Abstract

Built-up structures, such as airplanes, ships, and even refrigeration systems, which have many components, can be substructured to speed up and facilitate the process of calculating the vibratory response of the complete system. In many structures, there are rubber isolators that connect component parts, and these connections can each occur over a finite distributed area. It is often convenient and intuitive to substructure the system at the isolators. However, in previous work, it has been shown that the frequency response of the complete system does not always agree with the frequency response of the system calculated from the mobilities of the subsystems. It was thought that this was due to the distributed area connection of the isolators, and this motivated the study reported in this article. An investigation into some issues that occur when substructuring a system that contains soft distributed isolators is described. Using finite element models, it is shown that if a system is substructured, such that the interface between the substructures occurs at a soft rubber isolator, then there is a limited frequency range over which the frequency response function of the assembled system is accurate. It is further shown that it is far better to substructure the system, at stiff, discrete connections, if possible. The frequency range over which the frequency response of the assembled system should then be more accurate over a much wider frequency range.

References

References
1.
Klerk
,
D.
,
Rixen
,
D. J.
, and
Voormeeren
,
S. N.
,
2008
, “
General Framework for Dynamic Substructuring: History, Review and Classification of Techniques
,”
Am. Inst. Aeronaut. Astronaut. J.
,
46
(
5
), pp.
1169
1181
. 10.2514/1.33274
2.
Gardonio
,
P.
, and
Brennan
,
M. J.
,
2004
, “Mobility and Impedance Methods in Structural Dynamics,”
Advanced Applications in Acoustics, Noise and Vibration
,
F.
Fahy
and
J.
Walker
, eds.,
Spon Press
,
London
.
3.
Craig
,
R. R.
,
2000
, “
A Brief Tutorial on Substructure Analysis and Testing
,”
Proceedings of the 18th International Modal Analysis Conference
,
San Antonio, TX
,
Feb. 8–10
, pp.
899
908.
4.
Craig
,
R. R.
, and
Kurdila
,
A. J.
,
2006
,
Fundamentals of Structural Dynamics
,
2nd ed.
,
John Wiley & Sons
,
New Jersey
.
5.
Matthew
,
S. A.
,
Harrison
,
M. G.
, and
Randall
,
L. M.
,
2011
, “
Experimental Modal Substructuring to Estimate Fixed-Base Modes From Tests on a Flexible Fixture
,”
J. Sound Vib.
,
330
(
18–19
), pp.
4413
4428
. 10.1016/j.jsv.2011.04.010
6.
Mondot
,
J. M.
, and
Peterson
,
B. A. T.
,
1987
, “
Characterization of Structure-Borne Sound Sources: The Source Descriptor and the Coupling Function
,”
J. Sound Vib.
,
114
(
3
), pp.
507
518
. 10.1016/S0022-460X(87)80020-2
7.
Peterson
,
B. A. T.
, and
Plunt
,
J.
,
1982
, “
On Effective Mobilities in the Prediction of Structure-Borne Sound Transmission Between a Source and a Receiving Structure, Part II: Procedures for the Estimation of Mobilities
,”
J. Sound Vib.
,
82
(
4
), pp.
531
540
. 10.1016/0022-460X(82)90406-0
8.
Van Der Seijs
,
M. V.
,
Klerk
,
D.
, and
Rixen
,
D. J.
,
2005
, “
General Framework for Transfer Path Analysis: History, Theory and Classification of Techniques
,”
Mech. Syst. Signal Process.
,
68–69
, pp.
217
244
.10.1016/j.ymssp.2015.08.004
9.
Auweraer
,
V.
,
Mas
,
H.
,
Dom
,
P.
,
Vecchio
,
S.
and
Janssens
,
A.
,
2007
, “
Transfer Path Analysis in the Critical Path of Vehicle Refinement: The Role of Fast, Hybrid and Operational Path Analysis
,” SAE Technical Paper.
10.
Istvan
,
L.
, and
Beranek
,
L.
,
2006
,
Noise and Vibration Control Engineering: Principles and Applications
,
John Wiley & Sons
,
New York
.
11.
Manzato
,
S.
,
Risaliti
,
E.
,
Napoli
,
C.
,
Tamarozzi
,
T.
, and
Peeters
,
B.
,
2015
, “
A Review of Frequency-Based Substructuring Methods and Their Applicability to Engineering Structures
,”
Proceedings of the International Conference on Structural Engineering Dynamics
,
Lagos, Portugal
,
June 22–24
, pp.
997
1005
12.
Marques
,
V. C.
,
2010
, “
Auralização de um Sistema Vibroacústico Considerando a Influência dos Graus de Liberdade dos Acoplamentos
,”
Master’s dissertation
,
Universidade Federal de Santa Catarina
.
13.
Peeters
,
P.
,
Tamarozzi
,
T.
,
Vanhollebeke
,
F.
, and
Desmet
,
W.
,
2014
, “
A Robust Approach for Substructure Decoupling
,”
Proceedings of the International Conference on Noise and Vibration Engineering ISMA
,
Leuven, Belgium
,
Sept. 15–17
, pp.
3907
3921
.
14.
Klerk
,
D.
,
Rixen
,
D.
,
Voormeeren
,
S.
, and
Pasteuning
,
F.
,
2008
, “
Solving the RDoF Problem in Experimental Dynamic Substructuring
,”
Proceedings of the 26th International Modal Analysis Conference
,
Orlando, FL
,
Feb. 4–7
, pp.
1376
1384
.
15.
Duarte
,
M. L. M.
, and
Ewins
,
D. J.
,
2000
, “
Rotational Degrees of Freedom for Structural Coupling Analysis Via Finite-Difference Technique With Residual Compensation
,”
Mech. Syst. Signal Process
,
14
(
2
), pp.
205
227
. 10.1006/mssp.1999.1241
16.
Liu
,
W.
, and
Ewins
,
D.
,
1999
, “
The Importance Assessment of RDOF in FRF Coupling Analysis
,”
Proceedings of the 17th International Modal Analysis Conference
,
Kissimmee, FL
,
Feb. 8–11
, Vol. 3727, p.
1481
.
17.
Allen
,
M.
,
Mayes
,
R.
, and
Bergman
,
E.
,
2010
, “
Experimental Modal Substructuring to Couple and Uncouple Substructures With Flexible Fixtures and Multi-Point Connections
,”
J. Sound Vib.
,
329
(
23
), pp.
4891
4906
. 10.1016/j.jsv.2010.06.007
18.
Fahy
,
F.
, and
Gardonio
,
P.
,
2007
,
Sound and Structural Vibration: Radiation, Transmission and Response
,
2nd ed.
,
Elsevier
,
Reino Unido
.
19.
Dickens
,
J. D.
,
2002
, “
Review of Methods to Dynamically Represent Vibration Isolators
,”
Shock Vib. Dig.
,
34
(
6
), pp.
447
453
.
20.
Marques
,
V. C.
,
2017
, “
An Investigation Into Ways of Substructuring for a Vibratory System With Rubber Isolators
,”
Ph.D. thesis
,
Universidade Estadual Paulista “Julio de Mesquita Filho”
.
You do not currently have access to this content.