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TECHNICAL PAPERS

Multimode Approach to Nonlinear Supersonic Flutter of Imperfect Circular Cylindrical Shells

[+] Author and Article Information
M. Amabili

Dipartimento di Ingegneria Industriale, Università di Parma, Parco Area delle Scienze 181/A, Parma I-43100, Italy

F. Pellicano

Dipartimento di Scienze dell’ Ingegneria, Università di Modena e Reggio Emilia, Via Campi 213/B, Modena, I-41100, Italy

J. Appl. Mech 69(2), 117-129 (Oct 01, 2001) (13 pages) doi:10.1115/1.1435366 History: Received March 07, 2001; Revised October 01, 2001
Copyright © 2002 by ASME
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References

Figures

Grahic Jump Location
Amplitude of oscillatory solutions versus the freestream static pressure; n=23, linear piston theory. –, stable branches; ----, unstable branches. (a) Maximum amplitude of the first longitudinal mode A1,n(t)/h; (b) maximum amplitude of the first longitudinal mode B1,n(t)/h; (c) maximum amplitude of the second longitudinal mode A2,n(t)/h; (d) maximum amplitude of the second longitudinal mode B2,n(t)/h; (e) maximum amplitude of the third longitudinal mode A3,n(t)/h; (f ) maximum amplitude of the third longitudinal mode B3,n(t)/h; (g) maximum amplitude of the fourth longitudinal mode A4,n(t)/h; (h) maximum amplitude of the fourth longitudinal mode B4,n(t)/h; (i) maximum amplitude of the first mode with 2n circumferential waves A1,2n(t)/h; (j) maximum amplitude of the first axisymmetric mode A1,0(t)/h.
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Time histories of the shell for p=3800 Pa;n=23, linear piston theory. (a) Amplitude of the first longitudinal mode A1,n(t)/h; (b) amplitude of the first longitudinal mode B1,n(t)/h; (c) amplitude of the second longitudinal mode A2,n(t)/h; (d) amplitude of the second longitudinal mode B2,n(t)/h; (e) amplitude of the first longitudinal mode with 2n circumferential waves A1,2n(t)/h; (f ) amplitude of the axisymmetric mode A1,0(t)/h.
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Flutter response of the shell for p=7000 Pa;n=23, linear piston theory. (a) Time history of the first longitudinal mode A1,n(t)/h; (b) phase-plane plot of the first longitudinal mode A1,n(t)/h; (c) spectrum of the first longitudinal mode A1,n(t)/h.
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Nondimensional flutter amplitude versus nondimensional flutter frequency; ω1,n=2π×226.3 rad/s. –, stable branches; ----, unstable branches. (a) Amplitude of the first longitudinal mode with n circumferential waves; (b) amplitude of the first longitudinal mode with 2n circumferential waves.
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Amplitude of oscillatory solutions versus the freestream static pressure; n=23. –, third-order piston theory; ----, linear piston theory.
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Critical freestream static pressure versus the pressure differential across the shell skin pm for three different numbers of circumferential waves: ----, n=22; –, n=23, ⋅-⋅-⋅-⋅, n=24
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Critical freestream static pressure versus the pressure differential across the shell skin pm. –, theoretical results for imperfect shell, B̃1,24=0.18h,Ã3,24=0.0966h,Ã1,0=2.46h, and n=24; the gray area delimited by ⋅-⋅-⋅-⋅ represents the experimental data (19).
Grahic Jump Location
Amplitude of oscillatory solutions versus the freestream static pressure; n=24,pm=5000 Pa; imperfect shell (B̃1,24=0.18h,Ã3,24=0.0966h,Ã1,0=2.46h), linear piston theory. –, stable branches; ----, unstable branches. (a) Maximum amplitude of the first longitudinal mode A1,n(t)/h; (b) maximum amplitude of the first longitudinal mode B1,n(t)/h; (c) maximum amplitude of the second longitudinal mode A2,n(t)/h; (d) maximum amplitude of the second longitudinal mode B2,n(t)/h.
Grahic Jump Location
Flutter response of the shell for p=6500 Pa;n=24,pm=5000 Pa; imperfect shell (B̃1,24=0.18h,Ã3,24=0.0966h,Ã1,0=2.46h), linear piston theory. (a) Time history of the first longitudinal mode A1,n(t)/h; (b) experimental time history (3); (c) spectrum of the first longitudinal mode A1,n(t)/h; (d) experimental spectrum (3).

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