varying degrees of discretisation. (a) 1 positional DoF. (b) 2 positional DoFs. (c) 3 positional DoFs. (d) 4 positional DoFs.
(e) 5 positional DoFs
and yellow, respectively. Figure 14.4 clearly illustrates that the ICC converges to one as the number of DoFs used to describe
the interface is increased. Furthermore, the results highlight the difference between ICCz,ICC
˛and ICCˇ. Although sharing
an overall trend, clear differences can be observed. This suggests that a single ICC may not sufficiently describe the interface
completeness, and that multiple ICCs may be required for a more thorough insight. That said, the experimental effort required
to include additional response DoFs is minimal as no further excitations are required.
Shown in Fig. 14.5 are the ICCs corresponding to an interface description made up of 10 positional DoFs. In Fig. 14.5athe
coupling interface description includes both translational and rotational coordinate DoFs. In Fig. 14.5b the coupling interface
description includes only translational coordinate DoFs, i.e. the rotational DoFs were neglected. As one might expect, the
neglect of rotational coupling DoFs has resulted in a worsening of the ICC. Whilst this is an intuitively obvious result, it
highlights the importance of rotational DoFs in the description of a continuous interface and, furthermore, the ability of the
ICC to quantify it.
178 J. W. R. Meggitt et al.
102103
0
0.2
0.4
0.6
0.8
1
ICC
ICCabzICCabaICCabb
102103
0
0.2
0.4
0.6
0.8
1
ICC
102103
0
0.2
0.4
0.6
0.8
1
ICC
102103
0
0.2
0.4
0.6
0.8
1
ICC
102103
0
0.2
0.4
0.6
0.8
1
Frequency (Hz)
ICC
Fig. 14.4 Interface Completeness Criteria (ICC) for a continuous interface approximated using five different levels of discretisation (see Fig. 14.3).
From top to bottom, the interface is represented by 1, 2, 3, 4 and 5 positional DoFs, each of which includes translational zand x=yrotational DoFs,
˛and ˇ. The ICC is calculated using 15 source side positional DoFs (including z,˛and ˇat each) and a single receiver side DoF (including z,˛
and ˇ). An ICC is presented for each receiver DoF
14 On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’ 179
102103
0
0.2
0.4
0.6
0.8
1
ICC
ICCabzICCaba
a
b
ICCabb
102103
0
0.2
0.4
0.6
0.8
1
ICC
Fig. 14.5 Interface Completeness Criteria (ICC) for acontinuous interface approximated using 10 positional DoFs, both with (a) and without (b)
rotational coupling. The ICC is calculated using 15 source side positional DoFs (including z,˛and ˇat each) and a single receiver side DoF
(including z,˛and ˇ). An ICC is presented for each receiver DoF. (a) 10 positional DoFs. (b) 10 positional DoFs (translation zonly, neglecting ˛
and ˇ)
Fig. 14.6 Diagrammatic representation of the experimental study. Two rods are coupled via a single discrete interface (red line) in translational y
and z,andy=zrotational DoFs, ˇand
Lastly, it is perhaps worth noting the improvement in the ICC between Figs. 14.4 (bottom) and 14.5a due to the extra 5
positional DoFs.
14.5.2 Experimental: Point Connected Interface
The experimental case study presented here concerns the description of an interface between two rigidly coupled rods. A
diagrammatic illustration of the study is given in Fig. 14.6. The coupling interface, shown in red, was considered as a single
positional DoF, and therefore described, generally, by the 6 coordinate DoFs, x,y,z,˛,ˇand .
The aim of this study was to use the ICC to access various interface descriptions consisting of the DoFs; y,z,ˇand .
The in-plane DoF x(along the length of the rod) and its associated rotation ˛were neglected due to the difficulties associated
with their measurement.
The translational, rotational and cross mobilities associated with the retained DoFs considered were approximated using
the finite difference method [20], which itself imposes a limit on the validity of an interface description over a frequency
range related to the sensor spacing (taken here as 2 cm).
