# On Efficiency of Two-Degree-of-Freedom Galloping Energy Harvesters with Two Transducers
## 1 Introduction  
The ongoing energy crisis and burgeoning concept of the Internet of Things (IoT) [1] are continually motivating factors for researchers from various scientific fields to develop newer technologies that enable cheaper and more efficient generation of usable energy. Among the most innovative of these technologies are those that allow energy recovery from vibrations induced by flow. A commercial example of this is the Vortex Bladeless power plants [2], whose vibrations are excited by von Karman vortices. According to the manufacturer, the cost of energy production using these turbines is only 70% of the cost associated with traditional wind turbines of comparable size [2]. Moreover, their sleek, bladeless design allows for closer placement than standard turbines, facilitating more efficient use of wind farm space. The discussed advantages of vortex-induced vibration energy harvesters may be partially overshadowed by a significant limitation. Due to their reliance on resonance with the vortex frequency, these devices can generate energy only within a narrow flow speed range. An alternative type of power plant without this limitation is the galloping energy harvester (GEH). Transverse galloping [3] is a phenomenon where vibrations are induced due to the flow separation from a bluff body with an appropriate shape, leading to negative, speed-dependent aerodynamic (hydrodynamic) damping. When the flow speed exceeds a critical value, the negative aerodynamic (hydrodynamic) damping surpasses structural damping, resulting in the overall damping in the system becoming negative. In this situation, the damping will supply energy to the system rather than dissipate it, causing the system to become unstable. The key advantage of using transverse galloping as an excitation mechanism for energy harvesters is that, beyond the critical speed, the amplitude of oscillation increases indefinitely with the flow speed and remains independent of the frequency or the presence of von Karman vortices. Early studies [4] explore its potential for energy harvesting, emphasizing the crucial role of aerodynamic coefficients in its efficiency. Subsequent research [5] delves into analytical, numerical, and experimental analyses of GEHs, indicating the detrimental impact of structural damping on the performance of the device. Due to the critical importance of the aerodynamics of the flowing body, many subsequent works have been devoted to examining the efficiency provided by GEHs of various shapes. Building on this trend, it has been demonstrated, for instance in [6], that rhomboidal shapes exhibit a significant propensity for galloping. The article [7] is dedicated to the study of the properties of a device equipped with a bluff body in the shape of various variants of an isosceles triangle. Furthermore, research [8; 9] shows that adding a stream splitter favors power generation. The studies [10; 11; 12] have also demonstrated the benefits of employing non-typical shapes. According to the reports presented in [13; 14; 15; 16], the efficiency of a GEH can also be increased by giving its surface an appropriate geometric metastructure. Another extensively investigated area in the development of GEHs is the examination of the impact of nonlinear elasticity on its performance. Studies [17; 18] propose a method for analyzing the effect of the nonlinear elasticity coefficient on the characteristics of Hopf bifurcation. The study [19] focuses on improving the energy harvesting performance of galloping systems through the use of magnetic coupling. Conversely, the work [20] presents modeling and experimental investigations of asymmetric distances using magnetic coupling based on a galloping piezoelectric energy harvester, aiming to enhance the stability of the generated power. In the articles [21; 22], it has been demonstrated that incorporating nonlinear stiffness into the system can significantly increase its efficiency.