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- Olsson, Peter, et al.
(author)
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Wave splitting of the Timoshenko beam equation in the time domain
- 1994
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In: Zeitschrift für Angewandte Mathematik und Physik. - 1420-9039. ; 45:6, s. 866-881
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Journal article (peer-reviewed)abstract
- In recent years, wave splitting in conjunction with invariant imbedding and Green's function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives - the Euler-Bernoulli and the Rayleigh equations - is also provided.
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- Åberg, Ingegerd, et al.
(author)
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Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems
- 1994
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Reports (other academic/artistic)abstract
- Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.
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- Åberg, Ingegerd, et al.
(author)
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Transient waves in non-stationary media
- 1994
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Reports (other academic/artistic)abstract
- This paper treats propagation of transient waves in non-stationary media, which has many applications in e.g. electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first order 2×2 system of equations. The coefficients in this system depend only on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green functions (propagator kernels) equations are derived. Special attention is paid to the problem of non-stationary characteristics. A few numerical examples illustrate this problem.
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