Twelve source side DoFs (a) were excited whilst simultaneously measuring the response at the coupling interface (ci) and
the single receiver side DoF (b). This enabled the calculation of Y.c/
ba and Ycia. The interface DoFs were subsequently excited
and the mobilities Yciciand Ybcimeasured. Together, the above measurements allowed for the calculation of the mobility
180 J. W. R. Meggitt et al.
100 1000 5000
0
0.2
0.4
0.6
0.8
1
Frequency
ICC
4 DoFs 2 DoFs
a
b
c
100 1000 5000
0
0.2
0.4
0.6
0.8
1
ICC
100 1000 5000
0
0.2
0.4
0.6
0.8
1
ICC
Fig. 14.7 Interface Completeness Criteria (ICC) obtained from the experimental study using 4 different interface descriptions. (a)AnICC
comparison based on all 4 interface DoFs (z,y,,ˇ), and the reduced interface DoFs (z,). (b) An ICC based on the translational zDoF,
i.e. neglecting the rotational DoF, .(c) An ICC based on the translational and rotational DoFs, yand ˇ
Y.ci/
ba DYbciY1
ciciYcia. The ICC was then calculated as per Eq. 14.19. The importance of a particular DoF to the interface
description may be assessed by simply neglecting said DoF in the calculation of the ICC.
Shown in Fig. 14.7 are the ICCsobtained from the experimental study illustrated in Fig. 14.6 for a number of different
interface descriptions.
Presented in Fig. 14.7a are the ICCs associated with a 4 DoF description (blue) and a reduced 2 DoF description (orange),
where the DoFs yand ˇhave been neglected. It is interesting to note that the two ICCs are in near perfect agreement.
This suggests that the interface DoFs, yand ˇ, have a negligible effect on the coupling of the structure. It should be noted,
however, that this result was obtained from an ICC in which the source side excitation was made in the vertical zdirection.
Had additional excitations been applied in the ydirection, coupling in yand ˇwould likely have been of greater importance.
It is important to note that the calculation of the ICC, as per Eq. 14.19, is particularly sensitive to experimental error,
notably the error associated with inconsistent excitations in the measurement of the required mobility matrices. Errors of
this sort can lead to inconsistencies within the interface mobility matrix, Ycici, which may result in large errors following
its inversion. This effect is particularly relevant for under-damped systems, where structural anti-resonances are sensitive to
14 On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for ‘Completeness’ 181
excitation position. As an example, consider the sharp notch in the ICCs of Fig. 14.7a in the region of 200 Hz. This is likely
a result of inconsistencies in the measured mobilities due to the small amount of damping present in the rod, and not due to
an incomplete interface description.
Shown in Fig. 14.7b is the ICC associated with the single translational coupling DoF, z. A comparison against the reduced
description in Fig. 14.7a (orange) clearly illustrates a worsening of the ICC due to the now neglected rotational DoF, .The
effect is particularly pronounced in the region of 150 and 450 Hz. This suggests that in these regions the rotational coupling
of the interface is of greater importance.
Lastly, shown in Fig. 14.7c is the ICC associated with the coupling DoFs yand ˇ. As one would expect considering
Fig. 14.7a, the ICC suggests that, by themselves, the DoFs yand ˇprovide a very poor interface description.
14.6 Conclusion
This paper has been concerned with the development of an Interface Completeness Criterion (ICC) suitable for the
quantitative assessment of the degree to which a coupling interface has been described. The ICC is based on the mathematical
blocking of a subset of the coupling interface DoFs. This blocking allows for the separation of known and unknown DoFs,
and consequently the formulation of a bound completeness criterion, referred to here as the ICC. The application of the ICC
was illustrated by two case studies; the first a numerical simulation concerning the discretisation of a continuous interface,
and the second, and experimental study concerning a discrete interface.
Acknowledgements This work was funded through the EPSRC Research Grant EP/P005489/1, Design by Science.
