Geodesic
On the application of the asymptotic method of global instability in aeroelasticity problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 292-320

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The asymptotic method of global instability developed by A. G. Kulikovskii is an effective tool for determining the eigenfrequencies and stability boundary of one-dimensional or multidimensional systems of sufficiently large finite length. The effectiveness of the method was demonstrated on a number of one-dimensional problems; and since the mid-2000s, this method has been used in aeroelasticity problems, which are not strictly one-dimensional: such is only the elastic part of the problem, while the gas flow occupies an unbounded domain. In the present study, the eigenfrequencies and stability boundaries predicted by the method of global instability are compared with the results of direct calculation of the spectra of the corresponding problems. The size of systems is determined starting from which the method makes a quantitatively correct prediction for the stability boundary. 
@article{TM_2016_295_a16,
     author = {V. V. Vedeneev},
     title = {On the application of the asymptotic method of global instability in aeroelasticity problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {292--320},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_295_a16/}
}
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V. V. Vedeneev. On the application of the asymptotic method of global instability in aeroelasticity problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 292-320. http://geodesic.mathdoc.fr/item/TM_2016_295_a16/