## 1 Introduction  
Armed conflicts all over the world cover sea areas. Sea transport has always been, and will be the target of terrorists or pirates, whose activity is only increasing. These facts have significantly influenced the design of new ships and maritime facilities, as well as the modernization of existing ones by the need to protect these facilities against the effects of impact from non-contact underwater explosions, e.g., a sea mine, torpedo or IED (Improved Explosive Device). Marine mines and torpedoes--depending on the purpose and manner of detonation of the explosive charge--affect the structure of ships in different ways. The explosion generated can generally be divided into contact and non-contact; the latter can be further divided into near- and far-proximity explosions. The effects of these impacts may be different and depend on many factors, such as the mass of the explosive charge, the distance of the hull from the explosion epicenter, the size of the unit and its structure, location of the explosion (prow, midship, stern, starboard, port side), detonation depth, reflection of the detonation wave from the bottom and many other factors. Each explosion gives high value accelerations to the naval ship's construction, due to which mass forces deform and break the planking, along with the mechanisms. Contact explosions occur when the immersed part of the ship's hull is in the gas bubble impact zone. Hence, regardless of the amount of explosive charge, detonation occurs at a distance of 0 to 12 m. Most often, it is an explosion directly on the hull's planking, caused by a contact fuse or inertia fuse as a result of torpedo hits or mines on a ship. For a small, single-compartment vessel, this explosion usually ends in the ship's sinking. On the other hand, a multi-compartment vessel can maintain buoyancy and stability after such explosion. A contact explosion from a 100-200 kg trinitrotoluene (TNT) mine pierces a hole in a steel surface ship with a radius of one to three meters. In larger radii of up to 10 m, there is a destruction of mechanisms, installations and pipelines, cracks in the device housings, breakage of foundation bolts. A strong impact can be sensed on the entire ship's structure. Gases and high-temperature explosion products flow into the ship's hole, causing greater damage. Mid-sized units may even break in the place of explosion. In the event of explosion in the bow section, the ship will rotate around the axis, passing through the stern and vice versa. In the event of an explosion in the stern section, the ship will rotate around the axis passing through its bow. The effects of contact explosions, even for large units, are very serious, and if the unit is good enough to undergo renovation, it will be out-of-order for many months [1; 2]. If a floating mine contacts the hull (collision with a drifting mine), then the destruction of the ship is lesser, as most of the explosion energy is dispersed into the air, and the explosion hole has a smaller diameter. In this case, the ship should not break and sink. It can maintain mobility, and after shipyard repairs, can be further used. If the explosion takes place at some distance from the ship's hull making, and the gas bubble does not touch the ship's planking, then we refer to this as a non-contact explosion. In this case, only the pressure wave acts on the ship's hull. A close-field (close-proximity) explosion at a distance of 2-20 m with a pressure acting on the hull above eight megapascals cause the hull's piercing. In such cases, the piercings usually have a linear character, and follow along the plating braced structures such as frames and girders. As the gas bubble is not in contact with the ship, the products of explosion do not penetrate into it, and there is no direct interaction of high temperature. Mechanisms and devices are usually displaced and ripped off foundations, and their housings are damaged. With a close-proximity non-contact explosion, the damage zone is much larger than in the case of a contact explosion [1].