References
1. Gialamas, T., Tsahalis, D., Bregant, L., Dtte, D., Van Der Auweraer, H.: Substructuring by means of FRFs: some investigations on the
significance of rotational DOFs. In: Proceedings of the 14th International Modal Analysis Conference – IMAC, pp. 619–625, Jan 1996
2. Ewins, D.J., Liu, W.: The importance assessment of RDOF in FRF coupling analysis. IMAC XVII 2, 1481–1487 (1999)
3. Duarte, M.L.M., Ewins, D.J.: Some insights into the importance of rotational degrees-of-freedom and residual terms in coupled structure
analysis. In: Proceedings of the 13th International Modal Analysis Conference – IMAC, pp. 164–170, May 1995
4. Klerk, D.D., Rixen, D.J., Voormeeren, S.N., Pasteuning, F.: Solving the RDoF problem in experimental dynamic substructuring. In:
Proceedings of the 26th International Modal Analysis Conference – IMAC (2008)
5. D’Ambrogio, W., Fregolent, A.: Substructure decoupling without using rotational DoFs: fact or fiction? Mech. Syst. Signal Process. 72–73,
499–512 (2016)
6. Moorhouse, A.T., Elliot, A.S.: Indirect measurement of frequency response functions applied to the problem of substructure coupling. In:
NOVEM: Noise and Vibration – Emerging Methods, pp. 1–7 (2012)
7. Klerk, D.D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review and classification of techniques.
AIAA J. 46(5), 1169–1181 (2008)
8. Patil, N.S., Elliott, A.S., Moorhouse, A.T.: A blocked pressure based transfer path analysis (TPA) method to measure the sound insulation path
contributions of a partition subjected to an incident airborne field. In: 24th International Congress on Sound and Vibration, ICSV 2017, pp. 1–8
(2017)
9. Bonhoff, H.A., Petersson, B.A.T.: The influence of cross-order terms in interface mobilities for structure-borne sound source characterization:
plate-like structures. J. Sound Vib. 329(16), 3280–3303 (2007)
10. Elliott, A.S., Meggitt, J.W.R., Moorhouse, A.T.: Blocked forces for the characterisation of structure borne noise. In: Internoise2015, San
Fransisco, pp. 5798–5805 (2015)
11. Alber, T., Sturm, M., Moorhouse, A.T.: Independent characterization of structure-borne sound sources using the in-situ blocked force method.
In Proceedings of Internoise, pp. 7302–7313 (2016)
12. Lennström, D., Olsson, M., Wullens, F., Nykänen, A.: Validation of the blocked force method for various boundary conditions for automotive
source characterization. Appl. Acoust. 102, 108–119 (2016)
13. Moorhouse, A.T., Elliott, A.S., Evans, T.A.: In situ measurement of the blocked force of structure-borne sound sources. J. Sound Vib. 325(4–5),
679–685 (2009)
14. van der Seijs, M.V., Klerk, D.D., Rixen, D.J.: General framework for transfer path analysis: history, theory and classification of techniques.
Mech. Syst. Signal Process. 68, 1–28 (2015)
15. Meggitt, J.W.R., Elliott, A.S., Moorhouse, A.T.: Virtual assemblies and their use in the prediction of vibro-acoustic responses. In: Proceedings
of the Institute of Acoustics, Warickshire (2016)
16. Moorhouse, A.T., Elliott, A.S.: The “round trip” theory for reconstruction of Green’s functions at passive locations. J. Acoust. Soc. Am. 134(5),
3605–3612 (2013)
17. Magrans, F.X.: Method of measuring transmission paths. J. Sound Vib. 74(3), 321–330 (1981)
182 J. W. R. Meggitt et al.
18. Guasch, O., Magrans, F.X.: The global transfer direct transfer method applied to a finite simply supported elastic beam. J. Sound Vib. 276(1–2),
335–359 (2004)
19. Allemang, R.J.: The modal assurance criterion (MAC): twenty years of use and abuse. In: Proceedings of SPIE – the International Society for
Optical Engineering, vol. 4753, pp. 397–405 (2002)
20. Elliott, A.S., Moorhouse, A.T., Pavi´
c, G.: Moment excitation and the measurement of moment mobilities. J. Sound Vib. 331(1), 2499–2519
(2012)
... Measuring all 3 rotations around one interface point would thus require 3 sensors, or remounting and repeating the measurements 3 times (roving sensor). Despite the challenges of measuring them, including RDoF in the coupling process has been shown to be crucial for accurate results [36,39,48,86,98,113]. After all, coupling only the translational directions at a connection point would correspond to a ball joint instead of the needed rigid connection for e.g. the beam shown in figure 3.5. ...
