Bilayer of magnetostrictive and piezoelectric components. The bilayer of length is in the (or 1,2) plane with its thickness along the (or direction 3) and and are the thicknesses of piezoelectric and magnetic layers, respectively. In the plane defined by , each point moves only in the vertical direction and the bilayer interface is at from this plane. The bilayer is assumed to be poled with an electric field along . The longitudinal ME effect corresponds to a bias magnetic field and an ac magnetic field along and resulting ac electric field along . The transverse ME effect corresponds to ac and bias magnetic fields along and along .
Frequency dependence of longitudinal and transverse ME voltage coefficients for a bilayer of permendur and PZT showing the resonance enhancement of ME interactions at the bending mode frequency. The bilayer is free to bend at both ends so that the wavelength of the bending mode corresponds to length . The sample dimensions are and total thickness and the PZT volume fraction .
The PZT volume fraction dependence of peak transverse ME voltage coefficient and resonance frequency for the permendur–PZT bilayer that is free to bend at both ends.
Frequency dependence of the transverse ME voltage coefficient for the bilayer of permendur and PZT with simply supported ends for PZT volume fractions and 0.45.
Frequency dependence of the transverse ME voltage coefficient for the bilayer of permendur and PZT fixed at one end and free at the other for and 0.45.
Bending modes in terms of amplitude per unit magnetic field vs for the bilayer of permendur and PZT that is free at both ends, simply supported ends, or fixed one end.
The frequency of bending mode as a function of the length and thickness of the bilayer that is fixed at one end and free to bend at the other end.
Theoretical (line) and measured (circles) frequency dependence of transverse ME voltage coefficients for a permendur-PZT bilayer that is free to bend at both ends and with .
Material parameters (modulus of elasticity , piezomagnetic coupling , piezoelectric coefficient , permeability , and permittivity ) for PZT and permendur used for estimates in Figs. 2–8.
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