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Structural Engineering and Mechanics Volume 17, Number 6, June 2004 , pages 789-817 DOI: https://doi.org/10.12989/sem.2004.17.6.789 |
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The G. D. Q. method for the harmonic dynamic analysis of rotational shell structural elements |
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Erasmo Viola and Edoardo Artioli
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| Abstract | ||
| This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called delta-point?technique. | ||
| Key Words | ||
| shell of revolution; generalized differential quadrature method; modal analysis; numerical method; dynamic analysis. | ||
| Address | ||
| Erasmo Viola and Edoardo Artioli; D.I.S.T.A.R.T. - Scienza delle Costruzioni, University of Bologna, Viale Risorgimento 2, Bologna, Italy | ||