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RESEARCH PAPERS

Free Vibration Analysis of Spherical Caps Using a G.D.Q. Numerical Solution

[+] Author and Article Information
E. Artioli

 IMATI-CNR, 27100 Pavia, Italy

E. Viola

D.I.S.T.A.R.T., University of Bologna, 40136, Italy

J. Pressure Vessel Technol 128(3), 370-378 (Jul 06, 2005) (9 pages) doi:10.1115/1.2217970 History: Received June 17, 2003; Revised July 06, 2005

In this paper we present the frequency evaluation of spherical shells by means of the generalized differential quadrature method (G.D.Q.M.), an effective numerical procedure which pertains to the class of generalized collocation methods. The shell theory used in this study is a first-order shear deformation theory with transverse shearing deformations and rotatory inertia included. The shell governing equations in terms of mid-surface displacements are obtained and, after expansion in partial Fourier series of the circumferential coordinate, solved with the G.D.Q.M. Several comparisons are made with available results, showing the reliability and modeling capability of the numerical scheme in argument.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Spherical cap: coordinates

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Figure 2

Shell mid-surface element: displacements and geometry

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Figure 3

Internal actions: (a) force element and (b) couple element

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Figure 4

Eigenparameter convergence characteristic: clamped shell

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Figure 5

Eigenparameter convergence characteristic: hinged shell

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Figure 6

Eigenparameter comparison: clamped shell

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Figure 7

Eigenparameter comparison: clamped shell

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Figure 8

Eigenparameter comparison: clamped shell

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Figure 9

Eigenparameter comparison: clamped shell

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Figure 10

Mode shapes: clamped shell

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Figure 11

Mode shapes: clamped shell

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