## 1 Introduction  
In recent years there has been a great development of energy harvesting techniques based on piezoelectric devices. Piezoelectric cantilever harvesters have been successfully used for transforming ambient vibration energy into electrical energy for feeding sensors, biomedical equipment, and small electronic devices [1; 2; 3]. The trimming of the harvester to the vibration source is essential to improve the vibration-to-electric energy conversion. In the presence of harmonic vibrations, optimum trimming is achieved when the natural frequency of the harvester is set equal to the vibration frequency [4; 5]. When the difference between the frequency of ambient vibrations and the resonance frequency of the harvester is not very large (some tens of Hz) the problem of trimming is solved by adding a tip mass [5; 6; 7], which increases the excitation of the harvester because the inertia force due to the lumped mass adds to the inertia forces due to the distributed harvester mass. This phenomenon has a beneficial effect on the generated voltage, but it increases the stress inside the harvester, which may be damaged. When the frequency of ambient vibrations is very low (e.g., in energy harvesting from human motion) the tip mass able to trim the harvester would be impractically large. Therefore, several frequency-up strategies have been proposed: they are based on specific devices like a flexible stopper [8], a non-linear spectrum [9], or a pendulum magnetically coupled with the harvester [10]. The problem of harvester trimming is complex when ambient vibrations are characterized by variable frequency, by multiple harmonic components, and by the broadband spectrum as well. Several technical solutions have been developed to cope with these working conditions. Some researchers have proposed dynamically tunable harvesters, in which tuning can be achieved both by means of the interface circuit [11; 12] and by mini-actuators that modify the mechanical system [13]. Other researchers have developed wideband harvesters. One approach consists in exploiting several modes of vibration of the cantilever harvester (making use of segmented electrodes) [14] or of more complex structures, like L-shaped harvesters [15]. Another approach consists in making use of non-linear components like bi-stable cantilevers or ropes [16; 17; 18]. The possibility of widening the band of the cantilever harvester by increasing the number of degrees of freedom (DOFs) has been analyzed in some research. In particular, in [19; 20] two DOFs harvesters have been developed connecting cantilever harvesters with tip masses and the use of arrays of cantilever harvesters is reported in [5; 21; 22]. The problems of trimming and increasing the bandwidth of a piezoelectric harvester by increasing the number of DOFs can be analyzed with the theory of the Dynamic Vibration Absorber (DVA) [23]. Since the beginning of 20 th century, DVAs have been successfully used for controlling vibrations of many mechanical systems including crankshafts, ships, engines, and machine tools [24]. In the field of acoustics, the DVA is named the Helmholtz resonator [25] and it has been used in mufflers [26] and cavities [27]. Some studies dealing with the application of DVAs in the field of energy harvesting have been already carried out. For example [28] proposed to attach lead zirconate/lead titanate (PZT) patches (which harvest energy from vibrations) to an auxiliary structure that acts as a DVA for the main vibrating structure. Several researchers have studied dynamic magnifiers, which are spring-mass systems placed between the harvester and the moving base [29]. In [30] the dynamic magnifier was added to a piezoelectric stack harvester and the natural frequency of the dynamic magnifier was set equal to the one of the harvester. Numerical results showed the appearance of two resonance peaks, a large increment in the generated power and a significant widening of the bandwidth of the harvester. In [31] the concept of the dynamic magnifier was applied to cantilever harvesters.