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TECHNICAL PAPERS

Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results

[+] Author and Article Information
M. Amabili

Dipartimento di Ingegneria Industriale, Università di Parma, Parma, I-43100 Italy

F. Pellicano

Dipartimento di Scienze dell’Ingegneria, Università di Modena e Reggio Emilia, Modena, I-41100 Italy

A. F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Vib. Acoust 122(4), 346-354 (May 01, 2000) (9 pages) doi:10.1115/1.1288593 History: Received March 01, 1999; Revised May 01, 2000
Copyright © 2000 by ASME
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References

Figures

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Response-frequency curves and backbone curves for the driven mode without companion mode participation, case of Chen and Babcock 2. – present results; [[long_dash_short_dash]] Amabili et al. 1; [[dashed_line]] Chen and Babcock 2; ⋅-⋅-○-⋅ backbone of Ganapathi and Varadan 6.
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Response-frequency curve with companion mode participation, case of Chen and Babcock 2. (a) Maximum of A1,n(t)/h; (b) maximum of B1,n(t)/h; (c) maximum of A1,0(t)/h; (d) maximum of A3,0(t)/h. – stable solutions; [[dashed_line]] unstable solutions; integer numbers identify the different branches of the solution.
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Response-frequency curve with companion mode participation, case of 1:1:1:2 internal resonances and f1=0.01. (a) Maximum of A1,n(t)/h; (b) particular of Part (a); (c) maximum of B1,n(t)/h; (d) maximum of A1,0(t)/h; (e) maximum of A3,0(t)/h. – stable solutions; [[dashed_line]] unstable solutions; integer numbers identify the different branches of the solution.
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Time response for f1=0.01 and ω/ω1,n=1; case of 1:1:1:2 internal resonances. (a) A1,n(t)/h; (b) B1,n(t)/h; (c) A1,0(t)/h; (d) A3,0(t)/h.
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Response amplitude with companion mode participation versus the excitation amplitude. Case of 1:1:1:2 internal resonances with excitation frequency ω=ω1n. (a) Maximum of A1,n(t)/h; (b) particular of Part (a); (c) maximum of B1,n(t)/h; (d) maximum of A1,0(t)/h; (e) maximum of A3,0(t)/h. – stable solutions, by Auto ; [[dashed_line]] unstable solutions, by Auto ; • direct integration; integer numbers identify the different branches of the solution.

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