## 1 Introduction  
Because of the continuing improvements with respect to the power consumption of electronic integrated circuits, harvesting of the ambient energy is gaining importance for electronic devices such as wireless sensor networks [1]. Ambient mechanical vibrations represent promising sources of energy. In the majority of the practical cases, the energy from mechanical vibrations in the environment is distributed over a wide spectrum. Most of the previous works use resonant circuits, where the maximum performance can be achieved when the external frequency is close to the resonant frequency of the circuit. A piezoelectric (PE) cantilever beam is an example of such a circuit, where the piezoelectric effect is utilized for converting mechanical energy into electric energy. Operation close to the mechanical resonance is required in order to achieve large amplitudes of mechanical deformation. The favorability of the PE transduction mechanism in applications can be explained by the larger energy density in comparison to other available effects [2; 3; 4]. To be electromechanically effective, the PE resonant circuit must possess a high quality factor \(Q\), because the oscillation amplitude at resonance grows with the increasing parameter \(Q\). Unfortunately, this entails a narrow-band frequency behavior of a single circuit. [PERSON] et al. [5] and [PERSON] et al. [6] published comprehensive reviews on the available technologies and recent advances in broadband vibration-based energy harvesting. An obvious solution for increasing the bandwidth is to employ several piezoelectric cantilevers (PECs), whose mechanical resonance frequencies are distributed over the desired band in such a way that at any particular frequency at least one circuit operates close to its resonance frequency. The most general approach for designing an optimized mechanical band-pass filter has been provided by [PERSON] [7; 8], who developed a mathematical model where the eigenfrequency of a single beam is adjusted both by the proof mass and the beam stiffness, leading to the required dimensions of the beam. [PERSON] et al. [9] included the PE properties of the beam elements and the electrical circuitry into the calculations. It was shown that the frequency behavior of the entire system can be influenced by connecting the PE bimorphs either in series or parallel. [PERSON] et al. combined three commercially available PE bimorphs cantilevers into a single array, improving the effectiveness of the overall energy conversion across a wideband frequency spectrum over the case of a single converter [10]. The tuning of resonant frequency was achieved by varying the tip mass. A broadband PE energy harvester for low-frequency (\(\approx\)30-47 Hz) vibrations was developed by [PERSON] et al. [11] for micro-electro-mechanical system (MEMS) applications. Their device consisted of several beams with different stiffness and the same tip mass. In the following we refer to the mechanical vibrations as low-frequency oscillations if their frequency is below 60 Hz. [PERSON] et al. proposed to detune the eigenfrequency of individual standard PE bimorphs by means of magnetic force acting on the small magnet positioned at the beam tips [12]. By changing the magnetic force, the effective stiffness of the beam can be controlled. [PERSON] et al. [13] investigated an arrays of identical MEMS-based lead zirconate titanate (PZT) PEC beams and showed that the series connection of PECs allowed for an improvement of the power output because the small (below 1 V) voltages of individual PECs were added together and the losses in a rectifier circuit could be significantly reduced. This finding has been confirmed by [PERSON] et al. [14] with an array of MEMS-based aluminum nitride (AlN) PECs. Very recently, [PERSON] et al.