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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on September 18, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(4):443-456; doi:10.1093/qjmam/hbm016
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Q. Jl Mech. Appl. Math, Vol. 60. No. 4 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On the coupled theory of thermo-magnetoelectroelasticity

Moncef Aouadi{dagger}

( Rustaq Faculty of Education, Department of Mathematics and Computer Science, Rustaq 329, PO Box 10, Sultanate of Oman )

{dagger} < moncef_aouadi{at}yahoo.fr>

Received 27 November 2006. Revise 26 May 2007.
  Abstract

Within the context of the coupled theory of thermo-magnetoelectroelasticity, we derive some variational principles which fully characterize the solution of the boundary-initial-value problem. Then we establish a reciprocity relation using a new method of proof, which involves two thermoelastic processes at different instants. We show that this relation can be used to obtain reciprocity and uniqueness theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived without making restrictions on the positive definiteness of the elastic moduli or the conductivity tensor. There are also no restrictions on piezoelectric moduli, piezomagnetic moduli and thermal coupling coefficients other than symmetry conditions. The results obtained are applicable for some special cases which can be deduced from our model.


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