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The Saint‐Venant Problem for Monoclinic Piezoelectric Cylinders
Author(s) -
Bisegna Paolo
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199803)78:3<147::aid-zamm147>3.0.co;2-z
Subject(s) - piezoelectricity , dirichlet problem , mathematics , mathematical analysis , cylinder , classical mechanics , physics , geometry , acoustics , boundary value problem
Abstract The Saint‐Venant problem is formulated in the framework of the linear theory of piezoelectricity for homogeneous, monoclinic, piezoelectric cylinders. A relaxed version of this problem is stated and is proved to be well‐posed under Clebsch‐type assumptions. The general solution of the relaxed problem is explicitly given, up to the solution of a two‐dimensional Dirichlet‐type problem involving two scalar fields, and is decomposed into five “fundamental” solutions. Finally, a Saint‐Venant principle, related to the present relaxed formulation of the piezoelectric Saint‐Venant problem, is established. In particular, the exponential decay along the cylinder axis of the free energy stored into a piezoelectric cylinder, subject to self‐equilibrated loads on one base only, is proved.