ABSTRACT We present a systematic analysis of the eigenvalue problem associated with free, small-amplitude vibrations in an elastic body possessing piezoelectric, piezomagnetic, and magnetoelectric couplings. An abstract formulation is introduced. The operators in the abstract formulation are shown to be self-adjoint, from which a series of fundamental properties of resonant frequencies and vibration modes are proved concisely. A variational formulation and a perturbation analysis of the eigenvalue problem are also given, based on the abstract formulation.
Digital Object Identifier 10.1109/TUFFC.2008.699
© 2008, by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.