## 1 Introduction  
Dampers play an important role in achieving the optimum performance of dynamic systems. They are key components that ensure the effective suppression of shocks and other dynamic loads. This research deals with the development of a nonlinear damper with an original structure. The proposed damper is a passive damper with a simple structure; therefore, there is no need to apply a sophisticated control system to achieve the nonlinearity of its damping characteristic. In order to achieve effective operation of the damper, the dynamic properties of its main components need to be studied in detail. The most common type of damper is the hydraulic damper. Dampers are energy-dissipating elements that absorb kinetic energy, making them an effective means of controlling the rate of motion of mechanical components. The main elements related to the reduction in the rate of movement are as follows: reducing the vibration amplitude, preferably by reaching the critical damping ratio of the dynamic system; softening the impact effect by absorbing the impact energy; contributing to the precision of the movement by stabilizing the movement parameters, i.e., enabling even/smooth changes in the movement coordinates, velocities and accelerations; and regulating the movement velocity and acceleration, thus preventing the occurrence of high-inertia loads. Vehicle suspension systems are the most common applications for dampers. Here, the dampers act in synergy with the elastic elements and masses of the vehicle body and other structural components to ensure proper vehicle handling and ride comfort. Another common application is in civil engineering, in the construction of high buildings, bridges and towers subjected to random seismic or atmospheric (wind) excitation. Dampers are also used for vibration reduction and shock absorption in aerospace and railway systems. In technological machines, including robotic systems, dampers serve as important components in achieving motion precision and regulating motion parameters. Research into damper performance is an ongoing and intensive process. The simplest systems for modelling and simulation are linear systems, including linear dampers. However, better performance characteristics can be achieved by using nonlinear systems. Nonlinear dampers have variable damping characteristics; usually, their damping constant depends on the input displacement and velocity. This can be observed as a hysteresis loop in the damping force-displacement and damping force-velocity relationships. An important direction for achieving nonlinearity in mechanical systems is the development of nonlinear passive dampers. [PERSON] & [PERSON] [1] carried out a thorough review of passive vibration control with the aim of mitigating the response of dynamical systems to external excitation. Various configurations in mechanical systems that give geometrical nonlinearities are reviewed. Nonlinear dampers, including dry friction (Coulomb damping), viscous nonlinear dampers, and the application of smart materials for damping and energy harvesting are reviewed. It is concluded that linear vibro-isolation systems are effective in the narrow-frequency range, but for the broadband low-frequency spectrum (e.g., shocks and random excitation), nonlinear vibro-isolation systems are more effective. [PERSON] et al. [2] present a comprehensive review of nonlinear dissipative devices for vibration control. The limitation of linear dampers is their sensitivity to variations in excitation conditions due to their narrow bandwidth. For nonlinear dampers, however, this is eliminated due to their broadband response. The authors classify nonlinear dampers into three groups: nonlinear stiffness dampers, nonlinear-stiffness nonlinear-damping dampers, and nonlinear damping dampers. In this article, cylinder-type dampers with a special configuration of the orifice path for fluid flow and shear-type dampers in the form of a viscous damping wall are studied.