# Snap-Through Buckling Mechanism for Frequency-up Conversion in Piezoelectric Energy Harvesting
## 1 Introduction  
In recent years, energy harvesting (EH) has been the object of intensive investigations due to the ubiquity of natural unlimited energy sources which can be exploited, in particular the kinetic energy from ambient vibrations [1; 2; 3; 4; 5; 6; 7; 8; 9]. This and the recent progresses in the microelectronics and MEMS (Micro Electro-Mechanical System) field have made battery-less small electronic devices possible. As a matter of fact, the mechanical energy, by means of energy harvesters using different transduction mechanisms, can be scavenged and converted into electrical energy, which can be used to power electronic devices. One of the most common transduction mechanisms used in EH is based on the piezoelectric effect, due to higher energy density compared to electrostatic and electromagnetic conversion principles. Piezoelectric linear energy harvesters are generally manufactured as cantilever beams due to their high compliance and placed on a vibrating structure [10; 11; 12; 13; 14; 15]. The mechanical energy from ambient vibrations is generally distributed over a broad frequency spectrum in which frequency components lower than few hundreds of hertz are typically dominant. However, linear harvesters have the maximum effectiveness when they are excited close to their resonant frequencies, which are generally higher than the frequency of ambient vibrations. As aconsequence, this demands for bandwidth broadening, frequency translation, FuC, and non-resonant operation under non-sinusoidal or random excitation. Different solutions have been proposed to make piezoelectric harvesters more effective, for instance exploiting nonlinear phenomena. Geometrical nonlinearities or interactions with external objects, for instance magnets, are exploited as passive tuning method to modify the dynamic behavior of the linear harvester. In [16, 17], external magnets are employed to modify the stiffness and thus the resonant frequency of the piezoelectric cantilever beam. In [18], two magnets, placed close to the free end of a piezoelectric cantilever beam, are used to apply a force pulse on it and attain the FuC. Other harvesters exploit nonlinearities and can be modeled as Duffing oscillators [19, 20, 21]. In addition, strategies based on impact can be adopted [22, 23]. Moreover, to increase the collected power, arrays of converters can be considered [24]; this approach demands for suitable management circuits to combine the outputs of the converters [25, 26, 27]. A phenomenon generally used to attain FuC is STB: bistable mechanical structures can be employed for the converter itself or for the host structure. In the first case, a piezoelectric pre-buckled bistable beam can be used instead of a cantilever beam, as suggested in [28, 29, 30]: when the magnitude of the mechanical excitation exceeds a certain threshold, which depends on the geometrical and mechanical characteristics of the pre-buckled structure, the beam switches between its two stable states allowing the widening of the operational frequency spectrum of the device. Conversely, a harvester belonging to the second category has been proposed in [31], where the concept was to exploit a beam axially loaded and buckled into a stable configuration, a proof mass, and an array of piezoelectric cantilever beams. Because of the occurrence of FuC, a maximum power of \(41.7\,\mathrm{\SIUnitSymbolMicro W}\) was obtained for each cantilever beam having a resonant frequency of about \(230\,\mathrm{Hz}\) and with dimensions \(15\,\mathrm{mm}\times 4\,\mathrm{mm}\times 0.2\,\mathrm{mm}\), under a harmonic acceleration at a frequency of \(15\,\mathrm{Hz}\) (see [31] for additional details). The device presented in this paper belongs to the latter category: in detail, one piezolaminated cantilever beam is connected to a nonlinear bistable structure, which allows the triggering of FuC. Different from previous research, the bistable device does not rely on the presence of an axial force that could be difficult to achieve and mantain, especially for small-scale devices.