... The prediction is found to be good (also in the other channels), so the blocked forces are assumed to describe the excitation of the compressor sufficiently. Another valuable check for testing the 'completeness' of the interface description can be given by the interface completeness criterion (ICC), as introduced in [113]. Note that the two negative signs in the blocked force identification (6.10) and prediction of responses with the blocked forces (6.11) 20 are annihilating each other. ...
... For an easy to read, but insightful overview of the L-curve see [62]. In figure 8.8, the L-curves for the inverse force identification at different frequencies are shown (109)(110)(111)(112)(113)(114)(115)(116)(117)(118)(119). It can be observed that for some frequencies, both the residual ||µ # || and the blocked force magnitude ||f bl# 2 || is high (see the three curves in the upper right part of figure 8.7). ...
Thesis
Full-text available
[ Link to PhD defense video: https://www.youtube.com/watch?v=IEVuF2rJOYs&t=6s ] This thesis is the result of a 4-year collaboration between the Technical University of Munich and the BMW Group. The goal was to apply substructuring methods to the Noise Vibration Harshness (NVH) engineering needed for integrating electric climate compressors in upcoming vehicles. The compressor is one of the major contributors to the cabin noise in battery electric vehicles (BEVs). An accurate yet practical development process for its vehicle integration is crucial for industry. Specifically, the aim was to simulate the compressor noise in the cabin for different, virtual design variants of the isolation concept. Therefore, the methods from two broader fields were applied: First, the excitation of the compressor was modeled with component transfer path analysis (TPA) methods. Second, the full transfer path from the compressor to the driver’s ear is assembled from multiple subcomponent models, via dynamic substructuring (DS). For accomplishing the above mentioned goals, different gaps in the current technology have been identified, which will be addressed in this thesis. With frequency based substructuring (FBS), a subclass of DS, it is possible to couple experimental and numerical substructure models in a virtual assembly. For the compressor, it was found that including rigid body models in the transfer path is a valuable addition. The proper formulation and integration of rigid body models in the framework of FBS will be presented. Another bottleneck at the onset of this project, was the proper modeling of rubber bushings in the transfer path. A novel method for experimentally identifying accurate substructure models of rubber isolators was developed. The rotating components in the compressor introduce gyroscopic effects that influence its dynamics. A novel substructuring method for virtually coupling gyroscopic terms to a component could prove that these effects are not relevant for the compressor case. The compressors excitation is described by blocked forces. Applying the blocked forces to the substructured transfer path of the assembly allows to simulate the sound in a virtual prototype. One goal was to make the simulated results audible to non-acoustic experts, which required the creation of sound files. This allowed for a subjective comparison of different designs at an early development stage. Since the noise predictions with TPA are typically in the frequency domain, some signal processing is required to create sound files in the time domain. Different methods for auralization will be compared, which could not be found in the existing TPA literature. Due to the inverse process for identifying the blocked forces, measurement noise can be amplified to unacceptably high levels, which are audible in the sound predictions. Regularization methods have the potential to significantly suppress the noise amplification, which is explained and exemplified for blocked force TPA. Additionally, it was found that only the structure-borne sound transmission was not sufficient to describe the compressor noise in the cabin. The compressor is also directly radiating air-borne sound from its housing, which will be included in the NVH model by means of equivalent monopoles. The application examples at the thesis’ end are extending the current state-of-the-art, by showing how the modular vehicle models can be used for early phase, parametric design optimizations on a complex NVH problem.
... Then, in part two, the source is operated and the operation velocity v Cc is measured. For further details regarding practical considerations the reader is referred to [17,18]. ...
... The pseudo forces were then obtained as per Eq. (18). Note that when calculating the pseudo forces only 11 response measurements are used. ...
... As in the experimental case, the pseudo forces f Ca are obtained using Eq. (18), where v Cb are the measured operational shell responses. In this case, however, the structure mobility Y Cba has been computed using the shell FE model, instead of being determined experimentally. ...
Article
Full-text available
The purpose of this paper is to present a case study whereby a hybrid experimental-numerical model is used to analyse the structure-borne radiation from a domestic product (vacuum cleaner head). The passive (including radiative) properties of the structure considered are modelled using the Hybrid FE-SEA method. The product's operational activity, which lies beyond the capabilities of conventional modelling methods, is characterised experimentally using inverse force identification. The identified forces and passive model are combined to form a so called Hybrid FE-SEA-eXperimental model of the assembly. The FE-SEA-X model is then used to identify dominant contributions from the assembly's sub-components.
