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Modélisation du comportement vibratoire des structures par des méthodes énergétiques: formulation moyennée spatialement pour des systèmes unidimensionnels

Abstract : This work analyses the characteristics of energy quantities obtained from the classical wave equation, without any extra assumption, in order to develop a time- and space-averaged formulation which can model power tranfers in structures for a mid-frequency range.

First the concept of quadratic superposition is presented: if linear variables like the displacement field hold n different components, every quadratic variable like intensity or energy densities hold n² different terms. This is illustrated for the 2D case of two plane waves interfering.

Secondly the 1D case of two counter-propagative plane waves is studied as it gives spatial variations of energy fields at two different length scales.
Small scale variations of energy fields stand for the local structure of interferences
defined by a purely real wave number, whereas large scale variations match with global energy transfers due to the dissipation and defined by a purely imaginary wave number.

The next part deals with plate vibrations. Different types of waves are considered : quasi-longitudinal, shear horizontal and bending waves.
In 1D cases (semi-infinite plates), the analysis for quasi-longitudinal and shear horizontal waves is similar with the previously presented one.
The case of bending waves is more complicated due to the presence of evanescent components in the displacement field, which multiplies the number of components in energy variables. Yet an equivalent quadratic formulation was obtained for 1D bending waves.

The last part shows how it is possible to develop a space-averaged quadratic formulation for 1D plane waves, in which the averaging process removes small scale components of pseudo-periodic quadratic variables.
A differential equation is obtained for the complex intensity and energy densities are derived from this variable.
Next, boundary conditions accounting for both active and reactive intensities are computed either for passive or active junctions.
Passive junctions involve mixed conditions which look like impedance conditions in a displacement formulation, whereas active junctions involve not only impedances but also the input power density in the discontinuity of the averaged intensity. Then this space-averaged quadratic formulation can be applied to mid-frequency vibrations.
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Contributor : Cédric Devaux <>
Submitted on : Wednesday, February 21, 2007 - 11:45:56 AM
Last modification on : Tuesday, March 31, 2020 - 3:20:59 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 10:46:48 PM


  • HAL Id : tel-00132382, version 1


Cédric Devaux. Modélisation du comportement vibratoire des structures par des méthodes énergétiques: formulation moyennée spatialement pour des systèmes unidimensionnels. Acoustique [physics.class-ph]. Université du Maine, 2006. Français. ⟨tel-00132382⟩



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