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Proceedings Paper

Transducer tolerance theory for structural control
Author(s): Shawn Edward Burke; Robert L. Clark
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Paper Abstract

An expression for the mean and variance of a transducer array's modal coefficients is developed to quantify the effect of spatial errors on the transducer structural coupling, and on the transducer augmented plant's input/output frequency response. Transducer elements are modeled spatially via their position, aperture, and shading (e.g., spatial gain weighting). Each of these spatial parameters can be statistically modeled in terms of their mean and variance, assuming statistical independence. Modal coefficients are described via composition integrals of the transducer spatial kernel and the plant mode shapes. The probability density function of each parameter is then assumed to be unimodal, with characteristic scale smaller than any corresponding spatial scale of the modal coefficient's dependence on the parameter. Consequently, the mean values of the modal coefficients are the values of the corresponding integrals evaluated at the mean transducer position, aperture, and shading. The variance of the modal coefficients, derived via a Taylor series expansion to second order about their mean values, is expressed in terms of the partial derivatives of the modal coefficient with respect to the uncertain spatial parameters. This suggests that transducers whose shadings consist of low- order generalized function or modal expansions are less sensitive to spatial parameter variations. Variations in the modal coefficients are mapped to expressions for the mean and variance of transducer-augmented plant transfer functions. Simulation examples are presented that model variations in the input/output transfer functions characteristics of a flexible beam with a mis-registered point actuator, and a mis-registered modally-weighted piezo film sensor distribution. For even slight aperture mis-registrations--0.26% of the beam's length--the modal sensors no longer perfectly `sift out' non-targeted modes, and off-mode contributions grow by nearly an order of magnitude.

Paper Details

Date Published: 8 May 1995
PDF: 12 pages
Proc. SPIE 2443, Smart Structures and Materials 1995: Smart Structures and Integrated Systems, (8 May 1995); doi: 10.1117/12.208278
Show Author Affiliations
Shawn Edward Burke, Boston Univ. (United States)
Robert L. Clark, Duke Univ. (United States)

Published in SPIE Proceedings Vol. 2443:
Smart Structures and Materials 1995: Smart Structures and Integrated Systems
Inderjit Chopra, Editor(s)

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