7 methods for coupling deterministic (FEM) and random (SEA) systems are presented, and the hybrid FEM/SEA method is introduced by describing the coupling between FEM and SEA systems. Based on this, the effect of random on deterministic systems as far as the impact of deterministic on random subsystems is presented. The chapter closes with the global procedure of hybrid FEM/SEA modelling that calculates the joint response of both types of systems.
Chapter 8 applies these coupling formulas to several options of connections. Especially the coupling sections are often missing in text books on SEA for a certain reason: the calculation of coupling loss factors is not easy. However, as it is important to understand the assumptions and limits, the coupling loss factors of point, area, and line junctions are systematically derived. Since junctions are nothing else than noise paths, this chapter is also useful for practical applications, for example the acoustic transmission loss of plates that is an important quantity for airborne acoustic isolation.
The following chapters apply the theory to pure deterministic (chapter 9), pure random (chapter 10), and hybrid FEM/SEA examples (chapter 11). All examples are worked out in detail and show real engineering systems such as mufflers. In chapter 9 the transfer matrix method is introduced as an example of deterministic methods. This allows the simulation of complex lay-ups of noise control treatments applied in chapters 10 and 11.
The presented theory and the examples are calculated using Python scripts. The scripts and the related toolbox are made available as open source code. The author hopes that this toolbox helps to understand and to apply the presented topics. Further contributions to the code of the toolbox are very welcome. The documentation of the toolbox and the GIT repository can be found on the authors website www.docpeiffer.com.
As an acoustic engineer, I am in the somehow unique situation that I had the chance to work on several means of transportation: trains, aircraft, helicopters, launchers, satellites, and finally cars (mainly electric). Because of this experience I am convinced that a deep knowledge of vibroacoustic simulation methods is mandatory to create excellent and low-noise products. This know-how puts the acoustic engineer in the position to apply the right method in the right situation and frequency range. To underline this fact, chapter 12 presents models, basic ideas, pitfalls, and results of some industrial examples from aerospace, automotive, and train industries. Special thanks goes to my former colleague Ulf Orrenius who wrote the train and motivation section of chapter 12. His great experience and knowledge strongly enriched the content of this chapter.
This book is about simulation, but simulation is nothing without validation based on tests. In my view both – simulation and tests – are required to perform a good acoustic design and noise control engineering. Thus, chapter 13 briefly summarizes test and correlation methods together with an outlook to further topics of simulation and ongoing research in the field of acoustic simulation.
In most cases the life of an acoustic engineer means solving the target conflict between the acoustic performance and costs, weight, and space requirements. This is the reason why design engineers are not always the best friends of acousticians during the design phase. The more important it is that you are able to calculate the effect of your decisions for efficient application of the sometimes rare acoustic resources. I hope that this book provides some support for this demanding task.
Coming back to my initial motivation: If I would have to hold a lecture on vibroacoustic simulation now, I would sleep much better.
Alexander Peiffer
Planegg, Germany
15 October 2021
Acknowledgments
Special thanks goes to my former colleague Ulf Orrenius who wrote the train- and motivation section of chapter 12. His great experience and knowledge strongly enriched the content of this chapter.
I would also like to thank the Audi AG who provided the models to present the simulation strategy of automotive systems.
Acronyms
2DOFTwo degrees of freedommsMean squarermsRoot mean squareCFDComputational fluid dynamicsCFRPCarbon fiber reinforced plasticDFTDiscrete Fourier transformDVADynamic vibration absorberDOFDegree of freedomEMAExperimental modal analysisFEMFinite element methodFFTFast Fourier transformFTFourier transformGFRPGlass fiber reinforced plasticHVACHeating, ventilation, and air conditioningMACModal assurance criterionMDOFMultiple degrees of freedomMIMOMultiple input multiple outputNVHNoise, vibration, and harshnesPAXPassengerSDOFSingle degree of freedomSEAStatistical Energy AnalysisSISOSingle input single outputTBLTurbulent boundary layerTPATransfer path analysisTVATuned vibration absorber
1 Linear Systems, Random Process and Signals
Simple systems with properties constructed by lumped elements as masses, springs and dampers are a good playground to understand and investigate the physics of dynamic systems. Many phenomena of vibration as resonance, forced vibration and even first means of vibration control can be explained and visualized by these lumped systems.
In addition, a basic knowledge of signal and system analysis is required to put the principle of cause and effect in the right context. Every vibroacoustic system response depends on excitation by random, harmonic or specific signals in the time domain and we need a mathematical tool set to describe this.
An excellent test case to demonstrate and define the principle effects of vibration is the harmonic oscillator. It consists of a point mass, a spring and a damper. The combination of many point masses connected via simple springs and dampers provides some further insight into dynamic systems.
As those systems are described by components that have no dynamics in themselves they are called lumped systems. In principle all vibroacoustic systems can by modelled and approximated by this simplified approach.
1.1 The Damped Harmonic Oscillator
A realization of the harmonic oscillator is given by a concentrated point mass m fixed at massless spring with stiffness ks as in Figure 1.1. The static equilibrium is assumed at u = 0 being the displacement in x-direction. A damper connecting mass and fixation creates dissipation.
