Page 244 - Mechanics of Microelectromechanical Systems
P. 244
4. Microtransduction: actuation and sensing 231
as suggested in Fig. 4.44 (b). For a negative magnetostrictive material the
deformation instances presented above reverse.
The similarity with the piezoelectric materials also extends in the
modeling domain where the magneto-elastic equations replicate the electro-
elastic ones describing the piezoelectric effect. In essence, the equations that
describe the magnetostrictive effect can be written as:
It can be seen by comparing Eq. (4.120) to Eq. (4.99) that, formally, the only
difference consists in using the magnetic field H for magnetostrictive effects
instead of the electric field describing the piezoelectric effects. The subscript
ma was used to designate the magnetic charge constant matrix, whereas the
superscript H indicates that the compliance matrix is calculated under
constant-field conditions.
Figure 4.44 Deformation of a positive magnetostrictive material when: (a) the external
magnetic field is parallel to the polarization direction; (b) the external magnetic field is
perpendicular to the polarization direction
An equation similar to Eq. (4.107) also applies for piezomagnetic
materials in the form:
