## 1 Introduction
Conversely, larger \(\zeta\) values suggest dampened vibrations and suppression of energy flow from the vortices to the structure. The concept of self-tuning the natural frequency of the system by employing a freely sliding bluff body on a flexible cantilever beam with an attached piezoelectric layer was presented in [17]. Original methods for investigating vortex-induced vibrations (VIV) in the form of a Virtual Physical System (VPS) and a Virtual Physical Framework (VPF) were introduced by [PERSON] et al. [18; 19]. These approaches are based on the integration of numerical simulations with real physical systems and involve the digitalization of the system's physical parameters, such as mass, damping, and stiffness. Other parameters for assessing vortex structure formation around a bluff body include the Strouhal number (\(St\)), which considers vortex shedding frequencies, object dimension, and flow velocity, and the Reynolds number (\(Re\)), which defines the flow characteristics (laminar or turbulent). The Reynolds number significantly impacts the efficiency of piezoelectric energy harvesting from circular cylinder VIV, affecting the generated power level, the flow velocity range where lock-in occurs, and the system's global response characteristics [20]. The bluff body in VIV can take various shapes. The most common form is the circular cylinder, which provides stable vortex shedding. Other shapes include elongated bodies with square or prismatic cross-sections. Further variations include elastic bluff bodies in the form of plates or membranes, which can lead to flutter. The lateral surface of the body may be perforated to alter the conditions of boundary layer formation. The ability to harvest energy from vortex-induced vibrations using bluff bodies etched with different metasurface patterns was investigated in [21]. A concave hourglass amplified the VIV effect, while a concave circle, prism, and waterdrop suppressed it. Tandem configurations were also considered. The horizontal and vertical spacing between bluff bodies in such arrangements had a critical impact on the efficiency of energy harvesting from vortex-induced vibrations [22]. The use of dual fractal blunt bodies placed upstream of the main harvester significantly enhanced wind energy harvesting performance [23]. The length of the cylinder influences the stability of vortex structures along the flow axis. The ends of the object can generate additional turbulent structures, known as \"end plate\" effects. The advantages of these types of objects include their ability to operate at low flow velocities, with no need for external power, as well as modularity and simple construction. However, such systems also have several limitations, including a strong dependence on flow frequency, low efficiency outside the lock-in range, and limited durability under variable dynamic loads. Unusual bluff body shapes are also encountered. Research has explored energy harvesting from vortex-induced vibrations using a bluff body in the form of a cylinder inspired by the Amaryllis flower shape [24]. This study demonstrated a proportional relationship between the amplification of fluid dynamic forces and the shortening of vortex formation length. Other research has tested energy harvesting from vortex-induced vibrations using flexible piezoelectric flags [25]. Introducing a nonlinear L-shaped beam into the design of a flow-induced vibration energy harvester can lead to the utilization of higher vibrational harmonics and a significant increase in power density compared to traditional solutions [26]. A numerical study of VIV response for bluff bodies with different trailing edges revealed significant differences in amplitudes, frequencies, and vortex patterns depending on the geometry of the body's rear section [27]. Additionally, the use of four types of metasurface patterns (convex hemisphere, convex triangular prism, convex cylinder, and convex prism) to modify a standard cylindrical bluff body was investigated [28].