## 2 Materials and Methods  
This work was a continuation of research commenced in [20], where fabrication of multiferroic heterostructures was described in detail. Planar structures were fabricated, where an MAE layer was synthesized on a surface of a commercially available PVDF-based vibration sensor (LDT0-028K, Measurement Specialties, Hampton, VA, USA), and covered by a silicone-based adhesive (Figure 1). A silicone-based adhesive was used because of its chemical compatibility to the MAE layer. It has been demonstrated that the usage of such an adhesive improved the durability of bonding between MAE and a polymeric layer and enhanced the ME response [20]. The vibration sensor is denoted as PEP. PEP was a flexible component comprising a thin (thickness \(t_{\text{PE}}=28\) um) PE PVDF polymer film with screen-printed silver ink electrodes, laminated to a 0.125 mm polyester substrate, and fitted with two crimped contacts. As the PE film was displaced from the mechanical neutral axis, bending created a very high strain within the PVDF layer and high voltages were generated [23]. The drawing of the PEP component, with different views, is given in [23]. The employed MAE had an iron content of 80 wt% (\(\approx\)33 vol%). The shear modulus of the MAE material in the absence of a magnetic field was about 70 kPa. This particular material composition was used because in [20] it resulted in the largest ME response between all tested compositions. Five samples, with different thicknesses, \(t_{\text{MAE}}\), of the MAE layer between \(\approx\)0.85 and \(\approx\)4 mm, were fabricated. The samples were denoted S1-S5. Geometrical parameters of the MAE layer were \(L_{\text{MAE}}\approx 16.2\) mm and \(w\approx 14.2\) mm.  
The schematic diagram of the experimental setup is shown in Figure 2. A fabricated layered composite structure was placed inside the coil, which generated an alternating (AC) magnetic field \(h_{\text{ac}}(t)=h\cos(2\pi ft)\) with an amplitude \(h\) of up to 0.22 kA/m. A composite structure was clamped at a fixed distance of 20 mm (\(L\)) from the structure's edge using a massive holder. The clamping holder was positioned on a special stand in the gap of 55 mm between the poles of an electromagnet that generated a bias (DC) magnetic field \(H\) up to \(H_{\text{max}}=240\) kA/m. When the magnetic field was applied, the structure was deformed as a result of the magnetically induced strain and there was an ME voltage across the electrodes of the deformed PE layer. The electrodes of the PE layer were connected to a preamplifier (SR560, Stanford Research Systems, Sunnyvale, CA, USA) in differential input mode; the preamplifier output was connected to a voltmeter (AKIP-2401) with an input impedance of 1 M\(\Omega\). The preamplifier gain was \(K=1\) and the lower cutoff frequency was \(f_{\text{c}}=1\) Hz. The frequency dependences of the ME voltage amplitude \(u\) were measured at various values of the constant magnetic field \(H\) applied in the plane of the sample, parallel to its longest side. The magnetic field \(H\) was increased first from 1.8 kA/m to 8 kA/m and then, with constant steps of about 8 kA/m, up to 240 kA/m. Upon reaching the maximum constant magnetic field, its value was decreased in the same fashion, thus obtaining a set of frequency characteristics. A frequency sweep was carried out with a step of 0.1 Hz in the low-frequency region (up to 100 Hz) and with a step of 1 Hz in the rest of the frequency range. Single frequency dependence in a given magnetic field was obtained within 10 min. The measured curves were used to plot the field dependences of the ME voltage and the resonance frequency. The dependences of the ME voltage \(u\) on the amplitude of the alternating magnetic field \(h\) were also measured.