Combined finite element-normal mode expansion methods in electroelasticity and their application to piezoactive motors

The proposed numerical modelling technique combines the Finite Element Method (FEM) and the normal mode expansion method. These methods have been mainly used in structural analysis. They can be extended to steady-state or transient problems of electromechanical structures. This technique associates precise description of the three-dimensional electromechanical coupling e¤ects by FEM to lumped parameter equivalent circuits simplicity. This circuit is provided by expanding the transducer displacement Þeld with respect to the resonance mode basis. This operation results in relatively few matrix decompositions in computing the contact problems encountered in piezoactive motors analysis. It also gives an interesting insight to the physic of electromechanical energy conversion. In addition, the large rigid displacement of the rotor is easily taken into account. The proposed method is Þrst assessed through some classical problems to show some of its practical advantages and is subsequently applied to piezoactive motor modelling