Research Papers

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

[+] Author and Article Information
J. M. Balthazar

 UNESP-Rio Claro, Sao Paulo, Braziljmbaltha@rc.unesp.br

J. L. Felix

 UNESP-Rio Claro, Sao Paulo, Braziljorgelpfelix@yahoo.com.br

R. M. Brasil

Polytechnic School, University of Sao Paulo, Sao Paulo, Brazilreyolando.brasil@poli.usp.br

T. S. Krasnopolskaya

Institute of Hydromechanics, National Academy of Sciences, Kiev, Ukrainet.krasnopolskaya@tue.nl

A. Yu. Shvets

Kiev Polytechnical institute, National Technical University of Ukraine, Kiev, Ukrainealex.shvets@bigmir.net

J. Comput. Nonlinear Dynam 4(1), 011013 (Dec 16, 2008) (7 pages) doi:10.1115/1.3007909 History: Received August 14, 2007; Revised March 22, 2008; Published December 16, 2008

Interactions between the oscillations of piezoceramic transducer and the mechanism of its excitation—the generator of the electric current of limited power-supply—are analyzed in this paper. In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a dc motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a nonideal problem. In this work, we present certain phenomena as Sommerfeld effect, jump, saturation, and stability, through the influences of the parameters of the governing equations motion.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Scheme of the nonideal piezoceramic rod transducer (left circuit) and vacuum-tube generator (right circuit) system

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Figure 2

Time response for α0=0.5 and α4=0.23: (a) generator, (b) transducer

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Figure 3

Numerical result for α0=0.9 and α4=0.23: (a) and (b) generator response, (c) and (d) transducer response

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Figure 4

Amplitudes-parameter curves

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Figure 5

(a) and (b) Time histories; (c) and (d) phase planes for α0=0.5 and α4=0.103

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Figure 9

(a) and (b) Response of periodic motion when α7=0.0

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Figure 10

Phase plane for initial disturbance: small (a) small and (b) large

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Figure 6

(a) and (b) Time histories; (c) and (d) phase planes for α0=1.0 and α4=0.103

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Figure 7

Results of the nonideal and saturation phenomenon

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Figure 8

(a) and (b) Response of instability when α7=−0.06



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