Abstract
Saratov State Technical University named after Yu.A. Gagarin, 77, Politeknicheskaya st., 410054, Saratov, Russia,a.mochalin@inbox.ruWeconsideranisotropiccylindricalshellofvaryingthicknessanddensityalongthegeneratrix.Lettheshellbeunderpressure,whichis symmetric and also varying along the generatrix. We follow the polupostamenty theory by V. Z. Vlasov and consider the problemofthedynamicalstabilityoftheshell.Weobtaintheexactsolutioncorrespondingtothecertainrelationbetweenthickness,pressureanddensity.Suchkindofshellsofextentmediumisimportantinmechanicalandaerospaceengineeringforoptimalmassobtaining.Inthepaperweobtainminimumvaluesoftheexcitationcoefficientsforfiveboundaryvalueproblems,whichareofgreatimportancein engineering. We give the accuracy estimation of the WKB method for these problems. Numerical results are summarized in thetable.Key words: cylindrical shell, theory of shells, parametric oscillations of shells, radial loading, shell thickness, theory of elasticity,coefficients of excitation, dynamic stability.
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