Title :
Variational principles for polar piezoelectric media in elastic range
Author :
Altay, Gülay ; Dökmeci, M. Cengiz
Author_Institution :
Fac. of Eng., Bogazici Univ., Istanbul, Turkey
fDate :
9/1/2009 12:00:00 AM
Abstract :
The fundamental equations of polar piezoelectric media in differential form are alternatively established in variational forms with their well-known features. First, a 3-field variational principle with some constraint conditions is deduced for a regular region of media from a general principle of physics. The principle is modified by using an involutory transformation and a 9-field variational principle operating on all the field variables is derived. Next, this principle is extended and a unified variational principle is obtained for the region with a fixed internal surface of discontinuity. The unified variational principle is further generalized for the equations of a laminated polar region. The generalized variational principle with the only constraint of initial conditions yields all the equations of the laminae region, including the interface conditions, as its Euler-Lagrange equations. The variational principles are shown to recover some of earlier variational principles, as special cases.
Keywords :
elasticity; laminates; piezoelectric materials; variational techniques; 3-field variational principle; 9-field variational principle; Euler-Lagrange equations; elastic range; fixed internal surface; interface conditions; involutory transformation; laminae region; laminated polar region; polar piezoelectric media; Differential equations; Physics;
Journal_Title :
Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on
DOI :
10.1109/TUFFC.2009.1274