Structual-acoustic properties of automotive panels with shell elements

183 Pages·2017·6.32 MB·English

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Structual-acoustic properties
of automotive panels with
shell elements
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Structural-Acoustic Properties of
Automotive Panels with Shell
Elements
by
Gaurav Kumar
DOCTORAL THESIS
Submitted in partial fulfilment of the
requirements for the award of
Doctor of Philosophy
of Loughborough University
January 8, 2014
(cid:13)c by Gaurav Kumar 2014

Abstract
The automotive industry has witnessed a trend in the recent years of reducing the bulk
weight of the vehicle in order to achieve improved ride dynamics and economical fuel
consumption. Unfortunately, reducing the bulk weight often compromises the noise, vibra-
tion, and harshness (NVH) characteristics of the vehicle. In general, the automotive body
panels are made out of thin sheet metals (steel and aluminium) that have a very low bend-
ing stiffness. Hence, it becomes important to find countermeasures that will increase the
structural stiffness of these thin body panels without affecting their bulk weight. One such
countermeasure is to introduce the geometrical indentations on various body panels. The
geometrical indentation explained in this thesis is in the shape of elliptical dome, which
supports the increase of the structural stiffness whilst keeping the bulk weight constant.
Theprimaryreasontochooseellipticaldomesastheappliedgeometricalindentationisdue
to a significant amount of interest shown by Jaguar Land Rover. Moreover, the elliptical
domes, because of the nature of its design, can cover a larger surface area with minimal
depth, thereby, eliminating the possibility of sharp and pointy indentations.
This thesis presents a comprehensive study of the structural-acoustic behaviour of the
automotive-type panels with dome-shaped indentations. The ultimate aim of this research
is to establish a set of design guidelines in order to produce automotive-type panels with
optimiseddome-shapedindentations. Inordertodoso, anewdesignoptimisationstrategy
is proposed that results in the optimal placement of the required dome-shaped indenta-
tions. The optimisation problem addressed in this thesis is unlike a general mathematical
problem, and requires specific methodologies for its solution. Therefore, the use of genetic
algorithm is observed as the most suitable method in order to tackle this type of design
optimisation problem.
During the development of the optimisation procedure, the preliminary results show
a consistency in the design patterns. This led to the motivation to investigate a few
intuitively designed panels, which are inspired by the initial, trial, optimisation results.
Therefore, four intuitively designed panels are investigated for their structural-acoustic
characteristics. The study of the intuitively designed panels provided essential physical
insight into the design optimisation problem, which ultimately defined the guidelines in
ordertodeveloptheproposedoptimisationprocedure. Thistypeofoptimisationprocedure
is completely new in the domain of structural-acoustic optimisation. The efficiency of the
underlying work lies in the separate investigation of both the structural and the acoustic
properties of the panels with various dome-shaped indentations, and then utilising the
insights gained in order to develop a specific optimisation algorithm to stream-line the
dome-shaped panel design procedure.
Keywords: Finite element analysis, boundary element analysis, sensitivity analysis, ge-
netic algorithm, elastic shell elements, sound radiation, sound propagation, structural-
acoustic optimisation, topology optimisation, topography optimisation.

