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- Barbagallo, Mathias, et al.
(författare)
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A self-adjoint variational principle for anisotropic viscoelastic Biot’s equations
- 2013
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Ingår i: International Journal of Engineering Science. - : Elsevier BV. - 0020-7225 .- 1879-2197. ; 63, s. 71-83
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Barbagallo, Mathias, et al.
(författare)
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Spatial energy decay and indirect couplings in statistical energy analysis
- 2010
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Barbagallo, Mathias, 1983-
(författare)
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Statistical energy analysis and variational principles for the prediction of sound transmission in multilayered structures
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 8. |
- Birgersson, F., et al.
(författare)
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A spectral super element for modelling of plate vibration. Part 1 : general theory
- 2005
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Ingår i: Journal of Sound and Vibration. - : Elsevier BV. - 0022-460X .- 1095-8568. ; 287:02-jan, s. 297-314
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Tidskriftsartikel (refereegranskat)abstract
- The dynamic response of vibrating structures is studied with a proposed merger of the standard finite element method with the more computationally efficient spectral finite element method. First a plate structure is modelled with a newly developed spectral super element. Then this element is coupled to other parts that can have a more complex geometry and are modelled entirely with conventional finite elements. Some numerical examples are given to illustrate and validate the developed method and studies of numerical stability are also presented. In an accompanying paper the predicted and measured response of a turbulence excited aircraft panel are compared.
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| 9. |
- Birgersson, F., et al.
(författare)
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A spectral super element for modelling of plate vibration. Part 2 : turbulence excitation
- 2005
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Ingår i: Journal of Sound and Vibration. - : Elsevier BV. - 0022-460X .- 1095-8568. ; 287:02-jan, s. 315-328
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Tidskriftsartikel (refereegranskat)abstract
- In the accompanying paper, the suitability of a spectral super element to predict the response to point force excitation, was demonstrated. This paper expands the element formulation to also include distributed forces, which is useful when studying distributed excitation. First the sensitivity function, i.e. the structural response to a travelling pressure wave, is found. This sensitivity function and a wavenumber frequency description of the wall pressure are then used to predict the response of a turbulence excited panel in a numerically efficient way. The predictions were validated by a conventional finite element method and also compared to measurements.
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| 10. |
- Birgersson, F., et al.
(författare)
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Application of the spectral finite element method to turbulent boundary layer induced vibration of plates
- 2003
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Ingår i: Journal of Sound and Vibration. - : Elsevier BV. - 0022-460X .- 1095-8568. ; 259:4, s. 873-891
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Tidskriftsartikel (refereegranskat)abstract
- The spectral finite element method and equally the dynamic stiffness method use exponential functions as basis functions. Thus it is possible to find exact solutions to the homogeneous equations of motion for simple rod, beam, plate and shell structures. Normally, this restricts the analysis to elements where the excitation is at the element ends. This study removes the restriction for distributed excitation, that in particular has an exponential spatial dependence, by the inclusion of the particular solution in the set of basis functions. These elementary solutions, in turn, build up the solution for an arbitrary homogeneous random excitation. A numerical implementation for the vibration of a plate, excited by a turbulent boundary layer flow, is presented. The results compare favourably with results from conventional modal analysis.
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