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Research Papers

Effect of Boundary Conditions on Nonlinear Vibration and Flutter of Laminated Cylindrical Shells

[+] Author and Article Information
E. L. Jansen

Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The NetherlandsE.L.Jansen@TUDelft.nl

J. Vib. Acoust 130(1), 011003 (Nov 12, 2007) (8 pages) doi:10.1115/1.2775512 History: Received August 18, 2006; Revised May 24, 2007; Published November 12, 2007

A nonlinear vibration analysis of laminated cylindrical shells is presented in which the effect of the specified boundary conditions at the shell edges, including nonlinear fundamental state deformations, can be accurately taken into account. The method is based on a perturbation expansion for both the frequency parameter and the dependent variables. The present theory includes the effects of finite vibration amplitudes, initial geometric imperfections, and a nonlinear static deformation. Nonlinear Donnell-type equations formulated in terms of the radial displacement W and an Airy stress function F are used, and classical lamination theory is employed. Furthermore, an extension of the theory is presented to analyze linearized flutter in supersonic flow, based on piston theory. The effect of different types of boundary conditions on the nonlinear vibration and linearized flutter behavior of cylindrical shells is illustrated for several characteristic cases.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 3

Second-order modes characterizing the effect of imperfections and axial loading on Booton’s anisotropic shell (L∕R=1.414): (a) static second-order mode and (b) dynamic imperfect mode

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Figure 4

Effect of boundary conditions on flutter boundaries of isotropic shell (L=406.4mm, R=203.2mm, h=0.102mm) for varying circumferential wave number

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Figure 5

Flutter mode shapes and stress functions of Olson’s isotropic shell (L=406.4mm, R=203.2mm, h=0.102mm)

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Figure 2

Effect of imperfections and axial loading on the linearized frequency of Booton’s anisotropic shell (L∕R=1.414)

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Figure 1

Shell geometry, coordinate system, and applied loading

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