Geodesic
Parametric vibrations of thin-walled curved pipes made of reinforced plastics
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 166-179

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The article deals with the problem of parametric vibrations of thin-walled curved pipes under internal pulsating pressure. On the basis of semi-momentless theory of anisotropic laminated shells and Lagrange's equations a connected system of homogeneous differential equations with periodic stiffness coefficients has been developed. A calculation of natural modes and frequencies has been carried out. The results of the analytical solution have been compared with the data of FEM calculations and experiments. Using the small parameter method the boundaries of parametric excitation regions have been calculated. The disposition of resonance bands of the main simple and combinational parametric resonances has been analyzed depending on the constant pressure component, as well as the structural, geometric factors and damping.
Keywords: parametric vibrations, curved pipe, multilayer reinforced plastic, natural modes and frequencies, dynamic stability, parametric resonances. 
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     author = {A. V. Korotkov and Yu. A. Kulikov},
     title = {Parametric vibrations of thin-walled curved pipes made of reinforced plastics},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {166--179},
     publisher = {mathdoc},
     volume = {152},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a15/}
}
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A. V. Korotkov; Yu. A. Kulikov. Parametric vibrations of thin-walled curved pipes made of reinforced plastics. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 166-179. http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a15/