Vibration and stability of thin shell structures
Vibration and stability of thin shell structures
A finite element description of thin shell structures is presented. The basis of this description is a doubly curved quadrilateral shell element, with 36 degrees of freedom, developed by the author. Used in conjunction with a shell theory due to Sanders (1959, 1963) and constitutive equations for an anisotropic material (Lekhinitskii 1964), this element is suitable for the dynamic and geometrically nonlinear analysis of general thin shells. Equations governing the free vibration of thin shell structures are developed from Hamilton's Principle. These equations are then solved using the above finite element model, natural frequencies of the system being determined by the method of simultaneous (or subspace) iteration. The linear response and vibrational frequencies of a cylindrical panel (Clough and Wilson 1971) are used to check convergence of this model. Static stability equations are developed from the Principle of Minimum Potential Energy, and are again solved using the finite element formulation. In this case, the resulting equations are verified by comparison of the results with those for the linear bifurcation of thin cylindrical shells under both uniform pressure and wind loading (Wang and Billington 1974, Cole 1973). Finally, the concept of dynamic stability, as defined by Bolotin (1964), is introduced. Working from the Lagrange equations, the dynamic stability equations for a thin shell structure are developed, using the finite element method. It is shown that these equations are in fact Mathieu's equation, and solution for the boundary frequencies of the instability regions is considered. The techniques described are applied to thin shells of revolution under various loading conditions, and the practical consequences of the results are discussed.
University of Southampton
1980
Collington, David John
(1980)
Vibration and stability of thin shell structures.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A finite element description of thin shell structures is presented. The basis of this description is a doubly curved quadrilateral shell element, with 36 degrees of freedom, developed by the author. Used in conjunction with a shell theory due to Sanders (1959, 1963) and constitutive equations for an anisotropic material (Lekhinitskii 1964), this element is suitable for the dynamic and geometrically nonlinear analysis of general thin shells. Equations governing the free vibration of thin shell structures are developed from Hamilton's Principle. These equations are then solved using the above finite element model, natural frequencies of the system being determined by the method of simultaneous (or subspace) iteration. The linear response and vibrational frequencies of a cylindrical panel (Clough and Wilson 1971) are used to check convergence of this model. Static stability equations are developed from the Principle of Minimum Potential Energy, and are again solved using the finite element formulation. In this case, the resulting equations are verified by comparison of the results with those for the linear bifurcation of thin cylindrical shells under both uniform pressure and wind loading (Wang and Billington 1974, Cole 1973). Finally, the concept of dynamic stability, as defined by Bolotin (1964), is introduced. Working from the Lagrange equations, the dynamic stability equations for a thin shell structure are developed, using the finite element method. It is shown that these equations are in fact Mathieu's equation, and solution for the boundary frequencies of the instability regions is considered. The techniques described are applied to thin shells of revolution under various loading conditions, and the practical consequences of the results are discussed.
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Published date: 1980
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Local EPrints ID: 458990
URI: http://eprints.soton.ac.uk/id/eprint/458990
PURE UUID: 748778a6-fa69-4565-8f11-db9af84cf17b
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Date deposited: 04 Jul 2022 17:02
Last modified: 04 Jul 2022 17:02
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Author:
David John Collington
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