APPLICATION OF A THREE-DIMENSIONAL SHELL THEORY TO THE FREE VIBRATION OF SHELLS ARBITRARILY DEEP IN ONE DIRECTION

Author: YOUNG P.G.

Source: Journal of Sound and Vibration, Volume 238, Number 2, November 2000 , pp. 257-269(13)

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Abstract:

A three-dimensional shell theory is presented which is applicable to doubly curved thick open shells which are arbitrarily deep (have a large side-length to radius of curvature ratio) in one principal direction but are shallow in the other direction. The strain–displacement equations for the proposed “deep-shallow” shell theory are expressed in Cartesian co-ordinates and the limits of applicability of these equations are discussed. These equations are then used in a Ritz variational formulation with algebraic polynomials as trial functions to solve for the natural frequencies of a number of doubly curved shell problems. A novel approach is also proposed in which penalty functions are introduced to enforce continuity of displacements at two opposite ends of a shell of rectangular platform, increasing the range of problems which can be treated to include closed shells, such as cylinders, barrels, cooling-tower-type structures, toroids, rings, etc. (a sub-class of shells of revolution). Copyright 2000 Academic Press

Language: English

Document Type: Research article

Affiliations: School of Engineering and Computer Science, University of Exeter, Exeter Devon, EX4 4QF, England

Publication date: 2000-11-01