Direct magnetoelectric effect in two-layer composite structures Tb$_{0.12}$Dy$_{0.2}$Fe$_{0.68}$–PbZr$_{0.53}$Ti$_{0.47}$O$_3$ at bending and longitudinal vibrations

The direct magnetoelectric effect has been studied in samples of two-layer composites containing 8 $\times$ 6 $\times$ 0.3-mm layers of the piezoelectric material PbZr$_{0.53}$Ti$_{0.47}$O$_3$ and 6 $\times$ 6 $\times$ A-mm layers (A = 0.3, 0.6, 0.9, 1.2, and 1.5) of the ferromagnet Tb$_{0.12}$Dy$_{0.2}$Fe$_{0.68}$ and epoxy adhesive in the frequency range of 10–253 kHz at room temperature. It has been found that the magnetoelectric effect significantly increases at resonance frequencies (13.2–61.1 kHz) of the first harmonic of bending vibrations along the sample length, at resonance frequencies (39.5–90.7 kHz) of the first harmonic of bending vibrations along the sample width, and at resonance frequencies (123.3–141.0 kHz) of the first harmonic of longitudinal vibrations along the sample length. The magnetoelectric effect magnitudes at the resonance frequencies of the bending vibrations is found to be greater than that at the resonance frequencies of the longitudinal vibrations of the sample.