## Materials and Methods
Figure 1: The lumped parameter model of a single piezoelectric cantilever (PEC) drawn in LTspice. Figure 2: Simulation (sim) of the conventional (con) and adjusted (adj) lumped element model compared to the measurements (meas). The corresponding adjusted \(f_{0}\)' is equal to 40.39 Hz for the PEC used. The \"adj sim\"-curve corresponds to the parameters of the circuit shown in Figure 1.  
Table 1 summarizes the parameters of the effective circuit model, tuned to the resonance frequency of 40 Hz. These parameters are the basis for the simulation of the entire PEC array. The notation corresponds to that shown in Figure 1.  
For mass tuning, the stiffness of the cantilever beam remains the same and only the effective mass must be changed. Therefore, the inductance on the primary side of the transformer (or, equivalently, the effective mass) must be adjusted in the equivalent circuit. If the new resonance frequency \(f_{0}\)' is determined from Equation (1), the corrected inductance can be easily calculated with the following formula: m1\({}^{\prime}\) = m1 \(\times\) (\(f_{0}/f_{0}\))\({}^{2}\). For example, the adjusted effective mass in Figure 1 is related to the nominal effective mass of Table 1 as (40/40.39)\({}^{2}\). As explained by the authors of [24; 25; 26], the common equivalent circuit model, consisting of an RLC circuit, can be constructed by the simplification of the cantilever beam to the mass-spring-damper system. An RLC circuit denotes an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C) (see Figure 1). The details can be found elsewhere in [20; 21; 24; 25; 26]. In the following we briefly outline the procedure of determining the effective parameters of the equivalent circuit. The parallel capacitance was measured directly using the RCL meter Hioki IM3533-01 (Hioki E.E. Corporation, Nagano, Japan). The effective mass was determined by the precision scales (Kern PCB350, Kern & Sohn GmbH, Balingen, Germany). In Table 1 the numerical value of inductance in H corresponds to the numerical value in kg. The spring constant (stiffness) was calculated from the resonance frequency. The damping resistance was derived from the decay constant of the impulse response of the output voltage. The electromechanical coupling coefficient was determined from the series and parallel resonance frequencies of the PEC electrical impedance [2] measured with an impedance spectroscope (HF2 IS, Zurich Instruments, Zurich, Switzerland). In the following theoretical considerations, it is assumed that all parameters of the equivalent circuit remain constant, except for the effective mass and the amplitude of the excitation voltage (excitation force), which is proportional to the effective mass. It will be seen below that such an approximation is reasonable in the present case. The experiments were performed using the laboratory setup shown in Figure 3. The mechanical set up is mounted onto an electrodynamic shaker (Bruel & Kjaer Type 4826, Bruel & Kjaer Sound & Vibration, Narum, Denmark), driven by a power amplifier (Bruel & Kjaer 2721). The signal for exciting the shaker is supplied by a waveform generator (Rigol DG4062, Rigol Technologies EU GmbH, Puchheim, Germany). The PEC array is mounted with the rigid metal frame onto the shaker (base plate); the clamping of the PECs (mechanical fixation) is done according to the specifications of the manufacturer. The tuning is achieved by weights fixed on the tips of the PECs. For a rough adjustment of a tip mass, the metal screw was employed while a modeling clay material was used for the fine tuning of the tip mass. The acceleration sensor serves to control the given value of acceleration amplitude.