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There is increasing interest in the use of lighter and more flexible hydrodynamic lifting bodies, and the use of active and passive smart structures to simultaneously increase efficiency and maneuverability or to harvest flow kinetic energy. Hydrodynamic lifting bodies can behave very differently compared to aerodynamic lifting bodies because of the much higher fluid density. To focus on the physics, we will use a cantilevered rectangular hydrofoil as a canonical proxy to more complex lift generating devices such as propellers, turbines, wings, and control surfaces, etc. Specifically, we will investigate the maximum deformation and stability limit for hydrofoils made of different materials to quantify the feasible operation space. To efficiently explore the large parametric space, inviscid analytical equations are used to determine the governing non-dimensional material, geometric, and flow parameters, which are systematically varied to examine the passive hydroelastic responses and stability boundaries of canonical hydrofoils with spanwise flexibility. The results demonstrate the influence of the relative magnitude between the solid and fluid inertial, damping, and stiffness terms, and resulting impact on the hydroelastic response, governing instability mechanism, and instability boundaries. The results also demonstrate that lifting bodies in water have much lower natural frequencies and higher damping coefficients than in air because of higher fluid inertial and damping forces, both of which are proportional to the fluid density. While all components of the fluid forces are proportional to the fluid density, the fluid damping forces grow with the velocity, while the fluid disturbing forces grow with velocity square. Therefore, the static divergence tends to be the governing instability mode for lifting bodies in water, while the flutter is typically the governing instability mode for lifting bodies in air. The results indicate that the maximum tip deformations in water are limited to approximately the chord length for bending and less than two degrees for twisting to avoid the material or static divergence failure.
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