Transient vibrational power flows in slender random structures: Theoretical modeling and numerical simulations

Savin, Éric

doi:10.1016/j.probengmech.2011.08.012

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…The high-frequency limit ε → 0 in the previous setting shall be considered for quadratic observables of the wave displacement field u ε as explained now. We rely on the simple following example which was already discussed in [42,43]. The real function x → u ε (x) oscillating with an amplitude a(x) about its mean u(x):…”

Section: 3mentioning

confidence: 99%

Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

Baydoun¹,

Savin²,

Cottereau³

et al. 2014

Wave Motion

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Abstract. In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneitiesthe so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position × wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.

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Section: 3mentioning

confidence: 99%

Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

Baydoun¹,

Savin²,

Cottereau³

et al. 2014

Wave Motion

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show abstract

“…However the theory of micro-local analysis of wave sytems shows that the energy density associated with their HF solutions satisfies radiative transfer equations [3]. In this model, heterogeneities are introduced along the same lines as done by Savin in [4]. Here they are modeled by fluctuations of the material properties of the medium represented by second order stochastic processes.…”

Section: Introductionmentioning

confidence: 99%