Numerical Evaluation of Size Effect in Piezoelectric Micro-Beam with Linear Micromorphic Electroelastic Theory

The linear micromorphic electroelastic theory is proposed to solve bending problems of piezoelectric micro-beam in this paper. The basic governing equations with the boundary conditions are derived through the variational principle. Both the cantilever piezoelectric micro-beam subjected to a concent...

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Bibliographic Details
Published in:Journal of mechanics 2014-10, Vol.30 (5), p.467-476
Main Authors: Cao, W.-Z., Yang, X.-H., Tian, X.-B.
Format: Article
Language:English
Subjects:
Analysis
Approximation
Bending
Boundary conditions
Boundary value problems
Elasticity
Electronics
Mathematical analysis
Mathematical models
Mechanics
Piezoelectricity
Stress concentration
Studies
Variational principles
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Summary:The linear micromorphic electroelastic theory is proposed to solve bending problems of piezoelectric micro-beam in this paper. The basic governing equations with the boundary conditions are derived through the variational principle. Both the cantilever piezoelectric micro-beam subjected to a concentrated load at the free end and the simply supported micro-beam subjected to a distributed load are analyzed. It is found that the predictions from the micromorphic electroelastic theory are remarkably different from those from the classical theory when the micro-beam thickness is approximate or equal to the characteristic length scale parameter, but their difference is slight when the micro-beam thickness is much larger than the characteristic length scale parameter. As a result, it is concluded that the size effect is significant when the micro-beam thickness is comparable to the characteristic length scale parameter.
ISSN:1727-7191
1811-8216
DOI:10.1017/jmech.2014.25