... Interface completeness is a general issue encountered whenever characterisations are performed at the interface of one or more sub-structures [25]. This includes not only the characterisation of blocked forces, but also the coupling and decoupling of sub-structures. ...
... The so-called Interface Completeness Criterion (ICC) is based on the notion of mathematically blocking the set of known DoFs at the source-receiver interface, and observing the resultant response on the receiver. Its derivation, first presented in [25], is provided below for 'completeness'. ...
... The ICC as defined in Eq. (25) considers only a single receiver side DoF b [25]. In the case that multiple DoFs are of interest, the vectorised mobilities, ...
Article
Full-text available
Blocked forces can be used to describe, independently, the operational characteristics of a vibratory source. Their use within a computational model avoids the need to represent explicitly the complex mechanisms that lead to vibratory excitation. To obtain and apply an experimental blocked force with confidence it is important that likely sources of error are known, and measures of their severity are available. In this paper we introduce the notions of completeness and consistency, and detail their role in the introduction of systematic errors in a blocked force characterisation. Their mathematical origins are described and criteria to quantify their severity are proposed; the Interface Completeness Criterion (ICC), and the Measurement Consistency Criterion (MCC). These are illustrated through numerical and experimental examples. Completeness is related to the interface description adopted in a source characterisation (i.e. the number of degrees of freedom used). The ICC represents the quality of an interface description and can be quantified from in-situ measurements, i.e without having to remove the source from its assembly. Consistency is related to the underlying dynamics shared by active and passive quantities (whether measured or modelled). The issue of consistency is more general, completeness being a special case, and so a single criterion is hard to formulate. When an inconsistency arises between the blocked force of a vibration source and its corresponding free interface frequency response function matrix, the MCC provides a quantitative indication of its severity. Importantly, many of the concepts discussed apply equally in the context of experimental dynamic sub-structuring.
... With extension of the measurement to the several driving points, even more consistent hybrid models can be obtained. Quality of the decoupling step can be additionally validated using Interface Completeness Criterion (ICC) 180 [36,37] in order to ensure sufficient interface description. ...
Article
Full-text available
A reconstructed displacement field using near-field acoustic holography (NAH) serves as an alternative to conventional measurement methods when it comes to obtaining the high-resolution vibration response of a structure. The method is highly applicable as it enables direct, non-contact measurement of the 3D structural response based on a single acoustic measurement. Although useful, the method’s ill-posed nature limits its use in the field of structural dynamics. This problem can be effectively addressed by using regularization and/or field-separation techniques that can attenuate the noise and the presence of external acoustic sources. All these methods rely on the measurement of acoustic quantities; therefore, the reconstruction of structural admittances is based solely on the evaluation of the hologram(s). This article proposes an alternative approach to improving the accuracy of NAH-based structural admittances by integrating them with a few discrete response measurement on the structure itself. The formulation relies on the mixing of the high-resolution NAH measurement with accurate discrete measurements (e.g., accelerometer or laser vibrometer) using dynamic substructuring techniques. The proposed hybrid approach is a very powerful modeling methodology that can integrate high-resolution spatial measurements using NAH with the accuracy and consistency provided by precise translation discrete measurements. In order to mix two experimental response models System Equivalent Model Mixing (SEMM) method is proposed. An experimental case study on a T-shaped structure demonstrates the robustness and improved accuracy of the estimated structural admittances compared to the plain NAH formulation.
... This is also important for obtaining a set of blocked forces that can actually be transferred to a different vehicle design. Despite the challenges of measuring rotational DoF, it has been shown in dynamic substructuring applications that they are crucial for accurate results [11][12][13][14][15]. ...
