Added mass of whipping modes for ships at high Froude number by a free surface boundary element method coupled with strip theory

Abstract

Accurate prediction of the whipping response of a ship's structure following a wave impact is fundamental to both the prediction of instantaneous local stresses and global fatigue life assessment. In particular the added mass effect of the surrounding water has a profound effect on the modal frequencies. ``Strip theory'', routinely used for analysis of rigid body motions of ships in waves, is extended in this paper to include ship flexure. Moreover, the theoretical foundation of the method is discussed and it is shown that, although the theory becomes invalid for rigid body motions of high-speed vessels, the ship flexure problem is an ideal application of the theory. The associated two-dimensional free surface gravity wave problem is solved using a boundary element method based on wave functions given by Wehausen and Laitone (1960), which is also described. Results are validated against a fully three-dimensional solution, and incorporation of the added mass into a finite element model is shown to give excellent agreement with full scale measurements.