An Underwater Explosion-Induced Ship Whipping Analysis Method for use in Early-Stage Ship Design
Brainard V, Benjamin Chase
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This thesis presents an analysis method for determining the whipping response of a hull girder to underwater explosion (UNDEX) bubble pulse loading. A potential flow-based UNDEX bubble model capable of calculating the behavior of a migrating bubble for up to three pulses is developed. An approximate vertical plane ship vibration model is derived using fundamental beam theory by representing the ship as a free-free beam with varying cross-sectional properties along its length. The fluid-structure interaction is approximated using strip theory and the distant flow assumption. The most severe predicted whipping load conditions are applied to a MAESTRO finite element model of the ship as a quasi-static load case to determine the response of the structure to the whipping loads. The calculated hull girder bending moments are compared to the ultimate bending strength of the hull girder to determine if the girder will collapse. The analysis method is found to be a useful method for determining preliminary UNDEX-induced whipping design load cases for early-stage ship design. However, more detailed and accurate data is needed to validate and verify the predicted whipping responses. It is found that the most severe whipping loads occur as the result of an UNDEX event that occurs under the keel near midship and produces a bubble with a pulsation frequency similar to the natural vibration frequency of the ship in its third mode. Significant damage to the ship structure and hull girder collapse is possible as a result of these loads.
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