Vibroacoustic Simulation. Alexander Peiffer

hybrid FEM/SEA method. In addition, the hybrid FEM/SEA method allows a much clearer and more systematic approach to SEA compared to the original literature and might help to impart the knowledge to students and professionals. It is my persuasion, that every acoustic simulation engineer shall master these simulation techniques to be prepared for vibroacoustic prediction of the full audible frequency range.

      What is so special about vibroacoustics that so many methods are required? One answer is that the dynamic properties of structure and fluid systems are so different. This leads to distinct dynamic behavior. There may fit a lot of wavelengths of acoustic waves into a chamber of a machine or a passenger compartment filled with air, whereas the surrounding structure is often stiff and robust, and only a few wavelengths of the structural bending waves fit into the area of the surrounding walls. This strongly influences how energy is transmitted via the walls into the cavity and how small uncertainties affect the system response.

      Additionally, there is often a great variety of materials, like foams, fibers, rubbers, etc. in the structure or applied as noise and vibration control, all having different orders of magnitude in wavelengths or even completely different modes of wave propagation.

      As a consequence, vibroacoustics is a complex engineering discipline or science because the engineer has to master all those modes of wave propagation in the different systems and media as far as the coupling between those waves for connected subsystems. A thorough treatment of all wave types, couplings, and properties is not possible in a typical lecture or textbook, but it is possible to explain the main idea of how to deal with vibroacoustic phenomena and which means are required to solve the engineering problem. This book tries to extract the basic concepts, so that candidates are in a position to determine, investigate and categorize vibroacoustic systems and make the right decision on how to simulate them.

The frequency range of interest is covering four orders of magnitude from 20 to 20 000 Hz. That is one further reason why various methods for the description of these phenomena are required. At low frequencies it makes sense to investigate the modal behavior of a structure like the first modes of a string. In contrast to this, calculating all standing waves at high frequencies for a large room is not reasonable, as small changes at the boundaries or even temperature will lead to totally different wave forms in the room. Both regimes are addressed by different approaches categorized as (i) deterministic or (ii) statistic methods. The first occurs normally at lower frequencies, whereas the latter is valid at high frequencies. Because of the different wavelengths, it often appears that both cases occur in one vibroacoustic system, and both approaches are necessary. The combination of the two methods is called hybrid FEM/SEA method.

      As there are many books on the subjects of deterministic acoustics and vibration available, this book focuses on SEA and hybrid methods. However, as FEM systems of equations are involved in the hybrid method, a minimum understanding of deterministic systems is required.

      How is the book organized? It starts with a simple but excellent example for a vibrating system: the harmonic oscillator. In chapter 1 phenomena such as resonances, off resonance dynamics, and numerous damping mechanisms are explained based on this test case. A first step towards complex and FEM systems is made by introducing multiple coupled oscillators as an example for multiple degree of freedom systems. Real excitations often are of random nature. Hence, this chapter ends with tools and methods to describe random signals and processes as far as the response of linear systems to such signals.

      Chapters 2 and 3 deal with wave motion in fluids and structures, respectively. Both chapters bring into focus the physics of sources, because the source mechanisms reveal how energy is introduced into the wavefields and how the feedback to the excitation can be characterized. Furthermore, the source dynamics are required when systems are coupled. The dynamics of acoustic and structure systems are shown in chapters 4 and 5. This includes the natural resonances of such systems that will become important for the classification of random systems. Based on analytical models, the low and high frequency behavior of such systems is presented. One aim of the various examples is to illustrate that when sources are exciting those systems, the high frequency dynamics become similar to the free field results from chapters 2 and 3. Chapter 6 deals with the random description of systems. The concept of ensemble average and diffuse fields is applied to typical example systems by using Monte Carlo simulations. Based on such randomized systems and averaged values, it is shown that we get similar results to those you would get from deterministic methods when the uncertainty of dynamically complex systems is considered. This opens the door to the statistical energy analysis (SEA). Some typical one-, two-, and three-dimensional systems are presented in the very detail, so that the reader gets a feeling when and under which conditions the SEA assumptions are valid. The idea is to provide comprehensive examples for the rules of thumb usually used to determine if random methods are valid or not.

      In chapter 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