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Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures
KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg, MWL Marcus Wallenberg Laboratoriet. (Material and Structural Acoustics)
2013 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Stockholm: KTH Royal Institute of Technology, 2013. , s. xi, 41
Serie
Trita-AVE, ISSN 1651-7660 ; 2013:04
Emneord [en]
statistical energy analysis, porous materials, biot theory, variational principles, hamilton principle, double walls, multilayered structures
HSV kategori
Forskningsprogram
Järnvägsgruppen - Ljud och vibrationer
Identifikatorer
URN: urn:nbn:se:kth:diva-118427ISBN: 978-91-7501-648-1 (tryckt)OAI: oai:DiVA.org:kth-118427DiVA, id: diva2:606042
Disputas
2013-03-05, F3, Lindstedtsvägen 26, KTH, Stockholm, 13:15 (engelsk)
Opponent
Veileder
Merknad

QC 20130218

Tilgjengelig fra: 2013-02-18 Laget: 2013-02-18 Sist oppdatert: 2013-02-18bibliografisk kontrollert
Delarbeid
1. A cavity-wall element for the statistical energy analysis of the sound transmission through double walls
Åpne denne publikasjonen i ny fane eller vindu >>A cavity-wall element for the statistical energy analysis of the sound transmission through double walls
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
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.

HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-118436 (URN)
Forskningsfinansiär
Swedish Research Council, 621-2005-5754EU, FP7, Seventh Framework Programme, 218508
Merknad

QS 2013

Tilgjengelig fra: 2013-04-19 Laget: 2013-02-18 Sist oppdatert: 2013-04-19bibliografisk kontrollert
2. A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations
Åpne denne publikasjonen i ny fane eller vindu >>A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations
2013 (engelsk)Inngår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 63, s. 71-83Artikkel i tidsskrift (Fagfellevurdert) 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.

Emneord
Porous materials, Biot’s equations, Variational principles, Dissipative systems
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-118435 (URN)10.1016/j.ijengsci.2012.06.019 (DOI)000315363000008 ()
Forskningsfinansiär
Swedish Research Council, 621-2005-5754EU, European Research Council, 218508
Merknad

QC 20130218

Tilgjengelig fra: 2013-02-18 Laget: 2013-02-18 Sist oppdatert: 2017-12-06bibliografisk kontrollert
3. Statistical energy analysis of the sound transmission through layered panels using a variational formulation of the porous material
Åpne denne publikasjonen i ny fane eller vindu >>Statistical energy analysis of the sound transmission through layered panels using a variational formulation of the porous material
(engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-118437 (URN)
Merknad

QS 2013

Tilgjengelig fra: 2013-02-18 Laget: 2013-02-18 Sist oppdatert: 2013-02-18bibliografisk kontrollert
4. Characterization of the in vacuo viscoelastic material properties of porous foams used in vehicles
Åpne denne publikasjonen i ny fane eller vindu >>Characterization of the in vacuo viscoelastic material properties of porous foams used in vehicles
(engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-118440 (URN)
Merknad

QS 2013

Tilgjengelig fra: 2013-02-18 Laget: 2013-02-18 Sist oppdatert: 2013-02-18bibliografisk kontrollert
5. Characterisation of a generic trim-panel: sound reduction index and material parameters
Åpne denne publikasjonen i ny fane eller vindu >>Characterisation of a generic trim-panel: sound reduction index and material parameters
2013 (engelsk)Rapport (Annet vitenskapelig)
Publisher
s. 11
HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-118441 (URN)
Merknad

QC 20130218

Tilgjengelig fra: 2013-02-18 Laget: 2013-02-18 Sist oppdatert: 2013-02-18bibliografisk kontrollert
6. Spatial energy decay and indirect couplings in statistical energy analysis
Åpne denne publikasjonen i ny fane eller vindu >>Spatial energy decay and indirect couplings in statistical energy analysis
2010 (engelsk)Konferansepaper, Publicerat paper (Annet vitenskapelig)
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.

HSV kategori
Identifikatorer
urn:nbn:se:kth:diva-83534 (URN)000302905400164 ()2-s2.0-84951021626 (Scopus ID)978-90-73802-87-2 (ISBN)
Konferanse
International Conference on Noise and Vibration Engineering (ISMA)/Conference of USD Location: Leuven, BELGIUM Date: SEP 20-22, 2010
Merknad
QC 20120216Tilgjengelig fra: 2012-02-12 Laget: 2012-02-12 Sist oppdatert: 2013-02-18bibliografisk kontrollert

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