Existence and uniqueness of the solution in the frequency domain for the reflection-transmission problem in a viscoelastic layer

• Autorzy: Caviglia G. , Morro A.
• Języki publikacji: EN

Abstrakty

EN

Existence and uniqueness for the reflection-transmission process originated in a viscoelastic solid layer are investigated. Wave propagation is framed within the Fourier-transform domain and the oblique incidence is modelled by a factor involving a transverse wave vector. The backward-forward propagation in the axial direction is ascertained through the sign of an energy flux. Next, a connection is established between the energy flux and an Hermitian matrix whose eigenvalues are half positive and half negative. The proof is given that if the matrix has two diagonal blocks, one of which is positive definite and the other is negative definite, the solution to the reflection-transmission problem exists and is unique. The condition on the blocks is found to hold, e.g., for obliquely propagating homogeneous waves in anisotropic elasticity or normally propagating waves in isotropic viscoelasticity.

Słowa kluczowe

EN

viscoelastic layer; wave reflecsion-transmission; energy flux vector; Hermitian matrix; homogenous wave

PL

warstwa lepko-sprężysta; odbicie i przenoszenie fal; wektor strumienia energii; macierz hermitowska; fala jednorodna

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2004
• Tom: Vol. 56, nr 1
• Strony: 59--82
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Caviglia G.

• Department of Mathematics, 16146 Genova, Italy

autor

Morro A.

• University of Genoa, 16145 Genova, Italy

Bibliografia

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