Some similarity relationships for towing tank models used in combined ship structural and hydrodynamic experiments 1

Abstract

Hull bending stresses are related to hydrodynamic loads essentially by the rules of statics in the case of a ship heaving and pitching at the frequency of wave encounter. Vibratory bending stresses resulting from a slamming impact, however, depend on the elastic characteristics of the ship, and in particular depend on the ratio of the impact duration to the natural period of ship vibration. In order to maintain this ratio invariant in towing tank tests the flexural rigidity EI of the model must be scaled as the fifth power of the length. The attainment of a complete similarity in model and ship behavior in slam-caused vibration appears to be impossible, however, because of the difficulty in securing similarity in shear rigidity, and the dependence of structural damping on the vibration frequency. Interpretation of the vibratory response in model tests depends, therefore, on the application of transient vibration theory. Currently insufficient development of this theory necessitates recourse to digital-numerical or electronic-analog procedures in parallel application to the ship and its model with appropriate values of shear rigidity and damping in each case.