Mathematical model of the vessel motion during a planned grounding

The problem of transport services to points with an unequipped coast, a significant part of which is located on the coast of the Arctic seas and the Far East, continues to remain relevant for decades. Unlike the usual practice of cargo operations at berths and roadsteads, in conditions of an unequipped shore, unloading and loading often have to be carried out when the ship touches the ground, and damage to the hull occurs. Sometimes in an emergency, to save the crew and the ship, it is necessary to force the ship to ground. As a result, a system for preliminary assessment of contact conditions during partial running aground is necessary. To achieve this, a mathematical model for the rigid hull of a ship running aground, where the ground penetration is small compared to the elevation of the bow, is presented in the paper. The ship is considered as an elastic beam. It is shown that the first contact between the bow and the ground leads to a high peak load. The vessel then slides partially up the slope, wherein inertial forces in the approximation are considered small compared to ground reaction forces and hydrostatic forces. In addition to force effects, the dynamic characteristics of the sagging body design are taken into account. The resulting solution to the system of nonlinear ordinary differential equations describing the vessel movement when running aground includes longitudinal, vertical and inclined components. The proposed solution will make it possible to calculate the contact forces arising at the moment of contact of the hull with the ground, taking into account the shock load and the design features of the vessel.

1. Azovtsev, A., V. Kulesh, A. Ogay, and V. Petrov. “Ship’s construction development for cargo operations in condition of the unimproved port facilities in Arctic and Subarctic coast.” Polyarnaya mekhanika 3 (2016): 450–460.

2. Osipov, V. I. “Comparison of the numerical results of the method for calculating the process of longitudinal descent of the ship on the water and the method of landing the vessel on the ground.” Marine Intelligent Technologies 1–1(59) (2023): 51–58. DOI: 10.37220/MIT.2023.59.1.004

3. Petrov, V. A., and A. S. Ogai. Issledovanie tekhnologicheskikh i pravovykh uslovii obespecheniya bezopasnosti gruzovykh operatsii dlya sudov, ekspluatatsiya kotorykh predusmatrivaet posadku na grunt. M.: Rusains, 2018. 4. Kulesh, V. A., and V. A. Petrov. “Aktual’nost’ i bezopasnost’ gruzovykh operatsii pri posadke sudov na grunt.” Marine Intelligent Technologies 3–1(29) (2015): 75–80.

4. Azovtsev, A.I., B. I. Evenko, V. A. Kulesh, M. A. Kuteinikov, A. S. Ogai, and B. A. Petrov. “Proposal for rule requirements development for ships operating in contact with ground.” Research Bulletin by Russian Maritime Register of Shipping 42–43 (2016): 47–58.

5. Osipov, V. I. “Analytical comparison of longitudinal launching of a vessel into the water with grounding.” Marine Intelligent Technologies 3–1(53) (2021): 41–46.

6. German, Andrey P., Victor A. Kulesh, and Pham Trung Hiep. “Development of the vessel strengthening schemes for ground contact.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 12.5 (2020): 915–925. DOI: 10.21821/2309-5180-2020-12-5-915-925. 8. Kulesh, V. A., M. A. Kuteynikov, O. E. Surov, and T. H. Pham. “Design of local external structural protection from ground for vessel’s bottom.” Research Bulletin by Russian Maritime Register of Shipping 72–73 (2023): 39–47.

7. Korotkin, A. I. Prisoedinennye massy sudna. L.: Sudostroenie, 1986.

8. Kulesh, Victor Anatolievich. “Contact loads of ship hull impact against ground.” Marine Intelligent Technologies 3–1 (33) (2016): 71–76.

9. Kulesh, V., and T. H. Pham. “Method for calculating the parameters of vessels interaction with the ground.” FEFU: School of Engineering Bulletin 3(48) (2021): 39–48. DOI: 10.24866/2227-6858/2021-3-5.

10. Eliseeva, O. P., K. V. Shadt, N. S. Timofeeva, E. Kononova, and R. A. Sabirov. “Osobennosti primeneniya modeli S. P. Timoshenko v zadache opredeleniya progibov balok pri sovmestnom uchete izgiba i sdviga.” Aktual’nye problemy aviatsii i kosmonavtiki 1.7 (2011): 91–93.

11. Timoshenko, S. P. Staticheskie i dinamicheskie problemy teorii uprugosti. Kiev: NAUKOVA DUMKA, 1975.

12. Korn, G. A., and T. M. Korn. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. SPb.: Lan’, 2003.