i) Reduce exciting force amplitude, F. In propeller-induced ship vibration, the excitation may be reduced by changing the propeller unsteady hydrodynamics. This may involve lines or clearance changes to reduce the non-uniformity of the wake inflow or may involve geometric changes to the propeller itself. Specifics in this regard are addressed in Section 3.
ii) Increase stiffness, K. Stiffness is defined as spring force per unit deflection. In general, stiffness is to be increased rather than decreased when variations in natural frequency are to be accomplished by variations in stiffness. It is not a recommended practice to reduce system stiffness in attempts to reduce vibration.
iii) Avoid values of frequency ratio near unity; ω/ωn = 1 is the resonant condition. At resonance, the excitation is opposed only by damping. Note that ω/ωn can be varied by varying either excitation frequency ω or natural frequency ωn. The spectrum of ω can be changed by changing the RPM of a relevant rotating machinery source, or, in the case of propeller-induced vibration, by changing the propeller RPM or its number of blades. ωn is changed by changes in system mass and/or stiffness; increasing stiffness is the usual and preferred approach. Specific measures for resonance avoidance in ships are addressed in Section 4.
iv) Increase damping, ζ. Damping of structural systems in general, and of ships in particular, is small; ζ