Dynamic response of a wedge through asymmetric free fall in 2 degrees of freedom

In this article, a mathematical model is presented for simulation of the coupled roll and heave motions of the asymmetric impact of a two-dimensional wedge body. This model is developed based on the added mass theory and momentum variation. To this end, new formulations are introduced which are related to the added mass caused by heave and roll motions of the wedge. These relations are developed by including the asymmetrical effects and roll speed. In addition, by considering the roll speed, a particular method is presented for the time derivative of half-wetted beam of an asymmetric wedge. Furthermore, two equations are derived for the roll and heave motions in which damping terms appear. Validity of the proposed method is verified by comparing the predicted results against available experimental data in two conditions of roll motion and no roll motion. Favorable agreement is observed between the predicted results and experimental data. The pressure and hydrodynamic load are computed, and the differences between the results associated with the considered conditions are explored. Subsequently, the effects of different physical parameters including deadrise angle, initial roll angle, and initial velocity on the dynamic response of a two-dimensional wedge section are investigated. Ultimately, time histories of hydrodynamic coefficients are determined in order to provide a better understanding of the derived equations