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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Olsson, P., Kristensson, G. Wave splitting of the Timoshenko beam equation in the time domain. Z. angew. Math. Phys. 45, 866–881 (1994). https://doi.org/10.1007/BF00952082
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DOI: https://doi.org/10.1007/BF00952082