Geodesic
Evolution of disturbances on the surface of an elastic plate in supersonic gas flow
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1221-1237

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The evolution of two-dimensional disturbances on the surface of an infinite elastic plate placed in a supersonic inviscid gas flow is studied in the linear approximation. The initial disturbances are assumed to be localized within a bounded spatial domain. The problem is solved by applying an asymptotic method for estimating parameter-dependent integrals, namely, the saddle point method. The evolution of disturbances is analyzed without making any simplifications of the dispersion equation: the dependence of the oscillation frequency on the wave vector is used in implicit form. For various governing parameters of the problem, the amplification characteristics of disturbances and wave numbers are qualitatively analyzed depending on the group velocity. A particular problem is considered, specifically, the conditions under which the plate is absolutely unstable are found. The results are compared with those obtained earlier in the low free-stream density approximation. 
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     author = {D. S. Shaposhnikov},
     title = {Evolution of disturbances on the surface of an elastic plate in supersonic gas flow},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1221--1237},
     publisher = {mathdoc},
     volume = {55},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a10/}
}
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D. S. Shaposhnikov. Evolution of disturbances on the surface of an elastic plate in supersonic gas flow. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1221-1237. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a10/