Fundamentals and Software

Research and testing

Overview

Conventional and cutting-edge computational models can be used for planning and development processes. This was the basis for the development of the IBPsound software package, which comprises a set of modules each dedicated to a specific  computing task. For example, one module draws on the popular program "COMPAS" to tackle the computation of absorptive silencers in a new and enhanced form. The calculation of acoustic properties can be a highly complex task, requiring  the interpretation of many underlying factors which are of particular interest in the product optimization phase. The LAYERS program provides a solution for calculating the sound insulation of multi-layered panels. When it comes to noise control and room acoustics, it can be useful to make the acoustic effects of planning audible through the "Auralization" of calculation results which have been repeatedly applied for products such as partitions and sound absorbers.

Computation, Simulation

Eigenvibration of a cylinder
© Photo Fraunhofer IBP
Emphasis is on sound transmission loss and vibrations of building components. According to requirements the physical basis of the calculations is the theory of thin plates or - for the more general problems - anisotropic elastodynamics. The developed software tools are used for analysis, prediction and optimisation of building components.

Plate Vibrations
© Photo Fraunhofer IBP
Sound transmission
© Photo Fraunhofer IBP

Sound transmission loss of plates consisting of homogeneous Layers

without lateral boundaries, numerous layer types (solid, fluid, porous with rigid or elastic frame, elastically isotropic or anisotropic, membrane, thin plate)

Homogenisation periodic structures

Total and Partial Homogenisation for Low Frequencies and Small Wavenumbers in Elasticity 
 
Cleverly structured inhomogeneity is the key to modern smart materials. In order to design such structures, appropriate calculation methods are needed. This thesis shows how to compute the effective elastic properties of a structure, even if they cannot be derived from the classical theory of total homogenisation for periodic media. For determination of these properties, the material structure needs to be embedded in a practice-oriented periodic setup. It is subsequently homogenised by applying structural coarsening to the setup. This is based on perturbation analysis and comparison of energy densities. During the process of partial homogenisation each component of the setup is interpreted as an effective element with individual properties. In example of plastered masonry walls the influence of the geometric parameters is explored in detail. The experimental validation of the approach shows its superiority compared to the total homogenisation method in two dimensions. The presented novel and versatile calculation method promotes homogenisation to effective structural coarsening. Thus it can be used in a wider field of applications with extended applicability.

Sound transmission loss of double-leaf membrane constructions

Sound transmission loss of plates with peridic structures

thick plates as general case (GENERAL), thick plates at low frequencies (homogenisation and LAYERS), thin plates (HYPERAKUS)
 

Sound transmission loss of plates with local resonators

modelling by harmonic oscillators

Structure-borne sound intensity

in homogeneous plates and periodic structures
 

Sound Propagation in porous materials

including sound reflection and absoprtion at the surface 

Eigenvibrations of cuboids and cylinders (MODULI)

Determination of elastic moduli from experimental modal analysis
 

Vibration of two-dimensional rod structures (Swinging Graph)

From left to right: 440, 1060, 2790, 3040, 5540, 7780 Hz.

440Hz      1060 Hz       2790Hz        3040 Hz         5540 Hz      7780 Hz

                                                                   
Please click for the animation!

Introduction
To analyse and solve problems of structure-borne sound, simple computation models are frequently used, as detailed modelling, e.g. with finite elements, is complex. A verstile idealisation of reality leads to a system of straight rods, which are arranged in a plane and can be exited to vibrate (a quasi »multi-one-dimensional« structure). If already the real structure consists of rods and beams, the application of the model is obvious. But also in case of an appropriate arrangement of plates, idealisation to such a »rod structure« is reasonable, if it suffices to consider wave propagation only in the plane of the rod structure.

The model of the vibrating rod structure was continuosly applied for practical problems at the Fraunhofer IBP [1, 2]. However, a frequent application in acoustics and vibration technology - not at least for teaching purposes - was first of all constricted by fact that really flexible and user-friendly software was not available. This lack was eliminated by the development of the programme "Swinging Graph", equipped with a Windows user interface. The denomination of the programme alludes to the mathematical graph theory, where a graph consists of points (also calles "nodes" or "vertices") and lines ("edges") between points. In contrast to the graphical representation of mathematical graphs, however, lines (rods) in SwingingGraph must be straight.

