0
Research Papers

Numerical Investigation of the Flutter of a Spherical Shell

[+] Author and Article Information
Mohamed Menaa

Department of Mechanical Engineering,
Ecole Polytechnique de Montréal,
C.P. 6079 Succursale Centre-Ville,
Montréal H3C 3A7, Canada

e-mail: mohamed.menaa@polymtl.ca

Aouni A. Lakis

Department of Mechanical Engineering,
Ecole Polytechnique de Montréal,
C.P. 6079 Succursale Centre-Ville,
Montréal H3C 3A7, Canada
e-mail: Aouni.lakis@polymtl.ca

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 3, 2013; final manuscript received October 19, 2013; published online December 24, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 136(2), 021010 (Dec 24, 2013) (16 pages) Paper No: VIB-13-1190; doi: 10.1115/1.4025997 History: Received June 03, 2013; Revised October 19, 2013

In this study, aeroelastic analysis of a spherical shell subjected to external supersonic airflow is carried out. The structural model is based on a combination of the linear spherical shell theory and the classic finite element method (FEM). In this hybrid method, the nodal displacements are found from the exact solution of shell governing equations rather than approximated by polynomial functions. Therefore, the number of elements chosen is a function of the complexity of the structure. Convergence is rapid. It is not necessary to choose a large number of elements to obtain good results. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The linear mass, stiffness, and damping matrices are found using the hybrid finite element formulation. Aeroelastic equations are numerically derived and solved. The results are validated using the numerical and theoretical data available in literature. The analysis is accomplished for spherical shells with different boundary conditions, geometries, flow parameters, and radius to thickness ratios. the results show that the spherical shell loses its stability through coupled-mode flutter. This proposed hybrid FEM can be used efficiently for the design and analysis of spherical shells employed in high speed aircraft structures.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Geometry of the spherical shell

Grahic Jump Location
Fig. 2

Stress resultants and stress couples

Grahic Jump Location
Fig. 3

Spherical frustum element

Grahic Jump Location
Fig. 4

Definition of angle ϕ0

Grahic Jump Location
Fig. 5

Trajectories of the complex frequencies loci in the complex ω plane during the changing of the dynamic pressure parameter

Grahic Jump Location
Fig. 6

(a) Real part and (b) imaginary part of the complex frequencies versus the freestream static pressure parameter; static pressure evaluated by Eq. (36)

Grahic Jump Location
Fig. 7

(a) Real part and (b) imaginary part of the complex frequencies versus the freestream static pressure parameter; static pressure evaluated by Eq. (37)

Grahic Jump Location
Fig. 8

Variation of the critical freestream static pressure parameter with angle ϕ0 for the simply supported shell

Grahic Jump Location
Fig. 9

Variation of the critical freestream static pressure parameter with R/h for the simply supported shell

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In