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Modelling Techniques for Vibro-Acoustic Dynamics of Poroelastic Materials

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Abstract

Given the quest for mass reduction while preserving proper vibration and acoustic comfort levels in industrial machinery and vehicles, lightweight poroelastic materials have gained a lot of importance. Often, these materials are applied in a multilayered configuration, which can consist of a number of acoustic, elastic, viscoelastic and poroelastic layers. Among these, poroelastic materials are the main focus of this paper. A poroelastic material comprises two constituents, being the elastic solid constituent, also called the frame, and the fluid filling the voids. Depending on the frequency range of interest, the motion of both constituents can be strongly coupled. Poroelastic materials can dissipate energy very effectively by structural, thermal and viscous means. Considerable research effort has been put in the development of robust models and prediction techniques which are capable of accurately describing the damping phenomena of these materials. After a broad introduction, this paper reviews the most commonly used models, ranging from simple empirical relations to detailed models accounting for the coupled behaviour of both phases and the CAE modelling techniques currently being applied for the analysis of the time-harmonic vibro-acoustic behaviour of these materials. Commonly used methods, such as the Finite Element Method and the Transfer Matrix Method which are mainly fitted for low-freqency and high-frequency applications, respectively, are discussed as well as extensions to improve their efficiency and applicability. The two final sections pay special attention to the promising Wave Based Method, a Trefftz-based technique, the application range of which was recently extended towards poroelastic problems.

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Acknowledgments

Elke Deckers is a postdoctoral fellow of the Fund for Scientific Research, Flanders (F.W.O.). The Research Fund KU Leuven is also gratefully acknowledged for the support of the postdoctoral research of Elke Deckers and the institute for Promotion of Innovation by Science and Technology Flanders (Belgium) (IWT-Vlaanderen) is gratefully acknowledged for the support of the doctoral research of Stijn Jonckheere. Furthermore, the IWT Flanders within the ASTRA project, the Fund for Scientific Research-Flanders (F.W.O.), and the Research Fund KU Leuven are also gratefully acknowledged for their support. The EC within the FP7 eLiQuiD Marie Curie European Industry Doctorate (GA 316422) is also gratefully acknowledged for its support.

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  1. Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300B, Box 2420, 3001 , Leuven (Heverlee), Belgium

    Elke Deckers, Stijn Jonckheere, Dirk Vandepitte & Wim Desmet

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  1. Elke Deckers
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  2. Stijn Jonckheere
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Correspondence to Elke Deckers.

Appendix: Material Properties

Appendix: Material Properties

This appendix collects the material data used in the examples in this paper. Table 5 shows the air properties used.

Table 5 Material properties of air
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Table 6 summarises the data of the poroelastic materials used in this review paper. The material properties of melamine have been experimentally determined by the Department of Physics of KU Leuven, as described in [173]. In the calculations, the average values of the material properties have been used. The polyurethane material properties are taken from [60]. An arbitrary loss factor \(\eta _l\) has been added, as the augmented Hooke’s law has not been applied. The carpet material properties are taken from [63]. The fireflex material data are taken from [167]. It is a poluyrethane foam, which is fabricated by Recticel, Belgium.

Table 6 Material properties of the poroelastic media used in this review paper
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Deckers, E., Jonckheere, S., Vandepitte, D. et al. Modelling Techniques for Vibro-Acoustic Dynamics of Poroelastic Materials. Arch Computat Methods Eng 22, 183–236 (2015). https://doi.org/10.1007/s11831-014-9121-0

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