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Minimization variational principles for acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. (English) Zbl 1186.74044
Summary: The classical energy minimization principles of Dirichlet and Thompson are extended as minimization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at a fixed frequency. This is done by building upon the ideas of Cherkaev and Gibiansky, who derived minimization variational principles for quasistatics. In the absence of free current, the primary electromagnetic minimization variational principles have a minimum, which is the time-averaged electrical power dissipated in the body. The variational principles provide constraints on the boundary values of the fields when the moduli are known. Conversely, when the boundary values of the fields have been measured, then they provide information about the values of the moduli within the body. This should have applications to electromagnetic tomography. We also derive saddle-point variational principles that correspond to the variational principles of Gurtin, Willis and Borcea.

MSC:
74F15 Electromagnetic effects in solid mechanics
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
74B05 Classical linear elasticity
76Q05 Hydro- and aero-acoustics
76W05 Magnetohydrodynamics and electrohydrodynamics
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