Camber and ap e ects in the dynamic aeroelastic analysis of the typical aerofoil section

In classical aeroelasticity, the typical at plate section consists of two degrees of freedom, namely pitch and plunge. Current resources o er the capability of enhancing the response of the typical aerofoil by making it adaptive. This project investigates the dynamic aeroelastic e ects of two of these options: trailing edge aps and chordwise (camber) deformations. The structural model is assumed to be linear and damping is neglected. For the aerodynamic loads linear unsteady theory has been used, implementing Theodorsen's theory and Wagner's indicial response method. From the resulting equations of motion, utter speed has been computed by several procedures, both in the frequency domain (V-g method and stability of linear state-space systems) and time domain. In the case of the trailing edge ap, it has been proved that some results provided by Theodorsen [1] and Theodorsen and Garrick [2] were in error, as it had been previously reported by Zeiler [3]. In addition, a parametric study has been carried out in order to study the in uence of the parameters of the at plate on the utter speed. The stability boundary presents an important dip in the neighbourhood of ωβ ωα = 1 and most of the characteristic parameters only translate or scale this boundary. However, the natural frequency ratio ωh ωα plays a very important role and it can change the shape of the curve completely. The mass ratio κ is also critical, since the characteristic dip can be softened to a extent where the minimum utter velocity is nearly the same as the average value along the whole span of ωβ ωα . The inclusion of the camber degree of freedom in utter analysis represents a novelty. Although di erent models for chordwise deformation had been proposed [4], [5], [6] and [7], stability analysis has never been undertaken before. The model for camber is taken from Palacios and Cesnik [7] and aided by V-g plots and eigenvector analysis, mechanisms driving utter have been explained for one, two and three degrees-of-freedom systems that include camber. Unlike classical degrees of freedom pitch and plunge, camber mode alone can lead to utter. Critical velocity always happens at the same reduced frequency k, being the camber-wake interaction responsible for instability. This is contrary to pitch and plunge modes, where only interaction of both modes can cause utter. Pitch-camber and plunge-camber systems exhibit regions where camber-wake interaction governs utter, apart from where mode interaction prevails. In the case of three degrees of freedom, it has been found that the triple interaction among modes is crucial, as it dominates over a broad range of natural frequency ratios. Static divergence is also very important, since there are regions where it occurs before utter speed is reached.