Physical Model
A rod is characterised by material properties (density, Young's modulus and loss factor) as well as thickness and cross section. Longitudinal as well as bending waves including their near fields are admitted. The rod deflection due to bending waves exclusively accurs in the plane of the rod structure. If both possible propagation directions of the waves in rods of finite lenght (between two nodes) are considered, the motion of the rod is uniquely described by six amplitudes. For semi-infinite rods, running from one node to infinity, it is supposed that there is no sound energy arriving from infinity, meaning that only three amplitudes are required. All rods ought to be thin with the result of usual frequency-independent longitudinal wave velocities and frequency-dependent bending wave velocities.

Each node has three degrees of freedom: the two displacement components in the rod structure plane and the rotation around the axis through the node vertical to this plane (kinematic variables; in SwingingGraph: the related velocities). Correspondingly an external force (two components) and an external momentum can act on each node (dynamic variables). For each degree of freedom either the kinematic of the dynamic variable with magnitude and phase can be specified, e.g.a velocity in x-direction, an external force in y-direction and an external momentum, whereby sinusoidal time dependencies with a common frequency are a prerequisite. If the kinematic variable is set to zero, the node is held fixed in the corresponding degree of freedom (special case of kinematic excitation). And vice versa, if the dynamic variable is set to zero, the node can move freely in that degree of freedom (special case of dynamic excitation). Further properties can be assigned to each node, independent of rod characteristics: mass, moment of inertia, and whether the rods converging in a node are connected rigidly or flexibly. In the latter case, no external momentum can act on the node.

Conditions at the nodes, i. e. at the end points of the rods, determine the amplitudes and thus the vibrations of the whole rod structure. Mathematically speaking, this means to solve a linear equation system. Continuity of displacement and rotation (with the exception of flexible connection) as well as the balance of force and momentum is required at each node.

Thera are no fundamental difficulties in confering the model to a three-dimensional rod structure. In this case, additional bending waves and torsion waves must be taken into consideration. But the Programming of clear graphical representations requires remarkably more time and higher effort than in two dimensions.
 
Computational Options
The computation of the response of a rod structure to the specified excitations as function of frequency ("Response Function") gives a first glance at the vibration behaviour and follows the determination of resonance frequencies. The velocity component at a node or the mean velocity of a rod may be selected as response parameter.

Vibration forms and intensities (vibrational energy flows) can be computed at user-defined frequencies. The parameters of the graphs can be selected within a wide range, be it the spatial or temporal resolution in case of animation, be it the separate or combined representation of longitudinal and bending wave shares in case of intensities. The latter allows studying the conversion between longitudinal and bending waves, sometimes decisive for sound propagation.
 
Example

Fig. 1 shows the first modes of a tuning fork, which is composed of eight straight homogeneous rods and possesses an additional mass of 3 g at the left end (total lenght: 105 mm). Exitation is effected by a transversal force at the right lower end.  

Fig. 1 shows the first modes of a tuning fork, which is composed of eight straight homogeneous rods and possesses an additional mass of 3 g at the left end (total lenght: 105 mm). Exitation is effected by a transversal force at the right lower end.

The eigenfrequencies were determined by means of response functions presented in Fig. 2. 

The eigenfrequencies were determined by means of response functions presented in Fig. 2.

Fig. 3 describes how vibrational energy is propagated starting from the transfer point and dissipated. 

Fig. 3 describes how vibrational energy is propagated starting from the transfer point and dissipated.

Outlook
The programme SwingingGraph supplements the series of computation tools [3, 4], especially for the field of structure-borne sound transmission. There is a multitude of possible applications:stairs, flanking transmission, design of stud profiles of plasterboard walls, vibrational excitation of structures, to mention just a few. 

Literature
[1] Horner, J. L.; White, R. G.: Prediction of vibrational power transmission through bends and joints in beam-like structures. J. Sound Vib. 147 (1991)1, p. 87-103.

[2] Rosenhouse, G.; Ertel, H.; Mechel, F. P.: Theoretical and experimental investigation of structureborne sound transmission through a "T" joint in a finite system. J. Acoust. Soc. Am. 70 (1981) 2, p. 492-499.

[3] Maysenhölder, W.: LAYERS - ein Werkzeug zur Untersuchung der Schalldämmung von Platten aus homogenen anisotropen Schichten. IBP-Mitteilung 26 (1999), Nr. 347 (German)

   
[4] Maysenhölder, W.: HYPERAKUS - ein Werkzeug zur Untersuchung der Schalldämmung von periodisch strukturierten Wänden. IBP-Mitteilung 25 (1998), Nr. 330 (German)

Auralization

Interaktive Auralization
© Photo Fraunhofer IBP

Proven tools for acoustic planning, development and consultation

How good is the sound reduction of a construction or a building component? How good are the acoustics of a room? Questions, which experts answer with rating numbers and diagrams. But how does the room sound, how does exterior noise sound inside the room?

