# Snap-Through Buckling Mechanism for Frequency-up Conversion in Piezoelectric Energy Harvesting
## 3 Design of the STB-EH Device  
The proposed device consists of two components: a double-beam bistable structure, switching between the initial stable configuration and the reversed one, and vice versa, and a commercial bimorph piezoelectric cantilever beam, in the following simply referred to as _bimorph beam_, connected to the mechanism at the mid-span. In order to reduce the resonant frequency of the piezoelectric cantilever beam and increase the overall mass, a tip mass is placed at its free end. The bimorph beam used as energy harvester works predominantly in [3-1] mode: bending oscillations of the beam induce axial strains, in both the piezoelectric layers and of opposite sign in each of them, in the direction of the longitudinal axis and generate an electric voltage output across the electrodes, whose sign depends on the direction of polarization of the two piezoelectric  
Figure 1: Snap-through buckling (STB) of a double-curved-beam bistable mechanism (**a**), definition of geometrical parameters (**b**), simplified force–displacement curve for a bistable mechanism for \(Q>6\)[34] (**c**). layers. As the bistable mechanism snaps between its two stable states, the attached bimorph beam undergoes an acceleration which lets it oscillate in the free vibration regime characterized by a broad frequency spectrum, regardless of the excitation frequency, increasing the beam oscillations and thus the electrical output. The bistable mechanism is manufactured using an FR4 (flame retardant) substrate with thickness \(1.6\,\mathrm{mm}\) by means of a milling cutter (LPKF ProtoMat C30). The FR4 substrate is a glass-reinforced epoxy laminated material generally used as an electric insulator. A preliminary experimental assessment of the mechanical properties of the adopted FR4 substrate was carried out by means of three-point-bending tests, obtaining values of the Young's modulus of FR4 ranging between 10 GPa and 22 GPa, depending on the orientation of the fibers. The design follows the analytical expressions reported in the previous section and is refined by a series of numerical simulations. The simulations have been supported by preliminary experimental tests using different prototypes aimed to explore the influence of the thickness \(t\) and initial rise \(h\) of the curved beams. The final design is a trade-off between the structural robustness of the device and the achievable elastic flexural stiffness and hence elastic energy to avoid the failure of the clamped bimorph beam during the snap. Figure 2 shows a schematic representation of the designed prototype. The bimorph piezoelectric beam is glued and clamped to the central block of the bistable mechanism, which is is manufactured with a hole in the central block with the same dimensions of the cross-section of the bimorph beam. Two different layouts are considered. Model A is composed of the bistable mechanism and the piezoelectric beam, without the tip mass. This setup is then slightly modified and model B is obtained, by placing a lead spherical mass (having radius \(2.5\,\mathrm{mm}\) and hence mass approximately equal to \(740\,\mathrm{mg}\)) on the free end of the bimorph beam in order to lower its resonant frequency and increase its bending oscillations. The spherical tip mass is visible in Figure 2, with a dashed boundary. The bimorph beam, schematically shown in Figure 2(a), has dimensions \(L=$15\,\mathrm{mm}$\times w$=$1.5\,\mathrm{mm}$\times t$=$0.62\,\mathrm{mm}$\) and consists of three main layers: a titanium shim of thickness \(t_{\mathrm{s}}\) sandwiched between two piezoelectric layers of thickness \(t_{\mathrm{P}}\), which are oppositely poled. Each piezoelectric layer is represented in Figure 2(b), which shows the equivalent electric circuit of the series connection of the piezoelectric layers, by a current source \(t_{\mathrm{p}}\) and a parallel-connected capacitor \(C_{\mathrm{p}}\). The electrical capacitance \(C_{\mathrm{p}}\) and the electromechanical coupling factor are equal to \(1.5\,\mathrm{nF}\) and \(60\), respectively.