A theoretical analysis of wake-induced forced vibration of a trapezoidal, 2-way tapered, hollow marine spade rudder, is presented. The rudder acts in the turbulent propeller slipstream; which causes time-dependent harmonic hydrodynamic load on the pivoted rudder. The excitation frequency of propeller-induced vibration (PIV) equals the propeller blade passing frequency. The rudder operates behind the ship, at a Reynolds's number of the order of 10~8. The rudder has a span of 10 m, root chord of 6 m, and tip chord of 5 m. It is considered as a hollow Kirchhoff's plate, with the chord section as a NACA0018 profile. The four edges are completely free. The dry plate vibration is analyzed by the energy-based Galerkin's method. 3D panel method is used to generate the modal added masses, and hence the wet natural frequencies. The drag and the lift coefficient of the rudder, at various angles of attack, are estimated to find the spatial distribution of the total PIV-causing normal force. The mean flow velocity about the rudder is the velocity of advance behind the propeller. The fluid velocity past the aerofoil section depends on the profile thickness and the angle of attack, thereby influencing the local lift. The hydrodynamic pressure varies parabolically along the span. The effect of the wake developed by the propeller, the stern shape, and the rudder angle on the hydrodynamic loading on rudder, are included to express the transverse time-varying loading. The wet, forced vibration of the Kirchhoff's plate is analyzed. The maximum bending stress and twisting sheer at the rudder stock is calculated for various rudder angles.
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