Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 2: Perturbation Analysis

[+] Author and Article Information
F. Pellicano

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

M. Amabili

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

A. F. Vakakis

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

J. Vib. Acoust 122(4), 355-364 (May 01, 2000) (10 pages) doi:10.1115/1.1288591 History: Received March 01, 1999; Revised May 01, 2000
Copyright © 2000 by ASME
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Grahic Jump Location
Response amplitude versus the level of the modal excitation; exact resonance condition. Perturbation results: – stable solutions; [[dashed_line]] unstable solutions. Results of direct integrations: “○” companion mode participation; “×” absence of companion mode. (a) amplitude a1; (b) amplitude a2; (c) amplitude a3; (d) amplitude a4.
Grahic Jump Location
Response amplitude and phase versus the modal excitation frequency for f1=0.01. Perturbation results: – stable solutions; [[dashed_line]] unstable solutions. (a) Amplitude a1; (b) amplitude a2; (c) amplitude a3; (d) amplitude a4; (e) phase ϑ1.
Grahic Jump Location
Poincaré map for ω/ω1n=0.99 and f1=0.01 showing a limit cycle. (a) (A1n,Ȧ1n)-plane; (b) (B1n,Ḃ1n)-plane; (c) (A10,Ȧ10)-plane; (d) (A30,Ȧ30)-plane.
Grahic Jump Location
Response A1n in presence of the limit cycle condition: ω/ω1n=0.99 and f1=0.01. (a) Time history showing amplitude modulation; (b) spectrum of the time response.
Grahic Jump Location
Jump from an unstable steady oscillation to the stable one: ω/ω1n=1 and f1=0.01
Grahic Jump Location
Response amplitude and phase versus the external point excitation frequency for f1=0.01,f4=0.003,f2=f3=0. Perturbation results: –  stable solutions; [[dashed_line]]  unstable solutions. (a) amplitude a1; (b) amplitude a2; (c) amplitude a3; (d) amplitude a4; (e) phase ϑ1.




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