Geodesic
Preservation of the frequencies of oscillations of a~pipe with a~liquid
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 124-134

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We consider the direct and inverse problems of the flexural oscillations of a narrow pipe with an incompressible liquid. Results of the study of the influence of the parameters of the liquid on the values of the eigenfrequencies of its oscillations are given. We pose and solve the problem of the preservation of the given frequencies of the oscillations of a pipe with liquid. An algorithm is obtained for the determination of elastic fixings of the pipe that keep safe frequencies of oscillations under changes of the parameters of the liquid. We show that, for the preservation of the frequencies of the oscillations of a pipe under changes of the parameters of the liquid, it suffices to carry out the corresponding changes in the parameters of the elastic fixings of the pipe. Some examples are given.
Keywords: pipe with liquid, boundary value problem, frequencies of oscillations, diagnosing, parameters of the liquid, problem of the preservation of frequencies. 
@article{SJIM_2012_15_3_a11,
     author = {G. F. Safina},
     title = {Preservation of the frequencies of oscillations of a~pipe with a~liquid},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {124--134},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a11/}
}
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G. F. Safina. Preservation of the frequencies of oscillations of a~pipe with a~liquid. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 124-134. http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a11/