Conference Paper
Full-text available
Before performing a transfer path analysis (TPA), the engineer needs to think about the right modeling of the source's interface with the receiver. In practice, the vibration transfer from the source to the receiver is often modeled with three translational forces in each connection point. Mechanically this corresponds to a ball joint connection, which cannot transfer any moments. Our goal is to compare different complexities of interface descriptions on the industrial example of an electromagnetic roll control (ERC) in a passenger car. Therefore, different variants of interface degrees of freedom and matrix over-determination are compared: 1. Three hammer impact points in x,y,z-direction (no sensor over-determination). 2. Multiple impacts, transformed with the virtual point transformation (VPT) to 3 forces. 3. Multiple impacts, transformed with the VPT to 3 forces and 3 moments. These interface descriptions are compared in terms of an on-board validation, the interface-completeness-criterion and by evaluating the transferability to a modified vehicle design. It was found that the over-determination of the matrix inverse should be used in any case to avoid spurious noise artifacts. For best quality TPA results at higher frequencies, it was found necessary to include rotational moments in the interface description.
... FBS equations are used to calculate the coupled FRFs, applying truncation in the inversion. Ry is excluded from the coupling as its contribution doesn't appear to be necessary for a complete coupling interface [16]. A depiction of the process is shown in Figure 8. ...
Conference Paper
R oad induced noise is getting more and more significant in context of the electrification of the powertrain. The automotive industry is seeking for technologies to predict the contribution of vehicle components upfront, early in the development process. Classical Transfer Path Analysis (TPA) is a well-established technique that successfully identifies the transmission paths of noise and vibration from different excitation sources to the target responses. But it has a drawback: it requires the physical availability of the full vehicle. To achieve shorter development cycles, to avoid costly time-consuming design iterations and due to the limited availability of prototypes, engineers derived a method that addresses these requirements. Component-based TPA is a relatively new structure borne substructuring approach that allows to characterize the source excitation by a set of equivalent loads (blocked forces) independently from the receiver structure and to predict its behavior when coupled to different receivers. Frequency Based Substructuring, FBS, is applied in order to obtain the coupled assembly. However, there are a number of challenges affecting its applicability, such as the proper modelling of the coupling degrees of freedom and the difficulty to access the interface connection points. Geometrical reduction aims to solve those inconveniences. This paper aims to investigate these challenges of component-based TPA by measurements on a tire-wheel suspension in static condition. The source component (the tire-wheel) is characterized by a set of blocked forces and transfer functions identified on a dedicated tire-wheel test-rig. These calculated loads are combined with the FRFs of the fully assembled system. The FRFs are calculated by using experimental substructuring methods. The sensitivity of applying FBS together with geometrical reduction in the frame of component based TPA will be analyzed.
Article
Substructuring approaches have been extensively used since long time to predict the vibroacoustic behaviour of built-up mechanical systems. In the frequency domain, these methods build on the dynamic characterisation of the subsystems via frequency response functions at the coupling interfaces. Intensively used for subsystems connected by points, dynamic substructuring still constitutes an open area of research for systems comprising continuous interfaces. Within this framework, a method which allows to characterise subsystems connected along lines is presented. The approach is based on a discretisation of the continuous interfaces into a small set of points, where the information of the subsystems is condensed. For this purpose, an inverse approach is used, which allows to characterise the dynamics of the passive subsystem using data of the assembled system. A straightforward inversion, however, does not assure the physical consistency of the characterized subsystem. In other words, the subsystem extraction procedure must not only guarantee correct dynamic behaviour of the assembled system, but the obtained subsystem must also be reciprocal and passive. The central theme of this paper is the formulation of a constrained optimisation procedure for the enforcement of reciprocity and passivity on the inversely obtained subsystem characteristics. The method is validated on a structure made of two plates connected along a common edge through a beam.
Article
Blocked force determination is an alternative to the more routine method of inverse force determination using classical transfer path analysis. One advantage of determining blocked forces is that there is no need for the source to be detached or isolated from the system. Results are, in theory, valid so long as blocked forces are determined at the interface between the source and receiver system under the assumption that the interface is well defined. Another advantage is that calculated blocked forces are appropriate when modifications are made on the receiver side of the interface. This insures that the blocked forces are suitable for utilization in analysis models where receiver system modifications are considered. Difficulties in using the approach arise when interface locations are difficult to instrument. This paper demonstrates that blocked forces may also be determined along a continuous interface offset from bolted connections or isolators making the method more convenient to use. This offset interface strategy is demonstrated for plate structures using both simulation and measurement. Recommendations are made for selecting the number of forces and blocked force locations along this offset interface.
