Saint-Venant's Principle for a Piezoelectric Body

For a semi-infinite piezoelectric body with uniform or variable cross section we establish the exponential decay of the internal energy relative to the portion of the body beyond a distance x3from the base: Saint-Venant's principle. All possible combinations of physically admissible boundary co...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1998, Vol.59 (3), p.1098-1111
Main Authors: Borrelli, A., Patria, M. C.
Format: Article
Language:English
Subjects:
Boundary conditions
Cauchy Schwarz inequality
Crystals
Cylinders
Displacement vectors
Elastic bodies
Electric fields
Electrons
Energy
Inequality
Internal energy
Mathematical inequalities
Piezoelectricity
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Summary:For a semi-infinite piezoelectric body with uniform or variable cross section we establish the exponential decay of the internal energy relative to the portion of the body beyond a distance x3from the base: Saint-Venant's principle. All possible combinations of physically admissible boundary conditions are examined. The stabilizing effect of the electric field on the decay length is shown. Finally the total internal energy is estimated in terms of the data, making use also of the Korn inequality.
ISSN:0036-1399
1095-712X
DOI:10.1137/S0036139997319323