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Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. (Material and Structural Acoustics)
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Multilayered structures have many application in industry and society: they have peculiar properties and serve a variety of purposes, like structural support, thermal insulation, vibrational and acoustic isolation. This thesis concerns the prediction of sound transmission in multilayered structures. Two problems are herein investigated: the transmission of energy through structures and the transmission of energy along structures. The focus of the analysis is on the mid to high frequency range. To predict sound transmission in these structures, statistical energy analysis (SEA) is used.SEA models are devised for the prediction of the sound reduction index for two kinds of multilayered structures, double-walls used in buildings and trim-panels in vehicles; the double-walls comprise an air cavity in between flat plasterboard or glass plates, whereas the trim-panels a porous layer in between curved aluminium and rubber layers. The SEA models are based upon the wave-types carrying energy. The novelty in these SEAs is an element describing the waves in the air cavity, or in the porous layer, fully coupled to the mass-impeded external layers. Compared to measurements, the proposed SEA performs well: for double-walls, it performs better than previous models; for trim-panels, it is an original result. The parameters of the new SEA element, such as modal density, are derived from the coupling equations describing the fully coupled waves. For double-walls, these equations are derived via Newton's laws. For trim-panels, a variational approach based upon a modified Hamilton's principle valid for non-conservative systems is preferred, because it is a powerful machinery for deriving equations of motion and coupling conditions of a medium as complex as the porous layer. The modified Hamilton's principle for non-conservative systems is based upon a self-adjoint functional analogous to the Lagrangian, inspired by Morse and Feshbach's construction. A self-adjoint variational principle for Biot's equations in the displacement formulation is devised. An equivalent mixed formulation is obtained changing the coordinates of the displacement formulation via Lagrange multipliers. From this mixed formulation, the Lagrangian for a porous material with a limp frame is derived, which yields the continuity of the total displacement of the porous layer. Lagrange multipliers help to obtain the correct coupling functionals between a porous material and a solid. The Lagrange multipliers introducing the continuity of the frame and the solid displacements equal the traction of the in-vacuo frame, thus disappearing if the latter is limp. Measurements to gather material parameters for a Biot model of the porous layer have been conducted.The effects of spatial energy decay in the transmission along structures predicted by SEA is studied: a major effect is the increased relevance of indirect coupling loss factors between SEA elements. This may jeopardize the usefulness of SEA at higher frequencies.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xi, 41 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2013:04
Keyword [en]
statistical energy analysis, porous materials, biot theory, variational principles, hamilton principle, double walls, multilayered structures
National Category
Fluid Mechanics and Acoustics
Research subject
Järnvägsgruppen - Ljud och vibrationer
Identifiers
URN: urn:nbn:se:kth:diva-118427ISBN: 978-91-7501-648-1 (print)OAI: oai:DiVA.org:kth-118427DiVA: diva2:606042
Public defence
2013-03-05, F3, Lindstedtsvägen 26, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20130218

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-02-18Bibliographically approved
List of papers
1. A cavity-wall element for the statistical energy analysis of the sound transmission through double walls
Open this publication in new window or tab >>A cavity-wall element for the statistical energy analysis of the sound transmission through double walls
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The wave motion within a cavity between two flexible walls is first investigated numerically. The results then form the basis for a new SEA formulation in which each element describe one kind of coupled cavity-wall wave motion. This formulation obsoletes the non-resonant transmission path commonly used in SEA of sound transmission and compared to classical formulations it improves results at frequencies around and a bit above the double wall resonance. The new formulation is compared to three sets of measurements found in the literature showing fair agreements.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-118436 (URN)
Funder
Swedish Research Council, 621-2005-5754EU, FP7, Seventh Framework Programme, 218508
Note

QS 2013

Available from: 2013-04-19 Created: 2013-02-18 Last updated: 2013-04-19Bibliographically approved
2. A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations
Open this publication in new window or tab >>A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations
2013 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 63, 71-83 p.Article in journal (Refereed) Published
Abstract [en]

A variational principle for anisotropic viscoelastic Biot’s equations of motion is presented. It is based upon an extended Hamilton’s principle, also valid for dissipative systems. Using this principle, a functional analogous to the Lagrangian is defined, starting from Biot’s variational formulation based on frame and fluid displacements. Then, a mixed displacement–pressure formulation is presented, which reduces the number of variables of response from six to four. The corresponding functional analogous to the Lagrangian is derived making full use of variational calculus. The derived functionals are self-adjoint and stationary for true motion.

Keyword
Porous materials, Biot’s equations, Variational principles, Dissipative systems
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-118435 (URN)10.1016/j.ijengsci.2012.06.019 (DOI)000315363000008 ()
Funder
Swedish Research Council, 621-2005-5754EU, European Research Council, 218508
Note

QC 20130218

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2017-12-06Bibliographically approved
3. Statistical energy analysis of the sound transmission through layered panels using a variational formulation of the porous material
Open this publication in new window or tab >>Statistical energy analysis of the sound transmission through layered panels using a variational formulation of the porous material
(English)Article in journal (Other academic) Submitted
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-118437 (URN)
Note

QS 2013

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-02-18Bibliographically approved
4. Characterization of the in vacuo viscoelastic material properties of porous foams used in vehicles
Open this publication in new window or tab >>Characterization of the in vacuo viscoelastic material properties of porous foams used in vehicles
(English)Article in journal (Other academic) Submitted
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-118440 (URN)
Note

QS 2013

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-02-18Bibliographically approved
5. Characterisation of a generic trim-panel: sound reduction index and material parameters
Open this publication in new window or tab >>Characterisation of a generic trim-panel: sound reduction index and material parameters
2013 (English)Report (Other academic)
Publisher
11 p.
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-118441 (URN)
Note

QC 20130218

Available from: 2013-02-18 Created: 2013-02-18 Last updated: 2013-02-18Bibliographically approved
6. Spatial energy decay and indirect couplings in statistical energy analysis
Open this publication in new window or tab >>Spatial energy decay and indirect couplings in statistical energy analysis
2010 (English)Conference paper, Published paper (Other academic)
Abstract [en]

Spatial energy decay within elements affects the validity of SEA. This is particularly significant for chains of similar long well-connected structures such as ventilation ducts, fluid-filled pipes and rib-stiffened plates found in ships, aircraft and railway cars. The effects of spatial energy decay on the high frequency response of one-dimensional well-connected elements are herein studied by comparing calculations by an SEA, a spectral finite element method and an SEA-like model. An SEA only includes direct coupling loss factors (CLFs); conversely, an SEA-like model also contains indirect CLFs. At high frequencies, the spatial energy decay increases and SEA overestimates the energies in all elements away from the excitation. Moreover, the indirect CLFs in the SEA-like model have to be considered when evaluating the energy flows, as the accumulated spatial decay from the excitation to the observed point increases. Thus, SEA cannot predict the high frequency response of similar long well-connected elements and alternative formulations are needed.

National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-83534 (URN)000302905400164 ()2-s2.0-84951021626 (Scopus ID)978-90-73802-87-2 (ISBN)
Conference
International Conference on Noise and Vibration Engineering (ISMA)/Conference of USD Location: Leuven, BELGIUM Date: SEP 20-22, 2010
Note
QC 20120216Available from: 2012-02-12 Created: 2012-02-12 Last updated: 2013-02-18Bibliographically approved

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