Article
Full-text available
The airborne sound transmission through a building element such as a partition/panel is governed by the sound insulation of the partition, or the resistance the partition provides to the incident sound. Typically the airborne sound insulation of the wall is rated by a single number quantity given as the Sound Reduction Index (SRI) or the Sound Transmission Class (STC). However these ratings do not provide any information on the sound transmission through different paths in the partition. Such information may be useful in diagnosing weak sound insulation paths, weight optimisation, etc. The Airborne TPA method based on blocked force formulation has proven to be an effective technique to diagnose the sound transfer through individual paths. The paths can then be rated according to their sound pressure contributions. The Airborne TPA method however , can be time consuming in case of limited number of sensors and/or large size of partitions. Hence there is a need to provide a faster measurement method which would provide the diagnostic information about the sound insulation paths. In this paper, a simplified Airborne TPA approach based on measurement of blocked pressures is presented. The blocked pressure theory for the airborne sound transfer through partitions is discussed at first. Validation and diagnostic results are then presented for sound transfer through point connected dual leaf partition using the new approach. The blocked pressure method is significantly faster and can be automated. The accuracy of the measurement is dependent on the wavelength of the incident wave.
Conference Paper
Full-text available
The vibro-acoustic behavior of systems and components in modern vehicles play an increasingly important role in the development process of high quality products in automotive industry. In order to characterize the numerous mechanical, electrical and mechatronic systems, many of which embody significant sources of structure-borne sound and vibration, advanced measurement techniques are required. Ideally, such characterization techniques should allow specifying supplier components on a test rig without the necessity of conducting vehicle measurements to allow a better understanding of the NVH behavior at an early stage in the development process. This paper investigates the applicability of the in-situ blocked force method as a receiver-independent approach for the characterization of an electrical steering system. First, blocked forces are obtained from test bench measurements to characterize the system at its multiple connection points. In a second step, the blocked forces are transferred to a second structure to predict the receiver response in a different installation. The accuracy of the in-situ blocked force approach is investigated by comparing the predicted response with actual measurements. Finally, the usability of the obtained data for a virtual prediction of the interior sound pressure is discussed.
Conference Paper
Full-text available
In the field of experimental vibro-acoustics the ability to predict the response of a coupled assembly from the properties of its constituent parts can prove advantageous, particularly in the development of mechanical goods, such as domestic products, vehicles, and other machinery. A notable example is its use within virtual acoustic prototyping (VAP). It is the aim of this paper to outline a set of methodologies that together allow for the construction of 'virtual' assemblies, from which vibro-acoustic predictions can be made. Methods for independently characterising both sources of structure-borne sound and resilient elements are presented. Used in tandem these methods, along with a dynamic sub-structuring technique, provide the necessary tools to construct virtual assemblies. An experimental case study is presented as an example, whereby the response of a resiliently mounted pump is modelled virtually. Each component of the assembly is characterised experimentally via their free mobility, dynamic stiffness or blocked force, and coupled together using an impedance summation approach. The resulting virtual model is validated against the physically coupled assembly via measured and predicted operational receiver responses.
Article
Full-text available
Vibro-acoustic source characterization is an essential task in vehicle development to enable prediction of receiver response. For structure-borne noise, the interface forces in multiple degrees of freedom due to internal loads are often quantified for root cause analyses in a single system assembly, as in transfer path analysis (TPA). However, for a reliable prognosis of the acoustic performance of a known component such as a motor or pump, a receiver-independent source characterization is required, and the method of acquiring blocked forces from in-situ measurements has been shown to be a preferred technique for such purposes. The benefits of the method are the characterization of the intrinsic properties of the source and the possibilities of measuring the component attached to receivers with varying dynamic properties. There is to date a limited number of validation cases where blocked forces from in-situ measurements are acquired for automotive source–receiver assemblies. In this study the blocked forces of a vacuum pump in nine degrees of freedom were determined when connected to a bracket whose boundary conditions were modified in order to achieve four assemblies with different source/receiver dynamic properties. The results show that the blocked forces are transferable, i.e. the receiver response in one assembly was predicted in a wide frequency range by combining source–receiver transfer functions of that assembly with blocked forces estimated in another assembly. Furthermore, an in-situ blocked force TPA was applied to a double-isolated complete vehicle source–receiver case of an electric rear axle drive with interior compartment sound pressure as target. The reconstructed magnetic tonal harmonics agreed with the measured target response in the frequency range 50–500 Hz, which further motivates the use of the blocked force principles for TPA and source requirements specifications.
