This item was submitted to Loughborough University as a PhD thesis by the author and is made available in the Institutional Repository (https://dspace.lboro.ac.uk/) under the following Creative Commons Licence conditions. For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/ 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 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. The primary reason to choose elliptical domes as the applied geometrical indentation is due 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 optimised dome-shaped indentations. In order to do so, a new design optimisation strategy 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 order to develop the proposed optimisation procedure. This type of optimisation procedure 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 The inhomogeneous Helmholtz equation and introduction to Green’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 Figures 1.1 Example of compressions (C) and rarefactions (R) of the particles of the medium. 2 1.2 Different types of structural-acoustic analysis. In red, listed are the com- mon numerical methods, and in blue, are the various measurement-related techniques. 4 1.3 Block diagram of steps involved in a finite element analysis project. 6 1.4 Human audible range .