Geodesic
Resonance interaction of bending and shear modes in a non-uniform Timoshenko beam
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 258-284

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Interaction of two modes is considered which arise when their phase velocities intersect at a single point, in the high-frequency regime. The analogous problem of singularity propagation is also considered. 
@article{ZNSL_2000_264_a17,
     author = {M. V. Perel' and I. V. Fialkovskii and A. P. Kiselev},
     title = {Resonance interaction of bending and shear modes in a non-uniform {Timoshenko} beam},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {258--284},
     publisher = {mathdoc},
     volume = {264},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a17/}
}
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M. V. Perel'; I. V. Fialkovskii; A. P. Kiselev. Resonance interaction of bending and shear modes in a non-uniform Timoshenko beam. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 258-284. http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a17/