Article
Full-text available
Transfer Path Analysis (TPA) designates the family of test-based methodologies to study the transmission of mechanical vibrations. Since the first adaptation of electric network analogies in the field of mechanical engineering a century ago, a multitude of TPA methods have emerged and found their way into industrial development processes. Nowadays the TPA paradigm is largely commercialised into out-of-the-box testing products, making it difficult to articulate the differences and underlying concepts that are paramount to understanding the vibration transmission problem. The aim of this paper is to derive and review a wide repertoire of TPA techniques from their conceptual basics, liberating them from their typical field of application. A selection of historical references is provided to align methodological developments with particular milestones in science. Eleven variants of TPA are derived from a unified framework and classified into three categories, namely classical, component-based and transmissibility-based TPA. Current challenges and practical aspects are discussed and reference is made to related fields of research.
Conference Paper
The airborne sound insulation of a partition is measured by relevant parts of ISO 10140 to thereby give a single number quantity Rw-the Sound Reduction Index (SRI). These standard tests however, do not provide any information on how the sound is transferred through the partition or the contribution of the transfer paths involved to the total sound observed at a receiver position. In the automotive industry, wide use is made of methods such as Transfer Path Analysis (TPA) which provide diagnostic information about the sound transfer paths of structure-borne sound in a structure subjected to an applied excitation. This paper highlights and discusses an in-situ TPA technique based on blocked force approach, applied to the problem of diagnosing sound insulation paths in cavity backed partitions subjected to airborne excitation. Results are presented for the sound transmission through a cavity-backed plate for airborne excitation and a point connected dual leaf partition for structure borne and airborne excitation. Flanking has to be minimal for validating the methodology in the case of airborne excitation. The path contributions measured in presence of other flanking paths are still valid and show if the partition under consideration is a dominant path for sound transfer with respect to the flanking paths. For structure borne excitation, an interesting application of the method is source localization.
Article
In this paper it is shown that the inaccuracy of the sensor orientation is a first order error, which can affect magnitude and phase of Frequency Response Function (FRF) measurements. These bias errors can be minimized and estimated if a priori knowledge about the stiffness of the substructures is available. A least squares estimation procedure is developed which minimizes the sensor orientation errors. It is applied to modal analysis of machine tool structures.
Article
15 years of NVH applications make Transfer Path Analysis appear a commodity tool. This is however not the case. Required insight in the application constraints makes TPA remain an expert approach. This paper reviews past progress in TPA methodology and its limitations. It then introduces a number of innovative approaches addressing these, opening new application fields. This includes speed improvement (Fast TPA), structural modeling integration (Modal Contribution Analysis), CAE integration (Hybrid TPA), sound quality interpretation (TPA-sound synthesis) and supporting better exploitation of operational data (Operational Path Analysis). An outlook is given to the next challenge, the application to transient problems.
Article
In the framework of experimental dynamic substructuring, substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). On the contrary, substructure coupling identifies an assembled system starting from the component subsystems. The degrees of freedom (DoFs) of the assembled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In substructure coupling, whenever coupling DoFs include rotational DoFs, the related rotational FRFs must be obtained experimentally. Does this requirement holds for substructure decoupling too, as it is commonly believed? Decoupling can be ideally accomplished by adding the negative of the residual subsystem to the assembled system (direct decoupling) and by enforcing compatibility and equilibrium at enough interface DoFs. Ideally, every DoF of the residual subsystem belongs to the interface between the assembled system and the residual subsystem. Hopefully, not all the coupling DoFs are necessary to enforce compatibility and equilibrium. This may allow to skip coupling DoFs and specifically rotational DoFs. The goal of the paper is indeed to establish if rotational FRFs at coupling DoFs can be neglected in substructure decoupling. To this aim, after highlighting the possibility of avoiding the use of coupling DoFs from a theoretical standpoint, a test bed coupled through flexural and torsional DoFs is considered. Experimental results are presented and discussed.