## 1 Introduction  
Interactional effects between the main rotor and the fuselage are commonplace in rotorcraft. In particular, at low advance ratios of the main rotor, its wake can interact with the main fuselage and the empennage. The higher the helicopter weight, the stronger the rotor wake, and therefore interactional aerodynamics can be significant. [PERSON] [1, 2] carried out experiments on the topic and there are several numerical studies too. Nevertheless, amongst the current research reports there is little information on the effect of these aerodynamic interactions on the vibration and deformation of the tail-boom structure. This interaction is expected to be significant if a long tail-boom is used or if the employed structure is light with substantial weight added at the end of the boom due to the presence of the tail rotor, its rotor-head, the intermediate gear-box, fin and horizontal stabilizer. One can expect that the tail boom loads are not high, but estimating the vibration level is important for design and fatigue analysis of the boom. Therefore, this work aims to investigate the effect of unsteady aerodynamics on the vibration and deformation of a helicopter tail-boom. In contrast to earlier works [3] where the rotor aerodynamics is represented by blade-element methods, Computational Fluid Dynamics (CFD) is used here to compute the unsteady flow, and then the aerodynamic loads are used in conjunction with a simple structural model. The use of CFD allows for the details of the unsteady flow spectrum to be captured and preserved in the flow around the tail-boom.  
In terms of modeling the structure of the tail-boom, it was decided here to keep the model simple, based on the Euler-Bernoulli equation for coupling with CFD via embedding the model in the framework of a CFD solver. The Euler-Bernoulli equation for various end conditions allows for analytical or approximate solution of the natural and forced vibrations of uniform and non-uniform beams [4, 5, 6, 7, 8, 9].  
Detailed empennage models with structural optimization were considered in [10], where complete Finite Element Method (FEM) models are demonstrated for computing the natural mode shapes and frequencies of the structure. In [11], maintaining the non-dimensional amplitude of the forces against several lifting conditions were analyzed with the FEM approach. Nevertheless, these works did not proceed to compute the effects of wake aerodynamics on the tail boom.  
To determine the transverse vibrations of an Euler-Bernoulli uniform beam in the present study, an approximate analytical approach is used, based on the approach of [12]. According to [12], a solution of the Euler-Bernoulli can be presented as a series of spatial and time coordinates. The forced vibrations are computed using an approximation of the tail boom load obtained from CFD calculation of rotor-fuselage configuration.  
The selected test case is motivated by the Ansat light helicopter (Kazan Helicopters Public Stock Company, Kazan, Russia), although the results obtained serve to demonstrate the employed method and correspond to a generic interaction case. The aerodynamic predictions of the helicopter fuselage aerodynamics are validated against wind tunnel tests.