## 1 Introduction  
The recent increase in mechanical reliability, cost reduction, and possible shape customization of piezoelectric materials has consistently boosted their employment as active components embedded in energy harvester devices. The latter are envisaged to extract electrical energy from countless forms of mechanical one, enacting a deformation of the piezoelectric material which, in turn, induces a charge displacement and, therefore, an electrical field. Devices extracting energy from the environment encompass domains ranging from micro [1; 2; 3; 4; 5] to large scale [6], most of them being motivated by the need to ensure autonomous/off grid operation to users. Automatic mechanical adaptation to changes of the features of the external forcing has also been recently proposed [7]. Since typical applications require harvesting energy as a continuous power flow, most devices (referred to as Vibration Energy Harvesters) induce cyclic deformations: therefore, oscillating media are natural candidates as energy sources [8]. However, energy harvesting from non oscillating media, such as fluid flows featuring either steady or slow varying motion, can still be achieved by means of Flow Energy Harvesters (FEHs) [9], provided either the fluid flow is perturbed [10; 11; 12] or the FEHs are equipped with Vibration Inducers (VIs) [13; 14]. Many FEHs are cast in the form of cantilevers enclosing the active material, whose polarization and orientation is designed to best exploit the attainable deformation of the cantilever [15; 16]. FEH efficiency is strongly dependent on the ability of the VI to maximize amplitude, regularity and frequency of the oscillations. The cantilever-based FEHs are usually placed counter-flow, i.e., the free end is upstream of the fixed one, the former being equipped with a VI. Traditionally, VI are bluff bodies featuring various cross-sections [17], with a vast majority of the available studies focusing on standard (i.e., square, circular, flat) shapes [18; 19; 20; 21; 22] due to the availability of previous fundamental studies [23; 24] concerning the characteristics of flow around them. The oscillations of the VI placed in a steady flow mainly stem from two Fluid-Structure Interaction (FSI) phenomena: (i) the wake oscillation, resulting in the so-called Vortex Induced Vibrations (VIV); (ii) the variation of lift with the Angle of Attack (AoA), which is at the basis of both galloping and fluttering dynamics, the latter prevailing on the former if the higher order vibrational modes of the beam are substantially excited during the oscillations. To generate large oscillating loads on the tip of the beam, VIs generally have a span length much larger than the width of the cantilever, namely \(10/1\)[19; 25], \(5/1\)[22], \(3/1\)[18]. This may pose some limitations to the applicability of the resulting FEH. Moreover, so far, only VIs with regular sections (square, triangle, circle) have been envisaged [20]. A new class of VI, shaped as a semitubular cylinder, has been recently proposed [26; 27; 28] and analysed [29; 30; 31]. The concave part of the VI faces upstream in the form of a counterflow C-shape. Such shape has been demonstrated [30] to be able to induce larger amplitude oscillations and therefore an improved harvesting performance compared to the square shape. In this work, we present the modelling of a new version of the above mentioned VI shape, whose span is comparable to the width of the cantilever. The VI extends only laterally with respect to the beam, in the form of two lateral winglets. The rationale behind the design of these two peculiar features is twofold: (i) the C-shape allows for a consistent force to be applied on the tip along the direction of the unperturbed flow, promoting beam inflection especially around the resting position (small AoA) and resulting in an early (i.e., at low flow velocities) onset of the swaying motion; when the AoA increases, the aforementioned destabilizing force gives way to a lift force pointing towards the resting position.