Abstract
A two-dimensional unsteady potential flow outside an elastic partially cavitating wing is analyzed numerically by using the Birnbaum equation on the hydrofoil chord and the Lagrange–Cauchy integral on the cavity. The angle of attack has a small periodic perturbation, and cavity thickness and length also take perturbations. Wing vibration is considered to be vibration of a variable thickness beam with two clamp bolts near the beam center. A monofrequency flow perturbation induces monofrequency flexural vibration of a noncavitating wing, but the vibration of a cavitating wing has multifrequency. Computation of NACA-16009 hydrofoil vibration was made for various free-stream speeds, module of elasticity, fluid, and wing densities, and as a result, three frequency bands of a vibration increase are determined. The low-frequency band is connected with a cavity volume oscillation. There is a considerable influence of cavity length on vibration. The high-frequency band is connected with elastic resonances of the wing. A solitary resonance was found in the middle band. This resonance has a nonlinear dependence on the loss coefficient and does not have a dependence on cavity dimensions and wing elasticity. This resonance appearance is connected with an interaction of lift and media inertia forces.
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