Analytical study of the responses of bottom panels to slamming loads

The responses of boat hull bottom panels under slamming loads are studied analytically using a linear elastic Euler–Bernoulli beam as a representation of the cross section of a bottom panel. The slamming pressure is modeled as a high-intensity peak followed by a lower constant pressure, traveling at constant speed along the beam. The slamming response essentially consists of an initial slamming load arriving phase, followed by a vibration phase. The response of the beam is solved analytically. Deflection and bending moment as functions of time and position for different slamming speeds, bending stiffnesses, etc. are given. The response during the two phases are studied and compared. The maximum deflection and bending moment occur approximately when the time it takes for the slamming load to traverse the beam is comparable to the lowest natural period of the beam. At higher slamming speeds the response is less, and the responses do not peak out until after the slam has traversed the beam (i.e., it occurs during the vibration phase). The importance of the leading high-intensity pressure peak often encountered during slamming is also studied. It is seen that a high peak pressure does not necessarily lead to a large structural response, whereas the total load of the peak of the slam does influence the structural response significantly. For relatively slow moving slamming loads, this influence is limited. However, for faster moving loads it can be substantial.