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TECHNICAL PAPERS

Vibration Delocalization of Nearly Periodic Structures Using Coupled Piezoelectric Networks

[+] Author and Article Information
J. Tang

Department of Mechanical Engineering, The University of Connecticut, Storrs, CT 06269

K. W. Wang

Structural Dynamics and Controls Lab, The Pennsylvania State University, University Park, PA 16802

J. Vib. Acoust 125(1), 95-108 (Jan 06, 2003) (14 pages) doi:10.1115/1.1521951 History: Received March 01, 2001; Revised December 01, 2001; Online January 06, 2003
Copyright © 2003 by ASME
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References

Figures

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(a) Schematic of periodic structure; (b) Periodic structure augmented with coupled piezoelectric circuits; (c) Circuit diagram of the coupled piezoelectric circuits Va: equivalent voltage generator attributed to the piezoelectric effect; Cp: piezo capacitance; L: inductance; Ca: circuit coupling capacitance
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Vibration modes (a) perfectly periodic structure; (b) nearly periodic structure, σ=0.0025; (c) nearly periodic structure, σ=0.01. –Second mode; [[dotted_line]] 12th mode; -⋅-⋅ 32nd mode.
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Lyapunov exponents (localization factors) versus frequency (a) perfectly periodic structure; (b) perfectly periodic structure-zoom-in; (c) nearly periodic structure, σ=0.0025; (d) nearly periodic structure, σ=0.01
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Modal amplitudes in logarithm scale and localization factors (a) nearly periodic structure, σ=0.0025; (b) nearly periodic structure, σ=0.01. –Second mode; [[dotted_line]] 12th mode; -⋅-⋅ 32nd mode; – – slope indicating localization factor.
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Vibration modes of structure augmented with coupled piezoelectric circuits (a) perfectly periodic case; (b) nearly periodic case, σ=0.0025; (c) nearly periodic case, σ=0.01. Only the structural modal amplitudes are plotted. –Second mode; [[dotted_line]] 12th mode; –⋅–⋅ 112th mode.
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Lyapunov exponents of structure augmented with coupled piezoelectric circuits, δ=1,Ra=1 (a) perfectly periodic case; (b) nearly periodic case, σ=0.0025; (c) nearly periodic case, σ=0.01; (d) zoom-in of the first pass-band frequency range. In Fig. 6(d) –perfectly periodic; [[dotted_line]] σ=0.0025; –⋅–⋅ σ=0.01.
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Localization factors of structure augmented with coupled piezoelectric circuits, δ=1,Ra=1 (a) σ=0.0025; (b) σ=0.01. –Wolf’s algorithm; ° approximate solution.
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Localization indices at the first (a) and second (b) pass-bands
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Pass-band frequency ranges of the integrated system (a) δ=0.1; (b) δ=0.5; (c) δ=1; (d) δ=1.5. –first pass-band end frequencies; –⋅–⋅ second pass-band end frequencies.
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Lyapunov exponents of structure augmented with coupled piezoelectric circuits, with imperfections in circuitry elements (a) nearly periodic case, σ=0.0025; (b) nearly periodic case, σ=0.01 (c) zoom-in of the pass-bands overlap frequency range. –perfectly periodic; [[dotted_line]] σ=0.0025; –⋅– σ=0.01.
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Lyapunov exponents of structure augmented with coupled piezoelectric circuits (a) perfectly periodic case; (b) nearly periodic case, σ=0.0025; (c) nearly periodic case, σ=0.01; (d) zoom-in of pass-bands overlap frequency range. –perfectly periodic [[dotted_line]]; σ=0.0025 –⋅–⋅; σ=0.01.

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