A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT

The classical Theodorsen equation for the motions of two-degree-of-freedom foils is modified with associated mass parameter ε and circulation parameter δ by considering the 3D effect of low aspect ratios, and the comparison between the calculation and classical experimental values demonstrates the modified equation is effective. According to the shape of V-g curve which varies with the mass ratio μ, two types (Type Ⅰ and Type Ⅱ) of flutter are defined. The influences of the bracing stiffness k_h, the torsional stiffness k_α, the locations of the center of gravity x_α and the angle of attack AOA on the characteristics of the flutter of a hydrofoil-rod system have been analyzed, and the comparison with experimental values shows that the numerical results are reasonable. The calculation shows the significant impacts of k_h, k_α, x_α and AOA on the flutter speed V_F. When the values of the parameters are in certain ranges respectively, flutter Type Ⅱ may occur. Specifically, a larger kh or a smaller AOA leads into a larger V_F. While, V_F first increases and then decreases with the increase of k α or x_α. Moreover, V_F only exists in a relatively narrow range of x_α, which reflects that the vibration pattern of the hydrofoil-rod system is high sensitive to x_α. Therefore, the probability of the occurrence of flutter can be reduced by avoiding the narrow range of x_α during design phase. On the other hand, according to the slow reaction of V_F to k_h and k_α, once flutter occurs, flutter can be eliminated by locking the rigid shaft with hydraulic devices.