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

Bismarck-Nasr, M. N., 1996, “Finite Elements in Aeroelasticity of Plates and Shells,” ASME Appl. Mech. Rev., 49, pp. S17–S24. [CrossRef]
Dowell, E. H., 1975, Aeroelasticity of Plates and Shells, Noordhoff, Leyden, Netherlands.
Ashley, H. and Zartarian, G., 1956, “Piston Theory—New Aerodynamic Tool for Aeroelastician,” J. Aeronaut. Sci., 23, pp. 1109–1118. [CrossRef]
Fung, Y. C., and Olson, M. D., 1966, “Supersonic Flutter of Circular Cylindrical Shells Subjected to Internal Pressure and Axial Compression,” AIAA J., 4, pp. 858–864. [CrossRef]
Fung, Y. C., and OlsonM. D., 1967, “Comparing Theory and Experiment for Supersonic Flutter of Circular Cylindrical Shells,” AIAA J., 5, pp. 1849–1856. [CrossRef]
Evensen, D. A., and Olson, M. D., 1967, “Nonlinear Flutter of a Circular Cylindrical Shell in Supersonic Flow,” NASA Technical Note No. D-4265.
Evensen, D. A., and Olson, M. D., 1968, “Circumferentially Traveling Wave Flutter of Circular Cylindrical Shell,” AIAA J., 6, pp. 1522–1527. [CrossRef]
Dowell, E. H., 1966, “Flutter of Infinitely Long Plates and Shells. Part II,” AIAA J., 4, pp. 1510–1518. [CrossRef]
Carter, L. L., and Stearman, R. O., 1968, “Some Aspects of Cylindrical Panel Flutter,” AIAA J.6, pp. 37–43. [CrossRef]
Amabili, M. and Pellicano, F., “Nonlinear Supersonic Flutter of Circular Cylindrical Shells,” AIAA J.39, pp. 564–573. [CrossRef]
Bismarck-Nasr, M. N., 1976, “Finite Element Method Applied to the Supersonic Flutter of Circular Cylindrical Shells,” Int. J. Numer. Methods Eng., 10, pp. 423–435. [CrossRef]
Ganapathi, M., Varadan, T. K., and Jijen, J., 1994, “Field Consistent Element Applied to Flutter Analysis of Circular Cylindrical Shells,” J. Sound Vib., 171, pp. 509–527. [CrossRef]
Shulman,Y., 1959, “Vibration and Flutter of Cylindrical and Conical Shells,” MIT ASRL Report No. 74-2 (OSR Technical Report No. 59-776).
Ueda, T., Kobayashi, S., and Kihira, M., 1977, “Supersonic Flutter of Truncated Conical Shells,” Trans. Jpn. Soc. Aeronaut. Space Sci., 20, pp. 13–30.
Dixon, S. C., and Hudson, M. L., 1970, “Flutter, Vibration and Buckling of Truncated Orthotropic Conical Shells With Generalized Elastic Edge Restraint,” NASA Technical Note No. D-5759.
Miserento, R., and Dixon, S. C., 1971, “Vibration and Flutter Tests of a Pressurized Thin Walled Truncated Conical Shell,” NASA Technical Note No. D-6106.
Bismarck-Nasr, M. N., and Costa-Savio, H. R., 1979, “Finite Element Solution of the Supersonic Flutter of Conical Shells,” AIAA J.17, pp. 1148–1150. [CrossRef]
Sunder, P. J., Ramakrishnan, V. C., and Sengupta, S., 1983, “Finite Element Analysis of 3-Ply Laminated Conical Shell for Flutter,” Int. J. Numer Methods Eng., 19, pp. 1183–1192. [CrossRef]
Sunder, P. J., Ramakrishnan, V. C., and Sengupta, S., 1983, “Optimum Cone Angles in Aeroelastic Flutter,” Comput. Struct., 17, pp. 25–29. [CrossRef]
Mason, D. R., and Blotter, P. T., 1986, “Finite Element Application to Rocket Nozzle Aeroelasticity,” J. Propul. Power, 2, pp. 499–507. [CrossRef]
Pidaparti, R. M. V., and Yang Henry, T. Y., 1993, “Supersonic Flutter Analysis of Composite Plates and Shells,” AIAA J., 31, pp. 1109–1117. [CrossRef]
Kraus, H., 1967, Thin Elastic Shells, John Wiley and Sons, New York.
Narasimhan, M. C., and Alwar, R. S., 1992, “Free Vibration Analysis of Laminated Orthotropic Spherical Shell,” J. Sound Vib., 54, pp. 515–529. [CrossRef]
SaiRam, K. S., and SreedharBabu, T., 2002, “Free Vibration of Composite Spherical Shell Cap With and Without a Cutout,” Comput. Struct., 80, pp. 1749–1756. [CrossRef]
KalninsA., 1961, “Free Non-Symmetric Vibrations of Shallow Spherical Shells,” J. Acoust. Soc. Am., 33, pp. 1102–1107. [CrossRef]
Kalnins, A., 1964, “Effect of Bending on Vibration of Spherical Shell,” J. Acoust. Soc. Am., 36, pp. 74–81. [CrossRef]
Cohen, G. A., 1965, “Computer Analysis of Asymmetric Free Vibrations of Ring Stiffened Orthotropic Shells of Revolution,” AIAA J., 3, pp. 2305–2312. [CrossRef]
Navaratna, D. R., 1966, “Natural Vibration of Deep Spherical Shells,” AIAA J., 4, pp. 2056–2058. [CrossRef]
Webster, J. J., 1967, “Free Vibrations of Shells of Revolution Using Ring Finite Elements,” Int. J. Mech. Sci., 9, pp. 559–570. [CrossRef]
Greene, B. E., Jones, R. E., Mc Lay, R.W., and Strome, D. R., 1968, “Dynamic Analysis of Shells Using Doubly Curved Finite Elements,” Proceedings of the Second Conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, OH, October 15–17, Paper No. AFFDL-TR-68-150, pp. 185–212.
Tessler, A., and Spiridigliozzi, L., 1988, “Resolving Membrane and Shear Locking Phenomena in Curved Deformable Axisymmetric Shell Element,” Int. J. Numer. Methods Eng., 26, pp. 1071–1080. [CrossRef]
Gautham, B. P., and Ganesan, N., 1992, “Free Vibration Analysis of Thick Spherical Shells,” Comput. Struct., 45, pp. 307–313. [CrossRef]
Buchanan, G. R., and Rich, B. S., 2002, “Effect of Boundary Conditions on Free Vibrations of Thick Isotropic Spherical Shells,” J. Vib. Control, 8, pp. 389–403. [CrossRef]
Gautham, B. P., and Ganesan, N., 1997, “Free Vibration Characteristics of Isotropic and Laminated Orthotropic Shell Caps,” J. Sound Vib., 204, pp. 17–40. [CrossRef]
Ventsel, E. S., Naumenko, V., Strelnikova, E., and Yeseleva, E., 2010, “Free Vibrations of Shells of Revolution Filled With Fluid,” Eng. Anal. Boundary Elem., 34, pp. 856–862. [CrossRef]

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