An Investigation of the Stability and Vibration of a Hyperbolic Shell of one Sheet under Axisymmetric Loading

  • M. Kozarov
  • M. Kishkilov
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


This article deals with the stability and oscillation of an isotropic hyperbolic shell of one sheet. The loading is assumed axisymmetric and uniformly distributed along the edges of the shell. It is asumed that the load is of the type P(t)= P 0 Pt cos θt. The shell is simply supported. The basic equations are derived from Vlasov’s general theory of shells, by applying the Ostrogradsky-Hamilton variational principal. The basic system of differential equations is solved by using the Bubnov-Galerkin variational method.

In the most general case a system of differential equations of the Mathieu type is obtained. As a special case, the vibration and static stability of the structure are considered. At the conclusion a numerical exaniple is solved.


Cylindrical Shell Free Vibration Critical Stress Mathieu Equation Axisymmetric Loading 
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Copyright information

© Springer-Verlag, Berlin/Heidelberg 1976

Authors and Affiliations

  • M. Kozarov
    • 1
  • M. Kishkilov
    • 2
  1. 1.Applied Mechanics and Aerospace SciencesSofiaBulgaria
  2. 2.Technical Institute for Civil EngineeringSofiaBulgaria

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