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1
Content available remote Profile reconstruction of a continuously-stratified layer from reflection data on acoustic waves
Caviglia G., Morro A.
Archives of Mechanics
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2010
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Vol. 62, nr 1
73-98
EN
The paper investigates the reflection-transmission process of acoustic waves, generated by an inhomogeneous fluid layer of finite thickness, which is sandwiched between two semi-infinite homogeneous half-spaces. First a direct problem is solved by determining the reflection and transmission coefficients along with the wave solution in the layer, produced by a known incident wave. Owing to the planar stratification of the layer, the unknown acoustic pressure is looked at as a generalized plane wave. Upon the Fourier transformation, the second-order wave equation is written as a firstorder system of equations for the dependence on the depth of the pressure and the partial derivative. The corresponding Volterra integral equation gives the pressure in the layer as a series of repeated integrals of powers of the pertinent depth-dependent matrix of the system. The reflection and transmission coefficients of the layer are then determined for any incidence angle. Next an inverse problem is investigated. The derivatives of the reflection coefficient, with respect to the frequency, are shown to provide the thickness of the layer, the speed beyond the layer and the moments, of any order, of the refractive index.
2
Content available remote Reflection and transmission of transient acoustic waves with oblique incidence
Caviglia G., Morro A.
Archives of Mechanics
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2008
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Vol. 60, nr 3
243-262
EN
The aim of the paper is to determine, within the time domain, the waves produced by an oblique incident wave at the interface between two homogeneous half-spaces. By following the acoustic approximation, the wave solutions for the Fourier transform of the displacement field in a viscous fluid are established in a form which generalizes the concept of plane wave. Next the reflection-transmission problem, associated with the interface between an inviscid fluid and a viscous one, is investigated. The incident wave is supposed to propagate in the inviscid fluid. The reflected and transmitted waves, in the time domain, are eventually determined in two particular cases, namely that of normal incidence on a viscous half-space and that of oblique incidence, beyond the critical angle, on an inviscid half-space. In the first case it follows that, provided an approximation of band-limited data holds for the incident wave, the reflected and the transmitted waves are given by linear combinations of the values of the incident wave and of its time derivative. In the second case, the reflected (transmitted) wave is shown to be the sum of a term proportional to the incident wave and another one, proportional to the Hilbert transform of (a convolution of) the incident wave.
3
Content available remote Non-isothermal phase-field models and evolution equation
Morro A.
Archives of Mechanics
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2006
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Vol. 58, nr 3
257-271
EN
Phase transitions between two phases are modelled as space regions where a phase field, or order parameter, changes smoothly. The literature shows a seeming contradiction in that some papers lead to the use of the reduced chemical potential through the temperature, others do not. The paper has a threefold purpose. First, to revise the arguments of known approaches and possibly generalize the associated schemes. Secondly, to show that a further approach is possible which involves the phase field as an internal variable. Thirdly, to contrast the various schemes and the corresponding results. It follows that differences arise because different fields enter the models and different forms are considered for the balance of energy and the second law of thermodynamics.
4
Content available remote Existence and uniqueness of the solution in the frequency domain for the reflection-transmission problem in a viscoelastic layer
Caviglia G., Morro A.
Archives of Mechanics
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2004
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Vol. 56, nr 1
59-82
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.
5
Content available remote Multimode wave scattering problems in layered dissipative solids
Caviglia G., Morro A.
Archives of Mechanics
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1999
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Vol. 51, nr 5
533-546
EN
A general scheme within the frequency domain is elaborated for the scattering of obliquely-incident waves at a stratified, anisotropic, viscoelastic solid. Existence and uniqueness of the asymptotic wave propagator is established. Possible nonexistence of the scattering matrix at specific values of the incident field is then shown. Conditions for nonuniqueness or incompatibility of the direct scattering problem are provided.
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