Dynamic Stability of a Cylindrical Shell Stiffened with a Cylinder and Longitudinal Diaphragms at External Pressure

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A study has been made of the dynamic stability of a cylindrical orthotropic shell stiffened with a hollow cylinder and inhomogeneous longitudinal diaphragms under the action of axial forces and pulsating external pressure. The influence of the cylinder and diaphragms on the stability of the shell was taken account of in the form of elastic foundations whose moduli of subgrade reaction are determined from the equations of a three-dimensional theory of elasticity and the Timoshenko model respectively. A solution to the equation of motion of the shell has been found in the form of a trigonometric circumferential-coordinate series. To construct the principal region of instability of the shell, a binomial approximation was used in the obtained Mathieu–Hill equations. As a result, the problem was reduced to a system of two algebraic equations for normal displacement of the shell at diaphragm installation sites. For uniformly spaced identical diaphragms, a solution has been obtained in explicit form. The dependences of the principal region of instability of the shell on the number and rigidity of the diaphragms have been determined at different radii of the cylinder channel.

Keywords

dynamic stability stiffened cylindrical shell modulus of subgrade reaction three-dimensional elasticity theory 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. N. Bakulin
    • 1
  • E. V. Danilkin
    • 2
  • A. Ya. Nedbai
    • 2
  1. 1.Institute of Applied Mechanics, Russian Academy of SciencesMoscowRussia
  2. 2.Corporation ″Moscow Institute of Thermal Technology″MoscowRussia

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