Mathematical model of harmonic movement of a fixed cargo on the deck of a ship

Abstract

The research is aimed at creating a mathematical model that allows describing the movement of cargo fixed on the deck of a ship, depending on a number of physical parameters acting on the cargo. The study is relevant in connection with the need to minimize the harmonic movement of a fixed cargo on the deck and prevent its resonating with the vibration of the vessel. During the development of the model, a number of assumptions were made: the case was considered when the load moves along the deck in one plane, and the fastening system presses it to the surface of the deck with a given coefficient of resistance. Under the given constraints, a mathematical model was created that allows determining the trajectory of the cargo fixed on the deck. The cases are considered: the friction force of the load on the surface is zero, the friction force on the surface is proportional to the square of the speed of movement in accordance with the analytical equations of motion of the object fixed on the deck of the vessel. The analysis of the resulting model will allow us to develop measures to optimize the fastening of cargo on the deck.