Hamilton’s principle and associated variational principles in polar thermopiezoelectricity

M. Cengiz Dökmeci

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 15, 2966-2974

Abstract: We express Hamilton’s principle for a regular region of thermopiezoelectric polar materials. First, we obtain a four-field variational principle which leads, as its Euler–Lagrange equations, to the divergence equations and the associated natural boundary conditions only. Next, we adjoin the rest of the fundamental equations into the variational principle through an involutory transformation. Thus, we formulate a differential type of unified variational principles operating on all the field variables. The unified variational principle is extended for the region with a fixed internal surface of discontinuity and for a curvilinear laminated region as well. The principles derived in invariant form are expressible in a system of particular coordinate system most appropriate to the geometry of the regions. They are indicated to recover some of earlier principles as special cases.

Keywords: Hamilton’s principle; Variational principles; Polar thermopiezoelectric materials (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:15:p:2966-2974

DOI: 10.1016/j.physa.2010.01.002

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