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Technical Briefs

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

[+] Author and Article Information
Helio A. Navarro

 Department of Mechanical Engineering, São Carlos School of Engineering,University of São Paulo, Av. Trabalhador São-Carlense, 400, São Carlos, SP, 13566-590, Brazilhan@sc.usp.br

José M. Balthazar

 Geoscience and Exact Science Institute DEMAC, UNESP Universidade Estadual Paulista, P.O. Box 178, Rio Claro, SP, 13500-230, Braziljmbaltha@rc.unesp.br

Tatyana S. Krasnopolskaya

 Institute of Hydromechanics,National Academy of Sciences of Ukraine,Zhelyabov Street 8/4,03680, Kiev, Ukraine,t.krasnopolskaya@tue.nl

Aleksandr Yu. Shvets

 NTUU Kiev Polytechnic institute, Ave. Pobedy, 37, 03057, Kiev, Ukrainealex.shvets@bigmir.net

Fábio R. Chavarette

 Faculty of Engineering,UNESP Universidade Estadual Paulista, DM, Avenida Brasil, 56, Ilha Solteira, SP, 15385-000, Brazilfabioch@mat.feis.unesp.br

J. Vib. Acoust 134(4), 044501 (May 29, 2012) (6 pages) doi:10.1115/1.4005844 History: Received April 21, 2011; Revised October 17, 2011; Published May 29, 2012; Online May 29, 2012

We studied free surface oscillations of a fluid in a cylinder tank excited by an electric motor with limited power supply. We investigated the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Numerical experiments are carried out to present the existence of several types of regular and chaotic attractors. For the first time powers (power of the motor, power consumed by the damping force under fluid free surface oscillations, and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

System composed by liquid in tank and electric motor

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Figure 2

Various types of attractors

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Figure 3

Time history: (a) p2 , N1  = 1.05, (b) q2 , N1  = 1.05, (c) p2 , N1  = 1.95, and (d) q2 , N1  = 1.95

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Figure 4

Root mean square for parameters p2 (solid line) and q2 (dashed line) in function of N1 (τ =  20,000 and Δ N1=  0.05)

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Figure 5

Graphs of the power Pm (dash dot line), Pd (dotted line), and the total power P (solid line): (a) at N1  = 1.50 for the periodic regime and (b) chaotic regime for N1  = 1.95

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