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Asymptotic analysis of 3D thin anisotropic plates with a piezoelectric patch
Author(s) -
Leugering Günter R.,
Nazarov Serguei A.,
Slutskij Andrey S.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1566
Subject(s) - piecewise , asymptotic analysis , piezoelectricity , displacement (psychology) , mathematics , mathematical analysis , anisotropy , actuator , plane (geometry) , order (exchange) , geometry , acoustics , physics , optics , electrical engineering , engineering , psychology , finance , economics , psychotherapist
We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two‐dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth‐order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second‐order in‐plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures. Copyright © 2012 John Wiley & Sons, Ltd.