## 1 Introduction
These elements are well-suited for MEMS-scale objects (Micro-Electro-Mechanical Systems), such as powering Internet of Things (IoT) sensors. Piezoelectric generators sometimes have a more complex structure. A novel generator design consisting of a composite piezoelectric transducer placed inside a cylindrical shell is presented in [14]. This transducer utilizes two pre-bent piezoelectric beams and an additional cantilevered mass. The use of a pre-bent piezoelectric vibrator subjected only to unidirectional compressive stress aims to increase transducer reliability by avoiding tensile stresses, which are more detrimental to piezoelectric materials. The most commonly used piezoelectric material is lead zirconate titanate (PZT). Other materials include zinc oxide (ZnO), polyvinylidene fluoride (PVDF), and lead magnesium niobate-lead titanate (PMN-PT). In modern flexible wearable systems, bio-harvesting, and high-amplitude VIV harvesters, piezoelectric composites are also employed. The research presented in this paper utilized Macro Fiber Composite (MFC). This is a type of thin-film piezoactuator developed by NASA (National Aeronautics and Space Administration), where piezoelectric fibers (typically PZT) are embedded in a flexible polymer matrix and connected via interdigitated electrodes (IDT) on the surface. These electrodes are shaped as narrow, elongated strips that alternately pass one another. Such a structure provides a larger energy-receiving surface than standard electrodes, thereby increasing system efficiency. The authors of [15] investigated a device combining two electromechanical transduction mechanisms. Piezoelectric ceramic sheets (PZT) directly convert beam vibrations into electricity. A vibro-impact dielectric elastomer generator converts the energy of impacts from an internal ball striking elastomer membranes into electrical energy. These impacts are induced by the oscillations of the bluff body. A novel, fully polymer-based piezo-ion-electronic device utilizing a sandwich-structured PVDF/Nafion/PVDF (PNP) configuration was investigated by [PERSON] et al. [16]. Owing to the mutual coupling of piezoelectric and piezoionic effects at well-defined ion-electron interfaces, this structure achieves a significant enhancement in force-to-electricity conversion efficiency, representing a promising step forward in the development of piezoelectric generator technologies. An energy harvester system aims to achieve frequency synchronization (lock-in) with the frequency of aerodynamic vortices. This ensures the largest vibration amplitudes and, consequently, maximum energy recovery. The highest energy-harvesting efficiency occurs when the vortex shedding frequency \(f_{v}\) synchronizes with the system's natural frequency \(f_{v}\):  
\[f_{v}=f_{n} \tag{1}\]  
This phenomenon occurs for a reduced velocity \(U^{*}\):  
\[U^{*}=\frac{U}{f_{n}\cdot d} \tag{2}\]  
where  
\(U\)--flow velocity (m/s),  
\(f_{n}\)--natural frequency of the system vibrations (Hz),  
\(d\)--characteristic dimension of the bluff body, usually the diameter (m). VIV reaches maximum oscillation amplitudes when the vortex shedding frequency (Strouhal frequency) synchronizes with the natural frequency of the system within a specific range of \(U^{*}\) (typically 4-8 for a cylinder). The key parameter for determining the amplitude and efficiency of the harvester is the mass-damping parameter \(\zeta\):  
\[\zeta=\frac{c}{2\sqrt{km}} \tag{3}\]  
where  
\(\zeta\)--damping ratio (e.g., 0.01),  
\(c\)--damping coefficient (related to the interaction of the object with the fluid),  
\(k\)--stiffness of the system (usually related to material properties),  
\(m\)--mass of the vibrating system (kg). For a bluff body with a circular cross-section, the formula takes the following form:  
\[\zeta=\frac{c}{d\sqrt{k\cdot\rho\cdot\pi\cdot L}} \tag{4}\]  
where  
\(\rho\)--density of the body (kg/m\({}^{3}\)),  
\(d\)--diameter of the body (m),\(L\)--length of the body (m). A low \(\zeta\) indicates larger amplitudes but also a higher risk of structural overloads.