Auralization translates complex acoustic facts into close-to-reality hearing experiences. Even in the planning stage the acoustic effect of planning will become audible. A virtual acoustic test drive is reality.

Tools (Software)

Noise reduction auralization
Sound reduction effect of windows,
Different sources of exterior noise,
Presentation in real time.
Auralisation of rectangular rooms (AquA) 
Acoustics of rectangular rooms,
Interactive planning with sound absorbers,
Calculation in a second,
Presentation in real time.
Demonstration programs, Audio-CD
Selected results of auralization,
Easy and intuitive presentation.

Virtual Prototyping

Sound transmission
© Photo Fraunhofer IBP

The procedure of developing new building products is frequently performed as follows: experience - idea - prototype - no satisfying result - next prototype and so on. This method is cost-intensive and time-consuming. The application of modern computer technology, however, allows product development almost without any use of materials.

The process already begins with optimising targets, e.g. sound insulation of building components as function of frequency. Is the actual specification really the "best one"? By means of auralization you can already hear it and you can perform series of tests with test persons.

As soon as objectives are defined, our calculation programs
(LAYERSHYPERAKUS) are applied. These programs allow the calculation of sound insulation for any variation of a building component taken into consideration. According to the complexity of the problem, computational times of up to a few days may occur. (Undisturbed operational hours of our computers are at night or on weekends.) Visualisations help to understand sound transmission as well as indicate further optimisation. This results in design guidelines for a new building component.

Prototyping is generally necessary. The programs provide correct results within the scope of idealized physical models, but the differences between model and reality - e.g. at low frequencies - must not be ignored without verification. Thus, this uncertainty is eliminated.

Screenshot Program Layers

Acoustic Properties of Aluminium Foams - Measurements and Modelling

© Photo IFAM

Aluschaum







Snow as Prototype of Highly Efficient Sound Absorbers

© Photo Fraunhofer IBP
© Photo Fraunhofer IBP
© Photo Fraunhofer IBP


Snow absorbs sound. How this works in detail is the subject of the project "Snow as Prototype of Highly Efficient Sound Absorbers" within the framework of the research program   "Innovative Materials from Bionics" of the Landesstiftung Baden-Württemberg. In principle we know that the sound-absorbing capacity of a porous material is dependent on its structure. But until now the question as to which structural characteristics are significant has been insufficiently answered. Detailed investigations of snow are to explain this fact by precise measurements of sound absorption, by tomographic recording and integral-geometric description of the structures as well as by theoretical modeling of the acoustic processes. The experimental part of this study is performed in cooperation with the Swiss Federal Institute of Snow and Avalanche Research in Davos. A variety of snow samples was produced and prepared in the local cold laboratories and - after the acoustic measurements - analyzed in the micro-computer tomograph with a resolution of 0.01 mm. The structural images - produced by the  image analysis software MAVI show cubical snow sections of 6 mm edge lenght with porosities of 59% or 87%.

The measured absorption coefficients can be easily simulated by the theoretical Wilson model applying the measured porosity. The next step is to derive the parameters of the Wilson model as directly as possible from the geometrical structure. It seems reasonable to characterize the porous structure by appropriate mean values, e.g. by the Minkowski functionals of integral geometry. There are exactly four Minkowski functionals in three-dimensional space describing porosity, the surface of pores and mean values of the average curvature as well as of the Gaussian curvature. These functionals, however, are generally insufficient to predict sound absorption. Further geometrical parameters are required, especially to capture anisotropic behavior. The software MAVI offers a wide range of integral parameters fo this purpose.

If we understand the correlations between geometrical structure and sound absorption, the targeted search for structures with optimal absorption behavior will start. First of all, this is a purely theoretical task. The project, however, is also aimed at producing this kind of structures. The necessary scope is provided by the fact that not any geometrical detail but certain integral structural parameters are significant.

The Fraunhofer-Institute for Chemical Technology ICT in Pfinztal near Karlsruhe will produce porous materials as project partner. The ICT is already well-reputed for generating artificial snow ("theater snow") made of potato starch or polyethylene aimed at generating optical similiarity with falling snowflakes but no acoustical similiarity. The objektive, however, is now to simulate snow even acoustically by means of specifications on the geometrical structure. In addition, these innovative porous materials should be more profitable compared to traditional absorbers like mineral wool of foams with regard to costs and energy consumption for production, health risks, disposal and the entire life cycle assessment. Moreover, a self-supporting structure would be favorable. The frequency range of effective sound absorption can be extended by means of a layered structure or structural gradients (e.g. spatial variation of porosity).