Acknowledgements
This work has been carried out under the supervision of Dr. Stephen J. Walsh and Pro-
fessor Victor V. Krylov. I am thankful to their insightful guidance that has been essential
in the development of my understanding of the subject, which remains central to the com-
pletion of my research. It is their professional but relaxed attitude that helped me stay
focused onto my research without being under a lot of pressure. I received constant en-
couragement from both of my supervisors in order to keep publishing my research work
into the public domain. As a result, up until today, we have two research papers published
in different International conference proceedings, and one research paper published in the
journal ‘Applied Acoustics’. Also, it is with their financial support that I was able to
present my research work at various National and International conferences. Last but not
least, I would like to thank Dr. Dan J. O’Boy for his continued interest my PhD research,
and for the long discussions on the subject of vibration and acoustics over coffee.
I would like to pass my sincere gratitude to the NVH research team at Jaguar Land
Rover (JLR) for their input and feedback during the course of my research. I would also
like to thank Dr. Libin Wang from NVH research at JLR, and Mr. Stephen Fisher from
Body CAE at JLR for their constant support during the initial stages of my PhD research.
I am highly obliged to Dr. Libin Wang for his additional support during the development
of the optimisation algorithm.
I wish to take this opportunity to thank my team at LMS UK for being so supportive
and accommodating during my thesis write-up days. I am grateful to my manager Mr.
Andrew McQueen for taking interest in my PhD and engulfing in serious research discus-
sions, which not only helped me improve my thesis but also gave me a lot of confidence in
my research. I would also like to thank my colleagues from LMS HQ in Leuven, especially
Mr. Peter Segaert and Dr. Gabriel Ruiz, for sharing their vibro-acoustic expertise, which
indirectly helped me in improving my thesis.
Finally, but most importantly, I would like to express my gratitude to my parents. If
there is one person whom I would like to dedicate my PhD to, it would be my father. My
father, Mr. Yogendra Prasad, is a mechanical engineer by profession, and it is because of
him I was raised in an environment where we were fixing the common home appliances
ourselves. It is this environment at my home that laid the foundation for me to pursue my
career in the mechanical industries. I appreciate the confidence that my father has shown
in me by supporting me in every decision I have taken in my career so far. Also, I am very
grateful to my mother who visited me in the UK during my PhD, and spent the whole
winters with me. Luckily, that year the UK weather wasn’t too harsh on us.
In order to conclude, I would like to thank God for his blessings and giving me a
wonderful opportunity to pursue my career in the field of my interest.

Contents
Abstract iii
Acknowledgements v
List of Figures ix
List of Tables xiii
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Aims, Objectives, and Brief Structure of the Thesis . . . . . . . . . . . . . . 10
2 Literature Survey 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Discussion and Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Structural Modification of Panels 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Geometry Based Model Modification . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Direct FE model modification . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Examples of modification functions . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.1 Global modification function . . . . . . . . . . . . . . . . . . . . . . 36
3.4.2 Local modification function . . . . . . . . . . . . . . . . . . . . . . . 38
3.5 Discussion and Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Structural Properties of Automotive-type Panels 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Classical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Natural frequencies of a rectangular plate . . . . . . . . . . . . . . . 50
4.2.2 Modes of plate vibration . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.3 Forced vibration response functions . . . . . . . . . . . . . . . . . . . 56
4.3 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.1 Normal modes analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Frequency response analysis . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 Investigation of different automotive-type panel designs. . . . . . . . . . . . 65
4.4.1 Test panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.2 Experimental setup and testing procedure . . . . . . . . . . . . . . . 67
4.4.3 Structural results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
viii Contents
5 Radiation Characteristics of Automotive-type Panels 89
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Classical Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.1 The wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.2 The homogeneous Helmholtz equation . . . . . . . . . . . . . . . . . 92
5.2.3 TheinhomogeneousHelmholtzequationandintroductiontoGreen’s
function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.4 The time-averaged acoustic power output . . . . . . . . . . . . . . . 94
5.3 Numerical Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.1 Low-frequency techniques . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.2 High-frequency techniques . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4.1 Sound radiation measurement setup and processing . . . . . . . . . . 100
5.4.2 Test Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Sound Radiation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6 Numerical Optimisation Technique to Reduce Sound Radiation from
Automotive-type Panels 115
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.1.1 Genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.1.2 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2 Fundamentals of Structural-acoustic Optimisation . . . . . . . . . . . . . . . 120
6.2.1 Finite element method based structural analysis. . . . . . . . . . . . 121
6.2.2 Acoustic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.2.3 Choices of objective functions . . . . . . . . . . . . . . . . . . . . . . 123
6.3 Optimisation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 Optimised Panel Design and Results . . . . . . . . . . . . . . . . . . . . . . 131
6.5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.6 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7 Conclusion and Future Work 147
7.1 General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
References 157