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Technical Brief

Active Control of Viscoelastic Systems by the Method of Receptance

[+] Author and Article Information
Kumar V. Singh

Mechanical and Manufacturing Engineering Department,
Miami University,
Oxford, OH 45046
e-mail: singhkv@miamioh.edu

Xiaoxuan Ling

Mechanical and Manufacturing Engineering Department,
Miami University,
Oxford, OH 45046

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 20, 2017; final manuscript received September 7, 2017; published online October 4, 2017. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 140(2), 024501 (Oct 04, 2017) (6 pages) Paper No: VIB-17-1168; doi: 10.1115/1.4037959 History: Received April 20, 2017; Revised September 07, 2017

Viscoelastic materials have frequency and temperature-dependent properties and they can be used as passive controlling devices in wide range of vibration applications. In order to design active control for viscoelastic systems, an accurate mathematical modeling is needed. In practice, various material models and approximation techniques are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state-space models, which introduces several challenges such as introduction of nonphysical internal state variables and requirement of observer/state estimator design. In this paper, it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available receptance transfer functions (RTF) and hence eliminating the need for state-space modeling for control design. By using the recently developed receptance method, it is shown that active control for poles and zeros assignment of the viscoelastic systems can be achieved. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of RTF and solution of the set of linear system of equations.

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References

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Figures

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Fig. 1

(a) Discrete model of a viscoelastic structure and (b) A continuous beam supported by a viscoelastic element

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Fig. 2

(a) Schematic of active feedback control using RTF and (b) nested control schematic for structure supported by viscoelastic elements

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Fig. 3

Open- and closed-loop poles in complex plane

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Fig. 4

RTF showing the pole assignment as described in Table1

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Fig. 5

Pole assignment for desired damping in the modes

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Fig. 6

Multiple assignment of zeros at coordinate x1 ensuring no displacement for two different frequencies

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Fig. 7

Demonstration of the simultaneous poles and zero assignment

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Fig. 8

Pole placement in a beam supported by viscoelastic element at the end

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Fig. 9

Simultaneous pole and zero assignment in a beam supported by viscoelastic element